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latex: '\\cos(2 x) = 1 - 2 (\\sin(x))^2'}) CREATE (id1258245373:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'E'}) CREATE (id1259826355:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = (v - a t) t + \\frac{1}{2} a t^2'}) CREATE (id1265150401:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = \\frac{2 v_0 + a t}{2} t'}) CREATE (id1268845856:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: '[A_{\\rm adsorption}]'}) CREATE (id1277713901:expression { creation_date: '2020-05-06', author: '4a0987466473c589d2c328d12856760e', latex: 'd'}) CREATE (id1292735067:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{gravitational} = G \\frac{m_1 m_2}{r^2}'}) CREATE (id1293913110:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '0 = b'}) CREATE (id1293923844:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\lambda = v T'}) CREATE (id1306360899:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x = v_{0, x} t + x_0'}) CREATE (id1310571337:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_{\\rm refracted} = 90^{\\circ} - \\theta_{\\rm Brewster}'}) CREATE (id1311403394:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\alpha = \\frac{1}{V} \\frac{nR}{P} \\left( \\frac{\\partial T}{\\partial T} \\right)_P'}) CREATE (id1314464131:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\times \\frac{\\partial \\vec{H}}{\\partial t} = \\epsilon_0 \\frac{\\partial^2 \\vec{E}}{\\partial t^2}'}) CREATE (id1314864131:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\times \\vec{H} = \\epsilon_0 \\frac{\\partial }{\\partial t}\\vec{E}'}) CREATE (id1323602089:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'I_1'}) CREATE (id1330874553:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm escape} = \\sqrt{2 G \\frac{m_{\\rm Earth}}{r_{\\rm Earth}}}'}) CREATE (id1333474099:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm centripetal}'}) CREATE (id1357848476:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'A = |A| \\exp(i \\theta)'}) CREATE (id1377431959:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'R'}) CREATE (id1395858355:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\langle \\psi_{\\alpha}| a_{\\alpha} |\\psi_{\\beta}\\rangle'}) CREATE (id1405465835:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'y = - \\frac{1}{2} g t^2 + v_{0, y} t + y_0'}) CREATE (id1413137236:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'm_1'}) CREATE (id1439089569:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, x}'}) CREATE (id1451839362:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id1457415749:expression { name: 'total resistance for two resistors in parallel', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{R_{\\rm total}} = \\frac{1}{R_1} + \\frac{1}{R_2}'}) CREATE (id1484794622:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'R_2'}) CREATE (id1511199318:expression { creation_date: '2020-05-17', author: 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\\frac{ m_e e^4 }{ 32 \\pi^2 \\epsilon_0^2 \\hbar^2}'}) CREATE (id1559688463:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\left(\\frac{T_{\\rm geostationary\\ orbit}^2 G m_{\\rm Earth}}{4 \\pi^2}\\right)^{1/3} = r_{\\rm geostationary\\ orbit}'}) CREATE (id1571582377:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{gravitational} \\propto \\frac{1}{r^2}'}) CREATE (id1586866563:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\left( \\gamma^2 - c^2 \\gamma^2 \\left( \\frac{1-\\gamma^2}{\\gamma^2} \\right)^2 \\frac{1}{v^2} \\right) x^2 + y^2 + z^2 + \\left( -\\gamma^2 2 x v t - c^2 \\gamma^2 2 t \\left( \\frac{1-\\gamma^2}{\\gamma^2} \\right) \\frac{x}{v} \\right) = t^2 \\left( c^2 \\gamma^2 - \\gamma^2 v^2 \\right)'}) CREATE (id1590774089:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'dW = F dx'}) CREATE (id1608399874:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'V_2'}) CREATE (id1614343171:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'dt'}) CREATE (id1616666229:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm final}'}) CREATE (id1635147226:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'm_2'}) CREATE (id1636453295:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\times \\vec{ \\nabla} \\times \\vec{E} = - \\nabla^2 \\vec{E}'}) CREATE (id1638282134:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{p}_{\\rm before} = \\vec{p}_{\\rm after}'}) CREATE (id1639827492:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '- c^2 \\frac{(1-\\gamma^2)}{v^2 \\gamma^2} = 1'}) CREATE (id1648958381:expression { notes: 'https://physicsderivationgraph.blogspot.com/2020/09/representing-laplace-operator-nabla-in.html', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 \\psi \\left( \\vec{r},t \\right) = \\frac{i}{\\hbar} \\vec{p} \\cdot \\left( \\vec{ \\nabla} \\psi( \\vec{r},t) \\right)'}) CREATE (id1650441634:expression { notes: 'define coordinate system such that initial height is at origin', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'y_0 = 0'}) CREATE (id1676472948:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '0 = v_x - v_{0, x}'}) CREATE (id1702349646:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '-g dt = d v_y'}) CREATE (id1716984328:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: 'i x'}) CREATE 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'4a0987466473c589d2c328d12856760e', latex: 'U = Q + W'}) CREATE (id1819663717:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'a_x = \\frac{d}{dt} v_x'}) CREATE (id1823570358:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'C'}) CREATE (id1840080113:expression { notes: 'object is not moving at $x=\infty$', creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_2 = 0'}) CREATE (id1848400430:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F \\propto m'}) CREATE (id1857710291:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '0 = a \\sin(n \\pi)'}) CREATE (id1858578388:expression { notes: 'https://physicsderivationgraph.blogspot.com/2020/09/representing-laplace-operator-nabla-in.html', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 E( \\vec{r})\\exp(i \\omega t) = - \\omega^2 \\mu_0 \\epsilon_0 E( \\vec{r})\\exp(i \\omega t)'}) CREATE (id1858772113:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'k = \\frac{n \\pi}{W}'}) CREATE (id1888494137:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: '-\\sqrt{\\frac{k}{m}} = \\omega'}) CREATE (id1894894315:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'Z'}) CREATE (id1916173354:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '-\\gamma^2 v^2 + c^2 \\gamma^2 = c^2'}) CREATE (id1928085940:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'Z^* = |Z| \\exp( -i \\theta )'}) CREATE (id1931103031:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{k}{m} = \\omega^2'}) CREATE (id1934748140:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\int |\\psi(x)|^2 dx = 1'}) CREATE (id1935543849:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2 x^2 - \\gamma^2 2 x v t + \\gamma^2 v^2 t^2 + y^2 + z^2 = c^2 \\gamma^2 \\left(\\frac{1-\\gamma^2}{\\gamma^2}\\right)\\frac{x^2}{\\gamma^2} + c^2 \\gamma^2 2 t \\left(\\frac{1-\\gamma^2}{\\gamma^2}\\right)\\frac{x}{\\gamma} + c^2 \\gamma^2 t^2'}) CREATE (id1945487024:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'p_A [S]'}) CREATE (id1963253044:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, x} dt = dx'}) CREATE (id1967582749:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 't = \\frac{v - v_0}{a}'}) CREATE (id1974334644:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{x (1 - \\gamma^2 )}{\\gamma v} + \\frac{\\gamma^2 v t}{\\gamma v} = t\''}) CREATE (id1977955751:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '-g = \\frac{d}{dt} v_y'}) CREATE (id1994296484:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm satellite}^2 = G \\frac{m_{\\rm Earth}}{r}'}) CREATE (id2005061870:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v(r) = \\sqrt{\\frac{2 G m_2}{r}}'}) CREATE (id2016063530:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id2029293929:expression { notes: 'https://physicsderivationgraph.blogspot.com/2020/09/representing-laplace-operator-nabla-in.html', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 E( \\vec{r})\\exp(i \\omega t) = \\mu_0 \\epsilon_0 \\frac{\\partial^2}{\\partial t^2} E( \\vec{r})\\exp(i \\omega 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latex: 't'}) CREATE (id2086924031:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '0 = - \\frac{1}{2} g t_f + v_0 \\sin(\\theta)'}) CREATE (id2091584724:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'g_{\\rm Earth}'}) CREATE (id2096918413:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\gamma ( \\gamma x - \\gamma v t + v t\' )'}) CREATE (id2103023049:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin(x) = \\frac{1}{2i}\\left(\\exp(i x)-\\exp(-i x) \\right)'}) CREATE (id2113211456:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'f = 1/T'}) CREATE (id2114570475:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'm_{\\rm satellite}'}) CREATE (id2114909846:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_A = \\frac{[A_{\\rm adsorption}]}{[S_0]}'}) CREATE (id2121790783:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\tanh^2(x) = \\frac{ \\left(\\exp(x)-\\exp(-x)\\right)^2}{\\left(\\exp(x)+\\exp(-x)\\right)^2}'}) CREATE (id2123139121:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '-\\exp(-i x) = -\\cos(x)+i \\sin(x)'}) CREATE (id2131616531:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'T f = 1'}) CREATE (id2135482543:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id2148049269:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: '-\\frac{k}{m} A \\cos(\\omega t) = -A \\omega^2 \\cos(\\omega t)'}) CREATE (id2168306601:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: '[S_0] = \\left(\\frac{k_{\\rm desorption}}{k_{\\rm adsorption}} \\frac{1}{p_A} + 1\\right)[A_{\\rm adsorption}]'}) CREATE (id2186083170:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{KE_2 - KE_1}{t} = v F'}) CREATE (id2217103163:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{m_1 d_1}{d_2} = m_2'}) CREATE (id2226340358:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma v'}) CREATE (id2232825726:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'g_{\\rm Earth}'}) CREATE (id2236639474:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '(A + B)(A + B)^* = |A + B|^2'}) CREATE (id2242144313:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a'}) CREATE (id2257410739:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\left(\\frac{\\partial U}{\\partial T}\\right)_p = C_V \\left(\\frac{\\partial T}{\\partial T}\\right)_p + \\pi_T V \\alpha'}) CREATE (id2258485859:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '{\\cal H} \\psi \\left( \\vec{r},t \\right) = i \\hbar \\frac{\\partial}{\\partial t} \\psi( \\vec{r},t)'}) CREATE (id2267521164:expression { notes: 'object goes to $\infty$ away from gravitational source', creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_2 = 0'}) CREATE (id2271186630:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V = I_{\\rm total} R_{\\rm total}'}) CREATE (id2293352649:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta - \\phi'}) CREATE (id2297105551:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'd = v_0 \\frac{2 v_0 \\sin(\\theta)}{g} \\cos(\\theta)'}) CREATE (id2308660627:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'G \\frac{m_{\\rm Earth}}{r_{\\rm Earth}^2} = g_{\\rm Earth}'}) CREATE (id2334518266:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 'm a = -k x'}) CREATE (id2344320475:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'E_2'}) CREATE (id2346150725:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'r'}) CREATE (id2346952973:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id2366691988:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\int 0 dt = \\int d v_x'}) CREATE (id2378095808:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x_f = x_0 + d'}) CREATE (id2394240499:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x = a_{\\beta} \\langle \\psi_{\\alpha} | \\psi_{\\beta} \\rangle'}) CREATE (id2394853829:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(-i x) = \\cos(-x)+i \\sin(-x)'}) CREATE (id2394935831:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '( a_{\\beta} - a_{\\alpha} ) \\langle \\psi_{\\alpha} | \\psi_{\\beta} \\rangle = 0'}) CREATE (id2394935835:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\left(\\langle\\psi| \\hat{A} |\\psi \\rangle \\right)^+ = \\left(\\langle a \\rangle\\right)^+'}) CREATE (id2395958385:expression { notes: 'https://physicsderivationgraph.blogspot.com/2020/09/representing-laplace-operator-nabla-in.html', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 \\psi \\left( \\vec{r},t \\right) = \\frac{-p^2}{\\hbar} \\psi( \\vec{r},t)'}) CREATE (id2396787389:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Earth}'}) CREATE (id2397692197:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a^3'}) CREATE (id2403773761:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id2404934990:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle x^2\\rangle -2\\langle x \\rangle\\langle x \\rangle+\\langle x \\rangle^2 = \\langle x^2 \\rangle-\\langle x \\rangle^2'}) CREATE (id2405307372:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin(2 x) = 2 \\sin(x) \\cos(x)'}) CREATE (id2417941373:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '- c^2 \\gamma^2 \\frac{(1-\\gamma^2)^2}{v^2 \\gamma^4} = 1 - \\gamma^2'}) CREATE (id2431507955:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_2 = -F x_2'}) CREATE (id2461349007:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '- \\frac{1}{2} g t^2 + v_{0, y} t + y_0 = y'}) CREATE (id2472653783:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\alpha = \\frac{1}{T}'}) CREATE (id2484824786:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'F = m g'}) CREATE (id2494533900:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle x^2\\rangle -\\langle x \\rangle^2 = \\langle x^2 \\rangle-\\langle x \\rangle^2'}) CREATE (id2501591100:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(i \\pi) + 1 = 0'}) CREATE (id2503972039:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: '0 = KE_{\\rm escape} + PE_{\\rm Earth\\ surface}'}) CREATE (id2510804451:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '2/g'}) CREATE (id2519058903:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin(2 \\theta) = 2 \\sin(\\theta) \\cos(\\theta)'}) CREATE (id2542420160:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'c^2 \\gamma^2 - v^2 \\gamma^2 = c^2'}) CREATE (id2575937347:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'n_1 \\sin( \\theta_{\\rm Brewster} ) = n_2 \\sin( \\theta_{\\rm refracted} )'}) CREATE (id2613006036:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{PV}{T} = nR'}) CREATE (id2617541067:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\left(\\frac{T_{\\rm orbit}^2 G m_{\\rm Earth}}{4 \\pi^2}\\right)^{1/3} = r'}) CREATE (id2648958382:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 \\psi \\left( \\vec{r},t \\right) = \\frac{i}{\\hbar} \\vec{p} \\cdot \\left( \\frac{i}{\\hbar} \\vec{p} \\psi( \\vec{r},t) \\right)'}) CREATE (id2660368546:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'r'}) CREATE (id2674546234:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'm_{\\rm Earth}'}) CREATE (id2685587762:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{r_{\\rm Earth}^2}{G}'}) CREATE (id2698469612:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V'}) CREATE (id2700934933:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '2 \\cos(x) = \\left( \\exp(i (\\theta - \\phi)) + \\exp(-i (\\theta - \\phi)) \\right)'}) CREATE (id2715678478:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'I R_{\\rm total} = I R_1 + I R_2'}) CREATE (id2719691582:expression { notes: 'in a loop', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '|A| = |B|'}) CREATE (id2741489181:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'a_y = -g'}) CREATE (id2750380042:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm escape} = -\\sqrt{2 G \\frac{m_{\\rm Earth}}{r_{\\rm Earth}}}'}) CREATE (id2754264786:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id2762326680:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\cosh^2 x - \\sinh^2 x = \\frac{1}{4}\\left( \\exp(2x)+1+1+\\exp(-2x) - \\left(\\exp(2x)-1-1+\\exp(-2x)\\right) \\right)'}) CREATE (id2764966428:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'm_2'}) CREATE (id2768857871:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{\\sin( \\theta_{\\rm Brewster} )}{\\cos( \\theta_{\\rm Brewster} )} = \\frac{n_2}{n_1}'}) CREATE (id2770069250:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{E_2 - E_1}{t} = \\frac{(KE_2 - KE_1)}{t} + \\frac{(PE_2 - PE_1)}{t}'}) CREATE (id2773628333:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_1'}) CREATE (id2809345867:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{V}{R_{\\rm total}} = I_{\\rm total}'}) CREATE (id2848934890:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle a \\rangle^* = \\langle a \\rangle'}) CREATE (id2857430695:expression { name: 'acceleration', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'a = \\frac{v_2 - v_1}{t}'}) CREATE (id2858549874:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '- \\frac{1}{2} g t^2 + v_{0, y} t = y - y_0'}) CREATE (id2867848403:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'I'}) CREATE (id2883079365:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Schwarzschild} c^2 = 2 G m'}) CREATE (id2897612567:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\alpha c \\sqrt{ \\frac{m_e}{A m_p} }'}) CREATE (id2902772962:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\tanh(x) = \\frac{\\frac{1}{2}\\left( \\exp(x)-\\exp(-x) \\right)}{\\cosh(x)}'}) CREATE (id2906548078:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'T^2 = \\frac{r}{d_1+d_2} d_2 4 \\pi^2 \\frac{r^2}{G m_1}'}) CREATE (id2907404069:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm by\\ system} = W_{\\rm to\\ system}'}) CREATE (id2924222857:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm initial} = v(r=\\infty)'}) CREATE (id2944838499:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi(x) = a \\sin(\\frac{n \\pi}{W} x)'}) CREATE (id2957211007:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'm^3 kg^{-1} s^{-2}'}) CREATE (id2977457786:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: '2 G \\frac{m_{\\rm Earth}}{r_{\\rm Earth}} = v_{\\rm escape}^2'}) CREATE (id2983053062:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\gamma (x\' + v t\')'}) CREATE (id2998709778:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm initial} = 0'}) CREATE (id2999795755:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'c^2 \\gamma^2 = v^2 \\gamma^2 + c^2'}) CREATE (id3004158505:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{T^2}{r} F_{gravitational} = \\left( \\frac{4 \\pi^2 m r}{T^2} \\right)\\frac{T^2}{r}'}) CREATE (id3031116098:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'R_2'}) CREATE (id3041762466:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: 'i'}) CREATE (id3046191961:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm Earth\\ orbit} = \\frac{C_{\\rm Earth\\ orbit}}{t_{\\rm Earth\\ orbit}}'}) CREATE (id3060393541:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I_{\\rm incoherent} = 2|A|^2'}) CREATE (id3061811650:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'n_1 \\sin( \\theta_{\\rm Brewster} ) = n_2 \\cos( \\theta_{\\rm Brewster} )'}) CREATE (id3080027960:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm Earth\\ orbit} = \\frac{2 \\pi r_{\\rm Earth\\ orbit}}{t_{\\rm Earth\\ orbit}}'}) CREATE (id3085575328:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I = |A|^2 + |B|^2 + |A| |B| \\exp(i (\\theta - \\phi)) + |A| |B| \\exp(-i (\\theta - \\phi))'}) CREATE (id3088463019:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'm_2'}) CREATE (id3105350101:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_1'}) CREATE (id3121234211:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{k}{2\\pi} = \\lambda'}) CREATE (id3121234212:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'p = \\frac{h k}{2\\pi}'}) CREATE (id3121513111:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'k = \\frac{2 \\pi}{\\lambda}'}) CREATE (id3131111133:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'T = 1 / f'}) CREATE (id3131211131:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\omega = 2 \\pi f'}) CREATE (id3132131132:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\omega = \\frac{2\\pi}{T}'}) CREATE (id3147472131:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{\\omega}{2 \\pi} = f'}) CREATE (id3166466250:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'm_1'}) CREATE (id3169580383:expression { notes: 'acceleration is the change in speed over a duration', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{a} = \\frac{d\\vec{v}}{dt}'}) CREATE (id3176662571:expression { notes: 'applicable to any satellite orbit', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm centripetal} = F_{\\rm gravity}'}) CREATE (id3182633789:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2 - c^2 \\gamma^2 \\frac{(1-\\gamma^2)^2}{v^2 \\gamma^4} = 1'}) CREATE (id3182907803:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x_0'}) CREATE (id3183197515:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_1'}) CREATE (id3214170322:expression { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e', latex: 'v(r=\\infty) = 0'}) CREATE (id3219318145:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{365 {\\rm days}}{1 {\\rm year}} \\frac{24 {\\rm hours}}{1 {\\rm day}} \\frac{60 {\\rm minutes}}{1 {\\rm hour}} \\frac{60 {\\rm seconds}}{1 {\\rm minute}}'}) CREATE (id3236313290:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'd'}) CREATE (id3246378279:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id3253234559:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\frac{v_2^2 - v_1^2}{2 a}'}) CREATE (id3268645065:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id3270039798:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id3273630811:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id3274176452:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm initial}'}) CREATE (id3274926090:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 't = \\frac{x - x_0}{v_{0, x}}'}) CREATE (id3285732911:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '(\\cos(x))^2 = 1-(\\sin(x))^2'}) CREATE (id3291685884:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'E = \\frac{ m_e e^4 }{ 32 \\pi^2 \\epsilon_0^2 \\hbar^2}'}) CREATE (id3331824625:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(i \\pi) = -1'}) CREATE (id3342155559:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id3350802342:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_{\\rm initial}'}) CREATE (id3350830826:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'Z Z^* = |Z|^2'}) CREATE (id3353418803:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id3360172339:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = KE_2 - KE_1'}) CREATE (id3364286646:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'm_{\\rm Earth} = 5.972*10^{24} kg'}) CREATE (id3366703541:expression { notes: 'acceleration is the average change in speed over a duration', creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a = \\frac{v - v_0}{t}'}) CREATE (id3398368564:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'F'}) CREATE (id3411994811:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm average} = \\frac{d}{t}'}) CREATE (id3412946408:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'v^2 \\gamma^2'}) CREATE (id3417126140:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\tan( \\theta_{\\rm Brewster} ) = \\frac{ n_2 }{ n_1 }'}) CREATE (id3426941928:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\gamma ( \\gamma (x - v t) + v t\' )'}) CREATE (id3433441359:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V'}) CREATE (id3448601530:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{T^2}{r}'}) CREATE (id3462972452:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = v_0 + a t'}) CREATE (id3464107376:expression { notes: 'definition of expansion coefficient', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\alpha = \\frac{1}{V} \\left( \\frac{\\partial V}{\\partial T} \\right)_p'}) CREATE (id3470587782:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin(x) \\cos(x) = \\frac{1}{2i}\\left(\\exp(i x)-\\exp(-i x) \\right) \\frac{1}{2}\\left(\\exp(i x)+\\exp(-i x) \\right)'}) CREATE (id3472836147:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Earth\\ orbit} = 1.496\\ 10^8 {\\rm km}'}) CREATE (id3485125659:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x_f = v_0 t_f \\cos(\\theta) + x_0'}) CREATE (id3485475729:expression { notes: 'https://physicsderivationgraph.blogspot.com/2020/09/representing-laplace-operator-nabla-in.html', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 E( \\vec{r}) = - \\frac{\\omega^2}{c^2} E( \\vec{r})'}) CREATE (id3486213448:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'm_{\\rm satellite}'}) CREATE (id3488423948:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'k_{\\rm adsorption} p_A [S] = k_{\\rm desorption} [A_{\\rm adsorption}]'}) CREATE (id3495403335:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id3497828859:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'V = \\frac{n R T}{P}'}) CREATE (id3507029294:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'k_{\\rm adsorption} p_A [S] = r_{\\rm desorption}'}) CREATE (id3512166162:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = F x'}) CREATE (id3531380618:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v(r)'}) CREATE (id3547519267:expression { notes: 'assumes equally probable microstates', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'S = k_{\\rm Boltzmann} \\ln \\Omega'}) CREATE (id3566149658:expression { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm to\\ system} = \\int_{\\infty}^r \\frac{-G m_1 m_2}{x^2} dx'}) CREATE (id3585845894:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle \\left(x-\\langle x \\rangle\\right)^2 \\rangle = \\langle x^2 \\rangle-\\langle x \\rangle^2'}) CREATE (id3591237106:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{E_2 - E_1}{t} = \\frac{(KE_2 - KE_1)}{t} - F v'}) CREATE (id3594626260:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm gravity}'}) CREATE (id3599953931:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: '[S_0] = [S] + [A_{\\rm adsorption}]'}) CREATE (id3605073197:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\kappa_T = \\frac{-nRT}{V} \\left( \\frac{-1}{P^2}\\right)'}) CREATE (id3607070319:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'd = \\frac{v_0^2}{g} \\sin\\left(2 \\frac{\\pi}{4}\\right)'}) CREATE (id3614055652:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\frac{2 \\pi r}{T_{\\rm orbit}}'}) CREATE (id3634715785:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id3649797559:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm centripetal} = m_2 d_2 \\omega^2'}) CREATE (id3650370389:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{T^2}{r} F_{gravitational} = 4 \\pi^2 m'}) CREATE (id3650814381:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{gravitational} \\propto \\frac{m_1 m_2}{r^2}'}) CREATE (id3652511721:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id3660957533:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(x) = \\frac{1}{2} \\left( \\exp(i (\\theta - \\phi)) + \\exp(-i (\\theta - \\phi)) \\right)'}) CREATE (id3663007361:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id3676159007:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, x} \\int dt = \\int dx'}) CREATE (id3685779219:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\sqrt{f} \\approx 2'}) CREATE (id3722461713:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id3723096423:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: '6.3781*10^6'}) CREATE (id3731774096:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'KE'}) CREATE (id3736177473:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm adsorption} = k_{\\rm adsorption} p_A [S]'}) CREATE (id3749492596:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'E'}) CREATE (id3781109867:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'T^2 = \\frac{r^3 4 \\pi^2}{(d_1+d_2) \\frac{m_1}{d_2}G}'}) CREATE (id3806977900:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'E_2 - E_1 = 0'}) CREATE (id3809726424:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'PE'}) CREATE (id3829492824:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{2}\\left(\\exp(i x)+\\exp(-i x) \\right) = \\cos(x)'}) CREATE (id3846041519:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_{\\rm Earth\\ surface} = -G \\frac{m_{\\rm Earth} m}{r_{\\rm Earth}}'}) CREATE (id3846345263:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'T_{\\rm orbit}'}) CREATE (id3868998312:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '{\\rm sech}^2\\ x = \\frac{4}{\\left(\\exp(x)+\\exp(-x)\\right)^2}'}) CREATE (id3876446703:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id3896798826:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'm_2 d_2 \\omega^2 = G \\frac{m_1 m_2}{r^2}'}) CREATE (id3906710072:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'G \\frac{m_{\\rm Earth}}{r} = \\frac{4 \\pi^2 r^2}{T_{\\rm orbit}^2}'}) CREATE (id3911081515:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '-1'}) CREATE (id3920616792:expression { notes: 'this applies for geostationary orbits', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'T_{\\rm geostationary orbit} = 24\\ {\\rm hours}'}) CREATE (id3921072591:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'm_1'}) CREATE (id3924948349:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a_{\\beta} \\langle \\psi_{\\alpha} | \\psi_{\\beta} \\rangle - a_{\\alpha} \\langle \\psi_{\\alpha} | \\psi_{\\beta} \\rangle = 0'}) CREATE (id3935058307:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\sqrt{ \\frac{m_e}{m} \\frac{e^4}{32 \\pi^2 \\epsilon_0^2 \\hbar^2} }'}) CREATE (id3939572542:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_{\\rm final}'}) CREATE (id3942849294:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(i x)-\\exp(-i x) = 2 i \\sin(x)'}) CREATE (id3943939590:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x = a_{\\alpha} \\langle \\psi_{\\alpha}| \\psi_{\\beta}\\rangle'}) CREATE (id3947269979:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\times \\vec{ \\nabla} \\times \\vec{E} = -\\mu_0 \\epsilon_0 \\frac{\\partial^2 \\vec{E}}{\\partial t^2}'}) CREATE (id3948571256:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{\\partial}{\\partial t} \\psi( \\vec{r},t) = \\frac{-i}{\\hbar}E \\psi( \\vec{r},t)'}) CREATE (id3948574224:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi( \\vec{r},t) = \\psi_0 \\exp\\left(i\\left( \\vec{k}\\cdot\\vec{r} - \\omega t \\right) \\right)'}) CREATE (id3948574226:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi( \\vec{r},t) = \\psi_0 \\exp\\left(i\\left(\\frac{ \\vec{p}\\cdot\\vec{r}}{\\hbar} - \\omega t \\right) \\right)'}) CREATE (id3948574228:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi( \\vec{r},t) = \\psi_0 \\exp\\left(i\\left(\\frac{ \\vec{p}\\cdot\\vec{r}}{\\hbar} - \\frac{E t}{\\hbar} \\right) \\right)'}) CREATE (id3948574230:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi( \\vec{r},t) = \\psi_0 \\exp\\left(\\frac{i}{\\hbar}\\left( \\vec{p}\\cdot\\vec{r} - E t \\right) \\right)'}) CREATE (id3948574233:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{\\partial}{\\partial t} \\psi( \\vec{r},t) = \\psi_0 \\frac{\\partial}{\\partial t}\\exp\\left(i\\left(\\frac{ \\vec{p}\\cdot\\vec{r}}{\\hbar} - \\frac{E t}{\\hbar} \\right) \\right)'}) CREATE (id3951205425:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{p}_{\\rm after} = \\vec{p}_{1}'}) CREATE (id3967985562:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id4057686137:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'C'}) CREATE (id4072200527:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{m_{\\rm satellite} v_{\\rm satellite}^2}{r} = G \\frac{m_{\\rm Earth} m_{\\rm satellite}}{r^2}'}) CREATE (id4075539836:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'A A^* = |A|^2'}) CREATE (id4087145886:expression { name: 'Ohm's law', notes: 'https://en.wikipedia.org/wiki/Ohm%27s_law', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V = I R'}) CREATE (id4107032818:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'E_{\\rm Rydberg} = E'}) CREATE (id4128500715:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V = I_1 R_1'}) CREATE (id4139999399:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x - \\gamma^2 x = - \\gamma^2 v t + \\gamma v t\''}) CREATE (id4147101187:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'KE'}) CREATE (id4147472132:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'E = \\frac{h \\omega}{2 \\pi}'}) CREATE (id4153613253:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'm_{\\rm Earth}'}) CREATE (id4158986868:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'a_x \\hat{x} + a_y \\hat{y} = \\frac{d\\vec{v}}{dt}'}) CREATE (id4162188238:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 't_f'}) CREATE (id4166155526:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '{\\rm sech}\\ x = \\frac{2}{\\exp(x)+\\exp(-x)}'}) CREATE (id4167526462:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, y}'}) CREATE (id4180845508:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm Earth\\ orbit} = 29.8 \\frac{{\\rm km}}{{\\rm sec}}'}) CREATE (id4182362050:expression { notes: 'Z \in \mathbb{C}', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'Z = |Z| \\exp( i \\theta )'}) CREATE (id4188580242:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'T^2 = \\frac{r^3 4 \\pi^2}{\\left(m_1+\\left(\\frac{m_1}{d_2}d_1\\right)\\right)G}'}) CREATE (id4188639044:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id4192519596:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'B = |B| \\exp(i \\phi)'}) CREATE (id4202292449:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Earth\\ orbit}'}) CREATE (id4213426349:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'E_1'}) CREATE (id4218009993:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id4245712581:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\frac{2 \\pi r}{t}'}) CREATE (id4264859781:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F \\propto m_1'}) CREATE (id4267808354:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{gravitational} = m \\frac{v^2}{r}'}) CREATE (id4268085801:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x_0 + d = v_0 t_f \\cos(\\theta) + x_0'}) CREATE (id4270680309:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{KE_2 - KE_1}{t} = \\frac{1}{2} m \\frac{\\left( v_2^2 - v_1^2 \\right)}{t}'}) CREATE (id4275004561:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'c^2 = 2 G \\frac{m}{r_{\\rm Schwarzschild}}'}) CREATE (id4287102261:expression { notes: 'describes a spherical wavefront', creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x^2 + y^2 + z^2 = c^2 t^2'}) CREATE (id4298359835:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'E = \\frac{1}{2}m v^2'}) CREATE (id4298359845:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'E = \\frac{1}{2m}m^2 v^2'}) CREATE (id4298359851:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'E = \\frac{p^2}{2m}'}) CREATE (id4301729661:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: '[S_0] = \\frac{[A_{\\rm adsorption}]}{\\left( \\frac{k_{\\rm adsorption}}{k_{\\rm desorption}} \\right) p_A} + [A_{\\rm adsorption}]'}) CREATE (id4303372136:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'E_1 = KE_1 + PE_1'}) CREATE (id4319470443:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_2'}) CREATE (id4319544433:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '1/3'}) CREATE (id4341171256:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'i \\hbar \\frac{\\partial}{\\partial t} \\psi( \\vec{r},t) = \\frac{p^2}{2 m} \\psi( \\vec{r},t)'}) CREATE (id4348571256:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{\\partial}{\\partial t} \\psi( \\vec{r},t) = \\frac{-i}{\\hbar}\\frac{p^2}{2 m} \\psi( \\vec{r},t)'}) CREATE (id4370074654:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 't = t_f'}) CREATE (id4393258808:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm centripetal} = m r \\omega^2'}) CREATE (id4393670960:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm to\\ system} = \\frac{G m_1 m_2}{r}'}) CREATE (id4394958389:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla}\\cdot \\left( \\vec{ \\nabla} \\psi( \\vec{r},t) \\right) = \\frac{i}{\\hbar} \\vec{ \\nabla}\\cdot\\left( \\vec{p} \\psi( \\vec{r},t) \\right)'}) CREATE (id4428528271:expression { name: 'Hooke's law', notes: 'https://en.wikipedia.org/wiki/Hooke%27s_law', creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm{spring}} = -k x'}) CREATE (id4437214608:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'Z'}) CREATE (id4447113478:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: '\\int dW = G m_1 m_2 \\int_{ r_{\\rm Earth} }^{\\infty} \\frac{1}{x^2} dx'}) CREATE (id4470433702:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 't_{\\rm Earth\\ orbit}'}) CREATE (id4490788873:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F \\propto m_2'}) CREATE (id4501377629:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\tan( \\theta_{\\rm Brewster} ) = \\frac{ \\sin( \\theta_{\\rm Brewster} )}{\\cos( \\theta_{\\rm Brewster} )}'}) CREATE (id4504256452:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'B^* = |B| \\exp(-i \\phi)'}) CREATE (id4522137851:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_2'}) CREATE (id4560648264:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\sqrt{ \\frac{K + (4/3) G}{\\rho} }'}) CREATE (id4580545876:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = v t - a t^2 + \\frac{1}{2} a t^2'}) CREATE (id4583868070:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'B'}) CREATE (id4585828572:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\epsilon_0 \\mu_0 = \\frac{1}{c^2}'}) CREATE (id4585932229:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(x) = \\frac{1}{2}\\left(\\exp(i x)+\\exp(-i x) \\right)'}) CREATE (id4587046017:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'KE'}) CREATE (id4593428198:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm Earth\\ orbit} = \\frac{2 \\pi r_{\\rm Earth\\ orbit}}{3.16\\ 10^7 {\\rm seconds}}'}) CREATE (id4598294821:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(2 i x) = (\\cos(x))^2+2i\\cos(x)\\sin(x)-(\\sin(x))^2'}) CREATE (id4627284246:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm centripetal} = \\frac{m_{\\rm satellite} v_{\\rm satellite}^2}{r}'}) CREATE (id4638429483:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(2 i x) = (\\cos(x)+ i \\sin(x))(\\cos(x)+ i \\sin(x))'}) CREATE (id4648451961:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'v_2^2 - v_1^2 = (v_2 + v_1)(v_2 - v_1)'}) CREATE (id4651061153:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'm_2'}) CREATE (id4662369843:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x\' = \\gamma (x - v t)'}) CREATE (id4669290568:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_1 = -F x_1'}) CREATE (id4689334676:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_A = \\frac{K_{\\rm equilibrium}\\ p_A}{1+K_{\\rm equilibrium}\\ p_A}'}) CREATE (id4742644828:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(i x)+\\exp(-i x) = 2 \\cos(x)'}) CREATE (id4748157455:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a t = v - v_0'}) CREATE (id4755369593:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'x_2'}) CREATE (id4778077984:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 't_f = \\frac{2 v_0 \\sin(\\theta)}{g}'}) CREATE (id4784793837:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{KE_2 - KE_1}{t} = m v a'}) CREATE (id4798787814:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a t + v_0 = v'}) CREATE (id4800170179:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'F = m g_{\\rm Earth}'}) CREATE (id4805233006:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: 'i \\sin(i x) = \\frac{1}{2}\\left(\\exp(x) - \\exp(-x) \\right)'}) CREATE (id4811121942:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = \\frac{1}{2} m v_2^2 - \\frac{1}{2} m v_1^2'}) CREATE (id4820320578:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{gravitational} = F_{centripetal}'}) CREATE (id4827492911:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(2 x)+(\\sin(x))^2 = 1 - (\\sin(x))^2'}) CREATE (id4829590294:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 't_f'}) CREATE (id4830221561:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '{\\rm sech}^2\\ x + \\tanh^2(x) = \\frac{4+\\left(\\exp(2x)-1-1+\\exp(-2x)\\right)}{\\left(\\exp(x)+\\exp(-x)\\right)^2}'}) CREATE (id4830480629:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id4838429483:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(2 i x) = \\cos(2 x)+i \\sin(2 x)'}) CREATE (id4843995999:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{2 i}\\left(\\exp(i x)-\\exp(-i x) \\right) = \\sin(x)'}) CREATE (id4857472413:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '1 = \\int \\psi(x)\\psi(x)^* dx'}) CREATE (id4857475848:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{a^2} = \\frac{W}{2}'}) CREATE (id4858693811:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{T_{\\rm orbit}^2 G m_{\\rm Earth}}{4 \\pi^2} = r^3'}) CREATE (id4866160902:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{V}{R_{\\rm total}} = \\frac{V}{R_1} + \\frac{V}{R_2}'}) CREATE (id4872163189:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\tanh(x) = \\frac{\\sinh(x)}{\\cosh(x)}'}) CREATE (id4872970974:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{PE_2 - PE_1}{t} = -F v'}) CREATE (id4878728014:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin(i x) = \\frac{1}{2i}\\left(\\exp(-x) - \\exp(x) \\right)'}) CREATE (id4901237716:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '1'}) CREATE (id4923339482:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'i x = \\log(y)'}) CREATE (id4928007622:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_1 = \\frac{1}{2} m v_1^2'}) CREATE (id4928239482:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\log(y) = i x'}) CREATE (id4935235303:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id4938429482:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(-i x) = \\cos(x)+i \\sin(-x)'}) CREATE (id4938429483:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(i x) = \\cos(x)+i \\sin(x)'}) CREATE (id4938429484:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(-i x) = \\cos(x)-i \\sin(x)'}) CREATE (id4939880586:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V_{\\rm total} = I R_{\\rm total}'}) CREATE (id4943571230:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\psi( \\vec{r},t) = \\frac{i}{\\hbar} \\vec{p} \\psi_0 \\exp\\left(\\frac{i}{\\hbar}\\left( \\vec{p}\\cdot\\vec{r} - E t \\right) \\right)'}) CREATE (id4947831649:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{2} m_1 v_{\\rm final}^2 = W_{\\rm to\\ system}'}) CREATE (id4948763856:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: '2 a d + v_0^2 = v^2'}) CREATE (id4948934890:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle \\psi| \\hat{A} |\\psi \\rangle = \\langle a \\rangle^*'}) CREATE (id4949359835:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle x^2\\rangle -2\\langle x^2 \\rangle+\\langle x \\rangle^2 = \\langle x^2 \\rangle-\\langle x \\rangle^2'}) CREATE (id4961662865:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id4968680693:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\tan( x ) = \\frac{ \\sin( x )}{\\cos( x )}'}) CREATE (id4985825552:expression { notes: 'https://physicsderivationgraph.blogspot.com/2020/09/representing-laplace-operator-nabla-in.html', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 E( \\vec{r})\\exp(i \\omega t) = i \\omega \\mu_0 \\epsilon_0 \\frac{\\partial}{\\partial t} E( \\vec{r})\\exp(i \\omega t)'}) CREATE (id5002539602:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'dU = C_V dT + \\pi_T dV'}) CREATE (id5011888122:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_2'}) CREATE (id5021965469:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'KE'}) CREATE (id5050429607:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'G \\frac{m_{\\rm Earth} m}{r_{\\rm Earth}}'}) CREATE (id5074423401:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'V'}) CREATE (id5075406409:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'PE'}) CREATE (id5085809757:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{k_{\\rm adsorption}}{k_{\\rm desorption}} = \\frac{[A_{\\rm adsorption}]}{p_A [S]}'}) CREATE (id5089196493:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'F'}) CREATE (id5125940051:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I = |A|^2 + B B^* + A B^* + B A^*'}) CREATE (id5128670694:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'm_1 d_1 = m_2 d_2'}) CREATE (id5136652623:expression { name: 'mechanical energy is the sum of the potential plus kinetic energies', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'E = KE + PE'}) CREATE (id5144263777:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v^2 = v_0^2 + 2 a \\left( v_0 t +\\frac{1}{2} a t^2 \\right)'}) CREATE (id5148266645:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 't\' = \\frac{\\gamma x (1 - \\gamma^2 )}{\\gamma^2 v} + \\gamma t'}) CREATE (id5177311762:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\frac{2 \\pi r}{T}'}) CREATE (id5181421075:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'R_1'}) CREATE (id5194141542:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'x_f'}) CREATE (id5208737840:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'T_{\\rm geostationary\\ orbit}'}) CREATE (id5239755033:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_1'}) CREATE (id5258419993:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'R_1'}) CREATE (id5284610349:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2'}) CREATE (id5323719091:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: 'i \\sinh x = \\frac{1}{2i} \\left( \\exp(-x) - \\exp(x) \\right)'}) CREATE (id5345738321:expression { name: 'Newton's second law of motion', notes: 'https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton's_second_law', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'F = m a'}) CREATE (id5349669879:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\tanh(x) = \\frac{ \\exp(x)-\\exp(-x)}{\\exp(x)+\\exp(-x)}'}) CREATE (id5349866551:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{v} = v_x \\hat{x} + v_y \\hat{y}'}) CREATE (id5353282496:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'd = \\frac{v_0^2}{g}'}) CREATE (id5359471792:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{m_{\\rm satellite}}{r}'}) CREATE (id5373931751:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 't = t_f'}) CREATE (id5379546684:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'y_f = - \\frac{1}{2} g t_f^2 + v_0 t_f \\sin(\\theta) + y_0'}) CREATE (id5398681502:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id5398681503:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id5404822208:expression { name: 'escape velocity', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm escape} = \\sqrt{2 G \\frac{m}{r}}'}) CREATE (id5415824175:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 'x(t) = A \\cos(\\omega t)'}) CREATE (id5426308937:expression { creation_date: '2020-05-06', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\frac{d}{t}'}) CREATE (id5426418187:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '[A_{\\rm adsorption}]'}) CREATE (id5438722682:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x = v_0 t \\cos(\\theta) + x_0'}) CREATE (id5453995431:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\arctan{ x }'}) CREATE (id5463275819:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'I_2'}) CREATE (id5514556106:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'E_2 - E_1 = (KE_2 - KE_1) + (PE_2 - PE_1)'}) CREATE (id5516739892:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '-1'}) CREATE (id5530148480:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{p}_{1}-\\vec{p}_{2} = \\vec{p}_{electron}'}) CREATE (id5542390646:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: '2 a'}) CREATE (id5542528160:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: '\\int dW = F \\int_0^x dx'}) CREATE (id5563580265:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm gravity} = G \\frac{m_{\\rm Earth} m_{\\rm satellite}}{r^2}'}) CREATE (id5585739998:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'I'}) CREATE (id5586102077:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'r = d_1 + d_2'}) CREATE (id5591692598:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_1'}) CREATE (id5596822289:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm to\\ system} = -G m_1 m_2 \\left(\\left.\\frac{-1}{x}\\right|^r_{\\infty}\\right)'}) CREATE (id5611024898:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = \\frac{1}{2 a} (v^2 - v_0^2)'}) CREATE (id5620558729:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_0'}) CREATE (id5623794884:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'A + B'}) CREATE (id5632428182:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos( \\theta_{\\rm Brewster} )'}) CREATE (id5634116660:expression { notes: 'definition of internal pressure at constant temperature', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\pi_T = \\left(\\frac{\\partial U}{\\partial V}\\right)_T'}) CREATE (id5646314683:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'm = A m_p'}) CREATE (id5658865948:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'T^2 = \\frac{r^3 4 \\pi^2}{(m_1+m_2)G}'}) CREATE (id5667870149:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta'}) CREATE (id5669500954:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'v^2 \\gamma^2'}) CREATE (id5684907106:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{d_2 4 \\pi^2}'}) CREATE (id5693047217:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm final} = -\\sqrt{\\frac{2 G m_2}{r}}'}) CREATE (id5727578862:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d^2}{dx^2} \\psi(x) = -k^2 \\psi(x)'}) CREATE (id5732331610:expression { notes: '2022-03-25 BHP: Conversion between Latex and Sympy is incomplete', creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = G m_1 m_2 \\left( \\frac{1}{x} \\bigg\\rvert_{ r_{\\rm Earth} }^{\\infty} \\right)'}) CREATE (id5733146966:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_2 - KE_1 = \\frac{1}{2} m \\left(v_2^2 - v_1^2\\right)'}) CREATE (id5733721198:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = \\frac{1}{2} (v + v_0) \\left( \\frac{v - v_0}{a} \\right)'}) CREATE (id5763749235:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '-c^2 + c^2 \\gamma^2 = v^2 \\gamma^2'}) CREATE (id5770088141:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'r'}) CREATE (id5775658332:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id5778176146:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id5779256336:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm by\\ system} = KE_{\\rm final} - KE_{\\rm initial}'}) CREATE (id5781435087:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'g'}) CREATE (id5781981178:expression { name: 'difference of squares', notes: 'https://en.wikipedia.org/wiki/Difference_of_two_squares', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'x^2 - y^2 = (x+y)(x-y)'}) CREATE (id5787469164:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '1 - \\gamma^2'}) CREATE (id5789289057:expression { notes: 'equation 4 in the PDF', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\alpha c \\sqrt{ \\frac{m_e}{2 m} }'}) CREATE (id5799753649:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id5803210729:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_2'}) CREATE (id5832984291:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '(\\sin(x))^2 + (\\cos(x))^2 = 1'}) CREATE (id5838268428:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\alpha c = \\frac{1}{4 \\pi \\epsilon_0} \\frac{e^2}{\\hbar}'}) CREATE (id5846177002:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id5846639423:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm final} = \\sqrt{\\frac{2 G m_2}{r}}'}) CREATE (id5850144586:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm by\\ system} = KE_{\\rm final}'}) CREATE (id5857434758:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\int a dx = a x'}) CREATE (id5866629429:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '{\\rm sech}^2\\ x + \\tanh^2(x) = 1'}) CREATE (id5868688585:expression { notes: 'https://physicsderivationgraph.blogspot.com/2020/09/representing-laplace-operator-nabla-in.html', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{-\\hbar^2}{2m} \\nabla^2 \\psi \\left( \\vec{r},t \\right) = \\frac{p^2}{2m} \\psi( \\vec{r},t)'}) CREATE (id5868731041:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_0'}) CREATE (id5890617067:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'R'}) CREATE (id5900595848:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'k = \\frac{\\omega}{v}'}) CREATE (id5902985919:expression { name: 'Newton's law of universal gravitation', creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{F} = G \\frac{m_1 m_2}{x^2} \\hat{x}'}) CREATE (id5904227750:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id5928285821:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x^2 + 2 x (b/(2 a)) + (b/(2 a))^2 = (x + (b/(2 a)))^2'}) CREATE (id5928292841:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x^2 + (b/a)x + (b/(2 a))^2 = -c/a + (b/(2 a))^2'}) CREATE (id5938459282:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x^2 + (b/a)x = -c/a'}) CREATE (id5945893986:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d^2 x}{dt^2} = -A \\omega^2 \\cos(\\omega t)'}) CREATE (id5958392859:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x^2 + (b/a)x+(c/a) = 0'}) CREATE (id5959282914:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x^2 + x(b/a) + (b/(2 a))^2 = (x+(b/(2 a)))^2'}) CREATE (id5960438249:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'E_1'}) CREATE (id5962145508:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\alpha = \\frac{nR}{VP}'}) CREATE (id5978756813:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = G m_{\\rm Earth} m \\left( 0 - \\frac{-1}{ r_{\\rm Earth}} \\right)'}) CREATE (id5982958248:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x = -\\sqrt{(b/(2 a))^2 - (c/a)}-(b/(2 a))'}) CREATE (id5982958249:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x+(b/(2 a)) = -\\sqrt{(b/(2 a))^2 - (c/a)}'}) CREATE (id5985371230:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\psi( \\vec{r},t) = \\frac{i}{\\hbar} \\vec{p} \\psi( \\vec{r},t)'}) CREATE (id6023986360:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id6026694087:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{centripetal} = m \\frac{v^2}{r}'}) CREATE (id6031385191:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\sinh^2 x = \\left(\\frac{\\exp(x) - \\exp(-x)}{2}\\right)\\left(\\frac{\\exp(x) - \\exp(-x)}{2}\\right)'}) CREATE (id6038673136:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id6050070428:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, x}'}) CREATE (id6055078815:expression { notes: 'constant pressure', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\left(\\frac{\\partial U}{\\partial T}\\right)_p = C_V \\left(\\frac{\\partial T}{\\partial T}\\right)_p + \\pi_T \\left( \\frac{\\partial V}{\\partial T} \\right)_p'}) CREATE (id6061695358:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V_2 = I R_2'}) CREATE (id6083821265:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_0 \\cos(\\theta) = v_{0, x}'}) CREATE (id6091977310:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_{\\rm initial} = \\frac{1}{2} m_1 v_{\\rm initial}^2'}) CREATE (id6098638221:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'y_0'}) CREATE (id6131764194:expression { notes: 'https://physicsderivationgraph.blogspot.com/2020/09/evaluating-definite-integrals-for.html', creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = G m_{\\rm Earth} m \\left( \\frac{1}{x^2} \\bigg\\rvert_{ r_{\\rm Earth} }^{\\infty} \\right)'}) CREATE (id6134836751:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, x} = v_x'}) CREATE (id6158970683:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_1'}) CREATE (id6175547907:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm average} = \\frac{v + v_0}{2}'}) CREATE (id6204539227:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '-g t + v_{0, y} = \\frac{dy}{dt}'}) CREATE (id6238632840:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'r T_{\\rm orbit}^2'}) CREATE (id6239815585:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'C_{\\rm Earth\\ orbit}'}) CREATE (id6240206408:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I_{\\rm incoherent} = |A|^2 + |B|^2'}) CREATE (id6240546932:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{K_{equilibrium}} = \\frac{k_{\\rm desorption}}{k_{\\rm adsorption}}'}) CREATE (id6259833695:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'A'}) CREATE (id6268336290:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{gravitational} = \\frac{m}{r}\\left(\\frac{2\\pi r}{T}\\right)^2'}) CREATE (id6281834543:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'm_1'}) CREATE (id6296166842:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'P'}) CREATE (id6306552185:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I = (A + B)(A^* + B^*)'}) CREATE (id6346902704:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '1'}) CREATE (id6348260313:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 'C_{\\rm Earth\\ orbit} = 2 \\pi r_{\\rm Earth\\ orbit}'}) CREATE (id6353701615:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_{\\rm refracted}'}) CREATE (id6383056612:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'KE'}) CREATE (id6397683463:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'V \\alpha = \\left( \\frac{\\partial V}{\\partial T} \\right)_p'}) CREATE (id6404535647:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\cosh x = \\frac{\\exp(x) + \\exp(-x)}{2}'}) CREATE (id6408214498:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'c^2'}) CREATE (id6410818363:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta'}) CREATE (id6417359412:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v_0'}) CREATE (id6421241247:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = v t - \\frac{1}{2} a t^2'}) CREATE (id6450985774:expression { name: 'Law of Refraction', notes: 'eq 34-44 on page 819 in \cite{2001_HRW}', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'n_1 \\sin( \\theta_1 ) = n_2 \\sin( \\theta_2 )'}) CREATE (id6457044853:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v - a t = v_0'}) CREATE (id6457999644:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{[S_0]}{[A_{\\rm adsorption}]} = \\frac{1}{K_{\\rm equilibrium}} \\frac{1}{p_A} + 1'}) CREATE (id6463266449:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 't_f'}) CREATE (id6498985149:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm escape}'}) CREATE (id6504442697:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\sqrt{ \\frac{K}{\\rho} }'}) CREATE (id6529120965:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'B'}) CREATE (id6529793063:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I_{\\rm incoherent} = |A|^2 + |A|^2'}) CREATE (id6535639720:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Earth}'}) CREATE (id6546594355:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'R_{\\rm total}'}) CREATE (id6554292307:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id6555185548:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'A^* = |A| \\exp(-i \\theta)'}) CREATE (id6556875579:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{I_{\\rm coherent}}{I_{\\rm incoherent}} = 2'}) CREATE (id6572039835:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '-g t + v_{0, y} = v_y'}) CREATE (id6599829782:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm final}'}) CREATE (id6672141531:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'dt'}) CREATE (id6681646197:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id6701855578:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_2'}) CREATE (id6715248283:expression { name: 'potential energy', notes: 'https://en.wikipedia.org/wiki/Potential_energy', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'PE = -F x'}) CREATE (id6729698807:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v_0'}) CREATE (id6732786762:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id6742123016:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{p}_{electron}\\cdot\\vec{p}_{electron} = ( \\vec{p}_{1}\\cdot\\vec{p}_{1})+( \\vec{p}_{2}\\cdot\\vec{p}_{2})-2( \\vec{p}_{1}\\cdot\\vec{p}_{2})'}) CREATE (id6749533119:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_1'}) CREATE (id6753224061:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'I_{\\rm total} = I_1 + I_2'}) CREATE (id6774684564:expression { notes: 'for coherent waves', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta = \\phi'}) CREATE (id6783009163:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm adsorption} = r_{\\rm desorption}'}) CREATE (id6785303857:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 'C = 2 \\pi r'}) CREATE (id6800170830:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Schwarzschild} = \\frac{2 G m}{c^2}'}) CREATE (id6829281943:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{\\rm centripetal} = G \\frac{m_1 m_2}{r^2}'}) CREATE (id6831637424:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin( 90^{\\circ} - \\theta_{\\rm Brewster} ) = \\cos( \\theta_{\\rm Brewster} )'}) CREATE (id6831694380:expression { name: 'acceleration', creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 'a = \\frac{d^2 x}{dt^2}'}) CREATE (id6838659900:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_2'}) CREATE (id6870322215:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_{\\rm escape} = \\frac{1}{2} m v_{\\rm escape}^2'}) CREATE (id6885625907:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(i \\pi) = -1 + i 0'}) CREATE (id6892595652:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{2} m_1 v_{\\rm final}^2 = \\frac{G m_1 m_2}{r}'}) CREATE (id6908055431:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 'x(t) = A \\cos\\left(\\frac{k}{m} t\\right)'}) CREATE (id6925244346:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\alpha = \\frac{PV}{T} \\frac{1}{VP}'}) CREATE (id6935745841:expression { name: 'Newton's law of universal gravitation', notes: 'https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#Modern_form', creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'F = G \\frac{m_1 m_2}{x^2}'}) CREATE (id6946088325:expression { creation_date: '2020-05-06', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\frac{C}{t}'}) CREATE (id6955192897:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm desorption} = k_{\\rm desorption} [A_{\\rm adsorption}]'}) CREATE (id6964468708:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_1'}) CREATE (id6974054946:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{2} g t_f'}) CREATE (id6976493023:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id6998364753:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm Earth\\ orbit} = \\frac{2 \\pi \\left( 1.496\\ 10^8 {\\rm km} \\right)}{3.16\\ 10^7 {\\rm seconds}}'}) CREATE (id7002609475:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{V}{R_2} = I_2'}) CREATE (id7010294143:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'T_{\\rm orbit}^2 G m_{\\rm Earth} = 4 \\pi^2 r^3'}) CREATE (id7011114072:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = \\frac{(v_0 + a t) + v_0}{2} t'}) CREATE (id7049769409:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id7053449926:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm 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creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_2'}) CREATE (id7159989263:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: 'i x'}) CREATE (id7175416299:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 't_{\\rm Earth\\ orbit} = 1 {\\rm year}'}) CREATE (id7191277455:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'R'}) CREATE (id7194432406:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Schwarzschild}'}) CREATE (id7214442790:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id7215099603:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v^2 = v_0^2 + 2 a t v_0 + a^2 t^2'}) CREATE (id7217021879:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'R_{\\rm total} = R_1 + R_2'}) CREATE (id7233558441:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'd = v_0 t_f \\cos(\\theta)'}) CREATE (id7252338326:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_y = \\frac{dy}{dt}'}) CREATE (id7263534144:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'c^2'}) CREATE (id7267155233:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{PE_2 - PE_1}{t} = -F \\left( \\frac{x_2 - x_1}{t} \\right)'}) CREATE (id7267424860:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{\\theta_A} = \\frac{1+(K_{\\rm equilibrium}\\ p_A)}{K_{\\rm equilibrium}\\ p_A}'}) CREATE (id7321695558:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_{\\rm Brewster}'}) CREATE (id7326066466:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'G'}) CREATE (id7337056406:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2 x'}) CREATE (id7354529102:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'y = - \\frac{1}{2} g \\left( \\frac{x - x_0}{v_{0, x}} \\right)^2 + v_{0, y} \\frac{x - x_0}{v_{0, x}} + y_0'}) CREATE (id7375348852:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_{\\rm Brewster}'}) CREATE (id7376526845:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin(\\theta) = \\frac{v_{0, y}}{v_0}'}) CREATE (id7391837535:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(\\theta) = \\frac{v_{0, x}}{v_0}'}) CREATE (id7410124465:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'R_{\\rm total}'}) CREATE (id7410526982:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: '2/m_1'}) CREATE (id7445388869:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: '-1'}) CREATE (id7453225570:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id7455581657:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, x} = \\frac{dx}{dt}'}) CREATE (id7466829492:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\cdot \\vec{E} = 0'}) CREATE (id7473576008:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{-1}{A \\cos(\\omega t)}'}) CREATE (id7476820482:expression { creation_date: '2020-05-06', author: '4a0987466473c589d2c328d12856760e', latex: 'C'}) CREATE (id7497687256:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V'}) CREATE (id7513513483:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2 (c^2 - v^2) = c^2'}) CREATE (id7517073655:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '[S_0] = \\left(\\frac{1}{K_{\\rm equilibrium}} \\frac{1}{p_A} + 1\\right)[A_{\\rm adsorption}]'}) CREATE (id7556442438:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: '4 \\pi^2'}) CREATE (id7560908617:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id7564010952:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '-1'}) CREATE (id7564894985:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\int \\cos\\left(\\frac{2n\\pi}{W} x\\right) dx = \\frac{W}{2n\\pi}\\sin\\left(\\frac{2n\\pi}{W} x\\right)'}) CREATE (id7572664728:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(2 x) + 2 (\\sin(x))^2 = 1'}) CREATE (id7573835180:expression { notes: 'the potential energy at the surface of the Earth is equal to the work needed to get it from the center of the Earth to the surface', creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_{\\rm Earth\\ surface} = -W'}) CREATE (id7575738420:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\left(\\sin\\left(\\frac{n \\pi}{W}x\\right) \\right)^2 = \\frac{1-\\cos\\left(2\\frac{n \\pi}{W}x\\right)}{2}'}) CREATE (id7575859295:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\times \\vec{ \\nabla} \\times \\vec{E} = \\vec{ \\nabla}( \\vec{ \\nabla} \\cdot \\vec{E} - \\nabla^2 \\vec{E})'}) CREATE (id7575859300:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\epsilon^{i,j,k} \\hat{x}_i \\nabla_j ( \\vec{ \\nabla} \\times \\vec{E} )_k = \\vec{ \\nabla}( \\vec{ \\nabla} \\cdot \\vec{E} - \\nabla^2 \\vec{E})'}) CREATE (id7575859302:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\epsilon^{i,j,k} \\epsilon_{n,j,k} \\hat{x}_i \\nabla_j \\nabla^m E^n = \\vec{ \\nabla}( \\vec{ \\nabla} \\cdot \\vec{E} - \\nabla^2 \\vec{E})'}) CREATE (id7575859304:expression { notes: 'https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\epsilon^{i,j,k} \\epsilon_{n,j,k} = \\delta^{l}_{\\ \\ j} \\delta^{m}_{\\ \\ k} - \\delta^{l}_{\\ \\ k} \\delta^{m}_{\\ \\ h}'}) CREATE (id7575859306:expression { notes: 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\\nabla_m \\nabla^m E^n = \\vec{ \\nabla}( \\vec{ \\nabla} \\cdot \\vec{E} - \\nabla^2 \\vec{E})'}) CREATE (id7575859312:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla}( \\vec{ \\nabla} \\cdot \\vec{E} - \\nabla^2 \\vec{E}) = \\vec{ \\nabla}( \\vec{ \\nabla} \\cdot \\vec{E} - \\nabla^2 \\vec{E})'}) CREATE (id7587034465:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta'}) CREATE (id7607271250:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta'}) CREATE (id7621705408:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I = |A|^2 + |B|^2 + |A| |B| \\exp(-i \\theta) \\exp(i \\phi) + |A| |B| \\exp(i \\theta) \\exp(-i \\phi)'}) CREATE (id7630953440:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{K_{\\rm equilibrium} p_A}{K_{\\rm equilibrium} p_A}'}) CREATE (id7652131521:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{dx}{dt} = -A \\omega \\sin (\\omega t)'}) CREATE (id7672365885:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'F_{gravitational} = \\frac{4 \\pi^2 m r}{T^2}'}) CREATE (id7675171493:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V_1 = I R_1'}) CREATE (id7676652285:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_2 = \\frac{1}{2} m v_2^2'}) CREATE (id7696214507:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'n_1 \\sin( \\theta_{\\rm Brewster} ) = n_2 \\sin( 90^{\\circ} - \\theta_{\\rm Brewster} )'}) CREATE (id7701249282:expression { notes: 'when A = 1', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v_u = \\alpha c \\sqrt{ \\frac{m_e}{m_p} }'}) CREATE (id7708501762:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'C_{\\rm Earth\\ orbit}'}) CREATE (id7729413831:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'a_x \\hat{x} + a_y \\hat{y} = \\frac{d}{dt} \\left(v_x \\hat{x} + v_y \\hat{y} \\right)'}) CREATE (id7731226616:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '{\\rm sech}\\ x = \\frac{1}{\\cosh x}'}) CREATE (id7734996511:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_2 - PE_1 = -F ( x_2 - x_1 )'}) CREATE (id7735731560:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\cosh^2 x - \\sinh^2 x = \\frac{1}{4}\\left( \\exp(2x)+1+1+\\exp(-2x) - \\left(\\exp(2x)-1-1-\\exp(-2x)\\right) \\right)'}) CREATE (id7735737409:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{KE_2 - KE_1}{t} = m v \\frac{ v_2 - v_1 }{t}'}) CREATE (id7741202861:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\gamma^2 x - \\gamma^2 v t + \\gamma v t\''}) CREATE (id7743841045:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2'}) CREATE (id7749253510:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = G \\frac{m_{\\rm Earth} m }{ r_{\\rm Earth}}'}) CREATE (id7774819339:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'R'}) CREATE (id7798615279:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'I_{\\rm total}'}) CREATE (id7816982139:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'm/s^2'}) CREATE (id7819443873:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'r'}) CREATE (id7826132469:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\left(\\frac{\\partial U}{\\partial T}\\right)_p = C_V + \\pi_T V \\alpha'}) CREATE (id7837519722:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\sqrt{f} \\sqrt{\\frac{E}{m}}'}) CREATE (id7844317489:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'I'}) CREATE (id7846240076:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'm_{\\rm Earth} = \\frac{(9.80665 m/s^2) r_{\\rm Earth}^2}{G}'}) CREATE (id7857757625:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'n_1'}) CREATE (id7875206161:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'E_2 = KE_2 + PE_2'}) CREATE (id7882872592:expression { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm to\\ system} = \\int_{\\infty}^r \\vec{F}\\cdot d\\vec{r}'}) CREATE (id7905984866:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'm_1'}) CREATE (id7906112355:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2 = \\frac{c^2}{c^2 - \\gamma^2}'}) CREATE (id7912578203:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id7917051060:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{p}_{electron} = \\vec{p}_{1}-\\vec{p}_{2}'}) CREATE (id7924063906:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'K_{equilibrium} = \\frac{k_{\\rm adsorption}}{k_{\\rm desorption}}'}) CREATE (id7924842770:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'T'}) CREATE (id7928111771:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{\\theta_A} = \\frac{1}{K_{\\rm equilibrium} p_A} + 1'}) CREATE (id7935917166:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Earth}'}) CREATE (id7939765107:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v^2 = v_0^2 + 2 a d'}) CREATE (id7939947931:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_2'}) CREATE (id8014566709:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2 v t'}) CREATE (id8020058613:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'r'}) CREATE (id8044416349:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'd_2'}) CREATE (id8046208134:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I_{\\rm coherent} = |A|^2 + |A|^2 + |A| |A| 2'}) CREATE (id8049905441:expression { name: 'change in kinetic energy', creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: '\\Delta KE = KE_{\\rm final} - KE_{\\rm initial}'}) CREATE (id8059639673:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'v^2 = \\frac{4 \\pi^2 r^2}{T_{\\rm orbit}^2}'}) CREATE (id8061701434:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_1'}) CREATE (id8065128065:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I = A A^* + B B^* + A B^* + B A^*'}) CREATE (id8066819515:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id8072682558:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'x_0'}) CREATE (id8090924099:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\sqrt{ \\left( f\\frac{E}{a^3} \\right) \\frac{1}{\\rho} }'}) CREATE (id8106885760:expression { notes: 'fine structure constant definition', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\alpha = \\frac{1}{4 \\pi \\epsilon_0} \\frac{e^2}{\\hbar c}'}) CREATE (id8111389082:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id8120663858:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'y_f'}) CREATE (id8122039815:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d_1+d_2}{d_1+d_2}'}) CREATE (id8131665171:expression { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{\\theta_A} = \\frac{[S_0]}{[A_{\\rm adsorption}]}'}) CREATE (id8135396036:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id8139187332:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{p}_{1} = \\vec{p}_{2}+\\vec{p}_{electron}'}) CREATE (id8145337879:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '-g t dt + v_{0, y} dt = dy'}) CREATE (id8162179726:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: 'k_{\\rm adsorption} p_A'}) CREATE (id8173074178:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id8198310977:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '0 = - \\frac{1}{2} g t_f^2 + v_0 t_f \\sin(\\theta) + y_0'}) CREATE (id8228733125:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'a_y = \\frac{d}{dt} v_y'}) CREATE (id8257621077:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{p}_{\\rm before} = \\vec{p}_{1}'}) CREATE (id8269198922:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: '2 a d = v^2 - v_0^2'}) CREATE (id8283354808:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I_{\\rm coherent} = |A|^2 + |B|^2 + |A| |B| 2 \\cos( 0 )'}) CREATE (id8311458118:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{p}_{\\rm after} = \\vec{p}_{2}+\\vec{p}_{electron}'}) CREATE (id8332931442:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(i \\pi) = \\cos(\\pi)+i \\sin(\\pi)'}) CREATE (id8357234146:expression { name: 'kinetic energy', notes: 'https://en.wikipedia.org/wiki/Kinetic_energy', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'KE = \\frac{1}{2} m v^2'}) CREATE (id8360117126:expression { notes: 'not a physically valid result in this context', creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma = \\frac{-1}{\\sqrt{1-\\frac{v^2}{c^2}}}'}) CREATE (id8361238989:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'a_{centripetal} = \\frac{v^2}{r}'}) CREATE (id8362338572:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm escape}'}) CREATE (id8368984890:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\kappa_T = \\frac{-1}{V} \\left( \\frac{ \\partial }{\\partial P}\\left(\\frac{nRT}{P}\\right) \\right)_T'}) CREATE (id8396997949:expression { notes: 'intensity of two waves traveling opposite directions on same path', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I = | A + B |^2'}) CREATE (id8399484849:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle x^2 - 2 x \\langle x \\rangle + \\langle x \\rangle^2 \\rangle = \\langle x^2 \\rangle-\\langle x \\rangle^2'}) CREATE (id8405272745:expression { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm to\\ system} = -G m_1 m_2\\int_{\\infty}^r \\frac{1}{x^2} dx'}) CREATE (id8406170337:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'y'}) CREATE (id8416464049:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_{\\rm escape}'}) CREATE (id8418527415:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin(i x) = i \\sinh(x)'}) CREATE (id8435841627:expression { notes: 'https://en.wikipedia.org/wiki/Ideal_gas_law', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'P V = n R T'}) CREATE (id8460820419:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_x = \\frac{dx}{dt}'}) CREATE (id8483686863:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin(2 x) = \\frac{1}{2i}\\left(\\exp(i 2 x)-\\exp(-i 2 x) \\right)'}) CREATE (id8484544728:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '-a k^2\\sin(k x) + -b k^2\\cos(k x) = -a k^2 \\sin(kx) + -b k^2 \\cos(k x)'}) CREATE (id8485757728:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a \\frac{d^2}{dx^2}\\sin(kx) + b \\frac{d^2}{dx^2}\\cos(k x) = -a k^2 \\sin(kx) + -b k^2 \\cos(kx)'}) CREATE (id8485867742:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{2}{W} = a^2'}) CREATE (id8486706976:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, x} t + x_0 = x'}) CREATE (id8489593958:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd(u v) = u dv + v du'}) CREATE (id8489593960:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd(u v) - v du = u dv'}) CREATE (id8489593962:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'u dv = d(u v) - v du'}) CREATE (id8489593964:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\int u dv = u v - \\int v du'}) CREATE (id8494839423:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 \\vec{E} = \\mu_0 \\epsilon_0 \\frac{\\partial^2 \\vec{E}}{\\partial t^2}'}) CREATE (id8495187962:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_{\\rm Brewster} = \\arctan{ \\left( \\frac{ n_1 }{ n_2 } \\right) }'}) CREATE (id8497631728:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'I = |A|^2 + |B|^2 + |A| |B| 2 \\cos( \\theta - \\phi )'}) CREATE (id8515803375:expression { notes: 'frame of reference is moving only along x direction', creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'z\' = z'}) CREATE (id8532702080:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\cosh^2 x = \\left(\\frac{\\exp(x) + \\exp(-x)}{2}\\right)\\left(\\frac{\\exp(x) + \\exp(-x)}{2}\\right)'}) CREATE (id8552710882:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_{\\rm final} = \\frac{1}{2} m_1 v_{\\rm final}^2'}) CREATE (id8558338742:expression { name: 'conservation of energy', notes: 'https://en.wikipedia.org/wiki/Conservation_of_energy', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'E_2 = E_1'}) CREATE (id8563535636:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\cosh^2 x - \\sinh^2 x = \\left(\\frac{\\exp(x) + \\exp(-x)}{2}\\right)\\left(\\frac{\\exp(x) + \\exp(-x)}{2}\\right) - \\left(\\frac{\\exp(x) - \\exp(-x)}{2}\\right)\\left(\\frac{\\exp(x) - \\exp(-x)}{2}\\right)'}) CREATE (id8571466509:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'c^2 - \\gamma^2'}) CREATE (id8572657110:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '1 = \\int |\\psi(x)|^2 dx'}) CREATE (id8572852424:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{E} = E( \\vec{r},t)'}) CREATE (id8575746378:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\int \\frac{1}{2} dx = \\frac{1}{2} x'}) CREATE (id8575748999:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d^2}{dx^2} \\left(a \\sin(k x) + b \\cos(k x) \\right) = -k^2 \\left(a \\sin(kx) + b \\cos(kx) \\right)'}) CREATE (id8576785890:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '1 = \\int_0^W a^2 \\frac{1-\\cos\\left(2\\frac{n \\pi}{W}x\\right)}{2} dx'}) CREATE (id8577275751:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '0 = a \\sin(0) + b\\cos(0)'}) CREATE (id8582885111:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi(x) = a \\sin(kx) + b \\cos(kx)'}) CREATE (id8582954722:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x^2 + 2 x h + h^2 = (x + h)^2'}) CREATE (id8584698994:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '-g \\int dt = \\int d v_y'}) CREATE (id8588429722:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin( 90^{\\circ} - x ) = \\cos( x )'}) CREATE (id8602221482:expression { notes: 'incoherent light source', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle \\cos(\\theta - \\phi) \\rangle = 0'}) CREATE (id8602512487:expression { notes: 'decompose acceleration into two components', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{a} = a_x \\hat{x} + a_y \\hat{y}'}) CREATE (id8604483515:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'dW = G \\frac{m_1 m_2}{x^2} dx'}) CREATE (id8607458157:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'dt'}) CREATE (id8642992037:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id8651044341:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(i x) = \\frac{1}{2} \\left( \\exp(-x) + \\exp(x) \\right)'}) CREATE (id8655294002:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: 'a = -\\frac{k}{m}x'}) CREATE (id8661803554:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'F = G \\frac{m_{\\rm Earth} m}{r_{\\rm Earth}^2}'}) CREATE (id8688588981:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a^3 \\rho = m'}) CREATE (id8699789241:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '2 \\sin(x) \\cos(x) = \\frac{1}{2 i} \\left( \\exp(i 2 x) - 1 + 1 - \\exp(-i 2 x) \\right)'}) CREATE (id8706092970:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = \\left(\\frac{v + v_0}{2}\\right)t'}) CREATE (id8710504862:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'A'}) CREATE (id8717193282:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'dt'}) CREATE (id8721295221:expression { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e', latex: 't_{\\rm Earth\\ orbit} = 3.16 10^7 {\\rm seconds}'}) CREATE (id8730201316:expression { notes: 'first term was multiplied by \gamma/\gamma', creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{\\gamma x (1 - \\gamma^2 )}{\\gamma^2 v} + \\gamma t = t\''}) CREATE (id8747785338:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(i x) = \\cosh(x)'}) CREATE (id8750379055:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '0 = \\frac{d}{dt} v_x'}) CREATE (id8808860551:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '-g \\int t dt + v_{0, y} \\int dt = \\int dy'}) CREATE (id8849289982:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi(x)^* = a \\sin(\\frac{n \\pi}{W} x)'}) CREATE (id8854422847:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'dT'}) CREATE (id8857931498:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'c'}) CREATE (id8865085668:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 't'}) CREATE (id8871333437:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'PE_{\\rm Earth\\ surface}'}) CREATE (id8880467139:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '2'}) CREATE (id8889444440:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '1 = \\int_0^W a^2 \\left(\\sin\\left(\\frac{n \\pi}{W} x\\right) \\right)^2 dx'}) CREATE (id8908736791:expression { notes: 'geometry', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\rho = \\frac{m}{a^3}'}) CREATE (id8916428651:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id8922441655:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'd = \\frac{v_0^2}{g} \\sin(2 \\theta)'}) CREATE (id8945218208:expression { notes: 'based on figure 34-27 on page 824 in \cite{2001_HRW}', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_{\\rm Brewster} + \\theta_{\\rm refracted} = 90^{\\circ}'}) CREATE (id8946383937:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm escape}^2 = 2 G \\frac{m}{r}'}) CREATE (id8949329361:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_0 \\sin(\\theta) = v_{0, y}'}) CREATE (id8953094349:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = m a x'}) CREATE (id8960645192:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_2 + PE_2 = KE_1 + PE_1'}) CREATE (id8991236357:expression { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d^2 x}{dt^2} = -\\frac{k}{m} x'}) CREATE (id9025853427:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_{\\rm Brewster}'}) CREATE (id9029795851:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: '\\theta_{\\rm Brewster}'}) CREATE (id9031609275:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x (1 - \\gamma^2 ) = - \\gamma^2 v t + \\gamma v t\''}) CREATE (id9040079362:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'f'}) CREATE (id9053099840:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'I'}) CREATE (id9059289981:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi(x) = a \\sin(k x)'}) CREATE (id9063568209:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V_{\\rm total} = V_1 + V_2'}) CREATE (id9070394000:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'm_2 d_2 \\frac{4 \\pi^2}{T^2} = G \\frac{m_1 m_2}{r^2}'}) CREATE (id9070454719:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v_0^2'}) CREATE (id9072369552:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'm_{\\rm Earth}'}) CREATE (id9081138616:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'W_{\\rm by\\ system} = \\frac{1}{2} m_1 v_{\\rm final}^2'}) CREATE (id9110536742:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '2 x'}) CREATE (id9112191201:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'y_f = 0'}) CREATE (id9152823411:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{T^2} = \\frac{1}{d_2 4 \\pi^2} G \\frac{m_1}{r^2}'}) CREATE (id9170048197:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'T^2 = d_2 4 \\pi^2 \\frac{r^2}{G m_1}'}) CREATE (id9174439158:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'R_1'}) CREATE (id9180861128:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '2 \\sin(x) \\cos(x) = \\frac{1}{2 i} \\left( \\exp(i 2 x) - \\exp(-i 2 x) \\right)'}) CREATE (id9191880568:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'Z Z^* = |Z| |Z| \\exp( -i \\theta ) \\exp( i \\theta )'}) CREATE (id9226945488:expression { name: 'Centripetal force', notes: 'https://en.wikipedia.org/wiki/Centripetal_force', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'F = \\frac{m v^2}{r}'}) CREATE (id9243879541:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'V = I_2 R_2'}) CREATE (id9262596735:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'd = 2 \\pi r'}) CREATE (id9285928292:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'ax^2 + bx + c = 0'}) CREATE (id9291999979:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\times \\vec{ \\nabla} \\times \\vec{E} = -\\mu_0\\vec{ \\nabla} \\times \\frac{\\partial \\vec{H}}{\\partial t}'}) CREATE (id9294858532:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\hat{A}^+ = \\hat{A}'}) CREATE (id9305761407:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id9337785146:expression { name: 'average velocity', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\frac{x_2 - x_1}{t}'}) CREATE (id9341391925:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{v}_0 = v_{0, x} \\hat{x} + v_{0, y} \\hat{y}'}) CREATE (id9346215480:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'T_{\\rm orbit}'}) CREATE (id9350663581:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '\\pi'}) CREATE (id9350720370:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id9355039511:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: 'g'}) CREATE (id9356924046:expression { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{KE_2 - KE_1}{t} = m \\frac{v_2 + v_1}{2} \\frac{ v_2 - v_1 }{t}'}) CREATE (id9370882921:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_{\\rm escape}'}) CREATE (id9376481176:expression { notes: 'proportionality coefficient fvaries in the range 1-4 for a majority of elemental solids', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'K = f \\frac{E}{a^3}'}) CREATE (id9385938295:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '(x+(b/(2 a)))^2 = -(c/a) + (b/(2 a))^2'}) CREATE (id9393939991:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi(x) = -\\sqrt{\\frac{2}{W}} \\sin\\left(\\frac{n \\pi}{W} x\\right)'}) CREATE (id9393939992:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi(x) = \\sqrt{\\frac{2}{W}} \\sin\\left(\\frac{n \\pi}{W} x\\right)'}) CREATE (id9394939493:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 E( \\vec{r},t) = \\mu_0 \\epsilon_0 \\frac{\\partial^2}{\\partial t^2} E( \\vec{r},t)'}) CREATE (id9397152918:expression { name: 'average velocity', creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\frac{v_1 + v_2}{2}'}) CREATE (id9407192813:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'G \\frac{m_{\\rm Earth} m}{r_{\\rm Earth}^2} = m g_{\\rm Earth}'}) CREATE (id9409776983:expression { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e', latex: 'x (1 - \\gamma^2 ) + \\gamma^2 v t = \\gamma v t\''}) CREATE (id9412953728:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm escape}^2 = 2 G \\frac{m_{\\rm Earth}}{r_{\\rm Earth}}'}) CREATE (id9413609246:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: '\\cosh^2 x - \\sinh^2 x = 1'}) CREATE (id9413699705:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'W = m a \\frac{v_2^2 - v_1^2}{2 a}'}) CREATE (id9429829482:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d}{dx} y = -\\sin(x) + i\\cos(x)'}) CREATE (id9440616166:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'm_{\\rm Earth} = \\frac{g_{\\rm Earth} r_{\\rm Earth}^2}{G}'}) CREATE (id9482113948:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{dy}{y} = i dx'}) CREATE (id9482438243:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '(\\cos(x))^2 = \\cos(2 x) + (\\sin(x))^2'}) CREATE (id9482923849:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\exp(i x) = y'}) CREATE (id9482928242:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(2 x) = (\\cos(x))^2 - (\\sin(x))^2'}) CREATE (id9482928243:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(2 x) + (\\sin(x))^2 = (\\cos(x))^2'}) CREATE (id9482943948:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\log(y) = i dx'}) CREATE (id9482984922:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d}{dx} y = (i\\sin(x) + \\cos(x)) i'}) CREATE (id9483928192:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\cos(2 x) + i\\sin(2 x) = (\\cos(x))^2 + 2 i \\cos(x) \\sin(x) - (\\sin(x))^2'}) CREATE (id9485384858:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\nabla^2 E( \\vec{r})\\exp(i \\omega t) = - \\frac{\\omega^2}{c^2} E( \\vec{r})\\exp(i \\omega t)'}) CREATE (id9485747245:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\sqrt{\\frac{2}{W}} = a'}) CREATE (id9485747246:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '-\\sqrt{\\frac{2}{W}} = a'}) CREATE (id9492920340:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'y = \\cos(x)+i \\sin(x)'}) CREATE (id9495857278:expression { notes: '2022-03-25 BHP: Conversion between Latex and Sympy is incomplete', creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi(x=W) = 0'}) CREATE (id9499428242:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'E( \\vec{r},t) = E( \\vec{r})\\exp(i \\omega t)'}) CREATE (id9510328252:expression { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e', latex: 'KE_{\\rm initial} = 0'}) CREATE (id9524810853:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1/d_2}{1/d_2}'}) CREATE (id9562264720:expression { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e', latex: '[S] = \\frac{k_{\\rm desorption} [A_{\\rm adsorption}]}{k_{\\rm adsorption} p_A}'}) CREATE (id9565166889:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'T'}) CREATE (id9582958293:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\sqrt{(b/(2 a))^2 - (c/a)}-(b/(2 a))'}) CREATE (id9582958294:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x+(b/(2 a)) = \\sqrt{(b/(2 a))^2 - (c/a)}'}) CREATE (id9585727710:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\psi(x=0) = 0'}) CREATE (id9590696981:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: '9.80665'}) CREATE (id9594072504:expression { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e', latex: 'm_2'}) CREATE (id9596004948:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\langle\\psi_{\\alpha}| \\hat{A} |\\psi_{\\beta}\\rangle'}) CREATE (id9601500174:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm Earth\\ orbit}'}) CREATE (id9623791270:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'd'}) CREATE (id9640720571:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\frac{e^2}{4 \\pi \\epsilon_0 \\hbar} \\sqrt{\\frac{m_e}{2 m}}'}) CREATE (id9645178657:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'a t'}) CREATE (id9658195023:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'd = v_0 t + \\frac{1}{2} a t^2'}) CREATE (id9674924517:expression { notes: 'https://groups.google.com/g/sympy/c/yQ1KAaz7Gus/m/yfN-LaW1BQAJ', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'K >> G'}) CREATE (id9703482302:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: 'G \\frac{m_{\\rm Earth} m}{r_{\\rm Earth}} = \\frac{1}{2} m v_{\\rm escape}^2'}) CREATE (id9707028061:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'a_x = 0'}) CREATE (id9718685793:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\kappa_T = \\frac{1}{P}'}) CREATE (id9746066299:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'R_2'}) CREATE (id9749777192:expression { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e', latex: '0 = KE_1 + PE_1'}) CREATE (id9753878784:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: 'v'}) CREATE (id9756089533:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: '\\sin( \\theta_{\\rm Brewster} ) = \\frac{n_2}{n_1} \\cos( \\theta_{\\rm Brewster} )'}) CREATE (id9759901995:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v - v_0 = a t'}) CREATE (id9761485403:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'Z'}) CREATE (id9781951738:expression { notes: 'definition of isothermal compressibility', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\kappa_T = \\frac{-1}{V} \\left( \\frac{ \\partial V}{\\partial P} \\right)_T'}) CREATE (id9789485295:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{\\rm satellite}'}) CREATE (id9794128647:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'm_1'}) CREATE (id9805063945:expression { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e', latex: '\\gamma^2 (x - v t)^2 + y^2 + z^2 = c^2 \\gamma^2 \\left( t + \\frac{ 1 - \\gamma^2 }{ \\gamma^2 } \\frac{x}{v} \\right)^2'}) CREATE (id9830343096:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'V_1'}) CREATE (id9838128064:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'd_2 \\frac{4 \\pi^2}{T^2} = G \\frac{m_1}{r^2}'}) CREATE (id9847143017:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\kappa_T = \\frac{-PV}{V} \\left( \\frac{-1}{P^2}\\right)'}) CREATE (id9848292229:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'dy = y i dx'}) CREATE (id9848294829:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d}{dx} y = y i'}) CREATE (id9854442418:expression { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'v = \\sqrt{\\frac{E}{m}}'}) CREATE (id9858028950:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{1}{a^2} = \\int_0^W \\frac{1-\\cos\\left(2\\frac{n \\pi}{W}x\\right)}{2} dx'}) CREATE (id9862900242:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'y = - \\frac{1}{2} g t^2 + v_0 t \\sin(\\theta) + y_0'}) CREATE (id9881106100:expression { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e', latex: 'a'}) CREATE (id9882526611:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: 'v_{0, x} t = x - x_0'}) CREATE (id9884115626:expression { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e', latex: 'r'}) CREATE (id9885190237:expression { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e', latex: 'i'}) CREATE (id9889984281:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '2 (\\sin(x))^2 = 1 - \\cos(2 x)'}) CREATE (id9894826550:expression { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e', latex: '2 \\sin(x) \\cos(x) = \\frac{1}{2i}\\left(\\exp(i x)-\\exp(-i x) \\right) \\left(\\exp(i x)+\\exp(-i x) \\right)'}) CREATE (id9897284307:expression { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{d}{t} = \\frac{v + v_0}{2}'}) CREATE (id9903988330:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'm'}) CREATE (id9906920183:expression { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e', latex: 'x'}) CREATE (id9919999981:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\rho = 0'}) CREATE (id9933742680:expression { creation_date: '2020-06-03', author: '4a0987466473c589d2c328d12856760e', latex: 'r_{\\rm Schwarzschild}'}) CREATE (id9941599459:expression { notes: 'based on U(p, T, V) = U(T, V)', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e', latex: 'dU = \\left(\\frac{\\partial U}{\\partial T}\\right)_V dT + \\left(\\frac{\\partial U}{\\partial V}\\right)_T dV'}) CREATE (id9956609318:expression { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e', latex: '6.67430*10^{-11}'}) CREATE (id9958485859:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{-\\hbar^2}{2m} \\nabla^2 \\psi \\left( \\vec{r},t \\right) = i \\hbar \\frac{\\partial}{\\partial t} \\psi( \\vec{r},t)'}) CREATE (id9973952056:expression { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e', latex: '-g t = v_y - v_{0, y}'}) CREATE (id9988949211:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '(\\sin(x))^2 = \\frac{1 - \\cos(2 x)}{2}'}) CREATE (id9991999979:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\times \\vec{E} = -\\mu_0\\frac{\\partial \\vec{H}}{\\partial t}'}) CREATE (id9999998870:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{ \\vec{p}}{\\hbar} = \\vec{k}'}) CREATE (id9999999870:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{p}{\\hbar} = k'}) CREATE (id9999999960:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\hbar = h/(2 \\pi)'}) CREATE (id9999999961:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\frac{E}{\\hbar} = \\omega'}) CREATE (id9999999962:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'p = \\hbar k'}) CREATE (id9999999965:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'E = \\omega \\hbar'}) CREATE (id9999999968:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\frac{-b-\\sqrt{b^2-4ac}}{2 a}'}) CREATE (id9999999969:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: 'x = \\frac{-b+\\sqrt{b^2-4ac}}{2 a}'}) CREATE (id9999999975:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\langle \\psi| \\hat{A} |\\psi \\rangle = \\langle a \\rangle'}) CREATE (id9999999981:expression { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e', latex: '\\vec{ \\nabla} \\cdot \\vec{E} = \\rho/\\epsilon_0'}) CREATE (LHSofexpr1equalsLHSofexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'LHS of Eq.~\ref{eq:#1} is equal to LHS of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (RHSofexpr1equalsRHSofexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'RHS of Eq.~\ref{eq:#1} is equal to RHS of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (Xcrossbothsidesby:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Take cross product of $#1$ and Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (Xdotbothsides:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Take inner product of $#1$ with Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (addXtobothsides:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Add $#1$ to both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (addexpr1toexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Add Eq.~\ref{eq:#1} to Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#2}.'}) CREATE (addzerotoLHS:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Add zero to LHS of Eq.~\ref{eq:#2}, where $0=#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (addzerotoRHS:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Add zero to RHS of Eq.~\ref{eq:#2}, where $0=#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (applydivergence:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Apply divergence to both sides of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (applyfunctiontobothsidesofexpression:infrule { num_inputs: 1, num_feeds: 2, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-23, latex: 'Apply function $#1$ with argument $#2$ to Eq.~\ref{eq:#3}; yields Eq.~\ref{eq:#4}'}) CREATE (applygradienttoscalarfunction:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Apply gradient to both sides of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (applyoperatortobra:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-31, latex: 'Apply operator in Eq.~\ref{eq:#1} to bra; yields Eq.~\ref{eq:#2}.'}) CREATE (applyoperatortoket:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-31, latex: 'Apply operator in Eq.~\ref{eq:#1} to ket; yields Eq.~\ref{eq:#2}.'}) CREATE (assumeNdimensions:infrule { num_inputs: 0, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Assume $#1$ dimensions; decompose vector to be Eq.~\ref{eq:#2}.'}) CREATE (bothsidescrossX:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Take cross product of Eq.~\ref{eq:#2} and $#1$; yields Eq.~\ref{eq:#3}'}) CREATE (bothsidesdotX:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Take inner product of Eq.~\ref{eq:#2} with $#1$; yields Eq.~\ref{eq:#3}'}) CREATE (boundarycondition:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-17, latex: 'Boundary condition: Eq.~\ref{eq:#2} when Eq.~\ref{eq#1}.'}) CREATE (boundaryconditionforexpr:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'A boundary condition for Eq.~\ref{eq:#1} is Eq.~\ref{eq:#2}'}) CREATE (changefivevariablesinexpr:infrule { num_inputs: 1, num_feeds: 10, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ and $#7$ to $#8$ and $#9$ to $#10$ in Eq.~\ref{eq:#11}; yields Eq.~\ref{eq:#12}.'}) CREATE (changefourvariablesinexpr:infrule { num_inputs: 1, num_feeds: 8, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ and $#7$ to $#8$ in Eq.~\ref{eq:#9}; yields Eq.~\ref{eq:#10}.'}) CREATE (changesixvariablesinexpr:infrule { num_inputs: 1, num_feeds: 12, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ and $#7$ to $#8$ and $#9$ to $#10$ and $#11$ to $#12$ in Eq.~\ref{eq:#13}; yields Eq.~\ref{eq:#14}.'}) CREATE (changethreevariablesinexpr:infrule { num_inputs: 1, num_feeds: 6, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ in Eq.~\ref{eq:#7}; yields Eq.~\ref{eq:#8}.'}) CREATE (changetwovariablesinexpr:infrule { num_inputs: 1, num_feeds: 4, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.'}) CREATE (changevariableXtoY:infrule { num_inputs: 1, num_feeds: 2, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Change variable $#1$ to $#2$ in Eq.~\ref{eq:#3}; yields Eq.~\ref{eq:#4}.'}) CREATE (claimLHSequalsRHS:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 0, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Thus we see that LHS of Eq.~\ref{eq:#1} is equal to RHS.'}) CREATE (claimexpr1equalsexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 0, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Thus we see that Eq.~\ref{eq:#1} is equivalent to Eq.~\ref{eq:#2}.'}) CREATE (combineliketerms:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Combine like terms in Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (conjugatebothsides:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Conjugate both sides of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (conjugatefunctionX:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Conjugate $#1$ in Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (conjugatetransposebothsides:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Conjugate transpose of both sides of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (declareassumption:infrule { num_inputs: 0, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Eq.~\ref{eq:#1} is an assumption.'}) CREATE (declarefinalexpr:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 0, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Eq.~\ref{eq:#1} is one of the final equations.'}) CREATE (declareguesssolution:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Judicious choice as a guessed solution to Eq.~\ref{eq:#1} is Eq.~\ref{eq:#2},'}) CREATE (declareidentity:infrule { num_inputs: 0, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Eq.~\ref{eq:#1} is an identity.'}) CREATE (declareinitialexpr:infrule { num_inputs: 0, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Eq.~\ref{eq:#1} is an initial equation.'}) CREATE (differentiatewithrespectto:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Differentiate Eq.~\ref{eq:#2} with respect to $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (distributeconjugatetofactors:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Distribute conjugate to factors in Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (distributeconjugatetransposetofactors:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Distribute conjugate transpose to factors in Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (dividebothsidesby:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (divideexpr1byexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-17, latex: 'Divide Eq.~\ref{eq:#1} by Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (dropnondominantterm:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-06-14, latex: 'Based on the assumption $#1$, drop non-dominant term in Eq.~\ref{#2}; yeilds Eq.~\ref{#3}'}) CREATE (evaluatedefiniteintegral:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Evaluate definite integral Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (expandLHS:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Expand the LHS of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (expandRHS:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Expand the RHS of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (expandintegrand:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Expand integrand of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (expandmagnitudetoconjugate:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Expand $#1$ in Eq.~\ref{eq:#2} with conjugate; yields Eq.~\ref{eq:#3}.'}) CREATE (expr1isequivalenttoexpr2underthecondition:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-08, latex: 'Eq.~\ref{eq:#1} is equivalent to Eq.~\ref{eq:#2} under the condition in Eq.~\ref{eq:#3}.'}) CREATE (expr1istrueunderconditionexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Eq.~\ref{eq:#1} is valid when Eq.~\ref{eq:#2} occurs; yields Eq.~\ref{eq:#3}.'}) CREATE (factoroutX:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Factor $#1$ from Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (factoroutXfromLHS:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Factor $#1$ from the LHS of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (factoroutXfromRHS:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Factor $#1$ from the RHS of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (functioniseven:infrule { num_inputs: 1, num_feeds: 3, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: '$#1$ is even with respect to $#2$, so replace $#1$ with $#3$ in Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.'}) CREATE (functionisodd:infrule { num_inputs: 1, num_feeds: 3, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: '$#1$ is odd with respect to $#2$, so replace $#1$ with $#3$ in Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.'}) CREATE (indefiniteintegralover:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Indefinite integral of both sides of Eq.~\ref{eq:#2} over $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (indefiniteintegrateLHSover:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Indefinite integral of LHS of Eq.~\ref{eq:#2} over $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (indefiniteintegrateRHSover:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Indefinite integral of RHS of Eq.~\ref{eq:#2} over $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (indefiniteintegration:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Indefinite integral of both sides of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (integrate:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-24, latex: 'Integrate Eq.~ref{eq:#1}; yields Eq.~ref{eq:#2}.'}) CREATE (integrateoverfromto:infrule { num_inputs: 1, num_feeds: 3, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Integrate Eq.~\ref{eq:#4} over $#1$ from lower limit $#2$ to upper limit $#3$; yields Eq.~\ref{eq:#5}.'}) CREATE (makeexprpower:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Make Eq.~\ref{eq:#2} the power of $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (maximumofexpr:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-17, latex: 'The maximum of Eq.~\ref{eq:#2} with respect to $#1$ is Eq.~\ref{eq:#3}'}) CREATE (multiplyLHSbyunity:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Multiply LHS of Eq.~\ref{eq:#2} by 1, which in this case is $#1$; yields Eq.~\ref{eq:#3}'}) CREATE (multiplyRHSbyunity:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Multiply RHS of Eq.~\ref{eq:#2} by 1, which in this case is $#1$; yields Eq.~\ref{eq:#3}'}) CREATE (multiplybothsidesby:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (multiplyexpr1byexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Multiply Eq.~\ref{eq:#1} by Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (normalizationcondition:infrule { num_inputs: 0, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Normalization condition is Eq.~\ref{eq:#1}.'}) CREATE (partiallydifferentiatewithrespectto:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Partially differentiate Eq.~\ref{eq:#2} with respect to $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (raisebothsidestopower:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Raise both sides of Eq.~\ref{eq:#2} to $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (replaceconstantwithvalue:infrule { num_inputs: 1, num_feeds: 3, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-28, latex: 'Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}'}) CREATE (replacecurlwithLeviCevitasummationcontravariant:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Replace curl in Eq.~\ref{eq:#1} with Levi-Cevita contravariant; yields Eq.~\ref{eq:#2}.'}) CREATE (replacescalarwithvector:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Replace scalar variables in Eq.~\ref{eq:#1} with equivalent vector variables; yields Eq.~\ref{eq:#2}.'}) CREATE (replacesummationnotationwithvectornotation:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Replace summation notation in Eq.~\ref{eq:#1} with vector notation; yields Eq.~\ref{eq:#2}.'}) CREATE (selectimaginaryparts:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Select imaginary parts of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (selectrealparts:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Select real parts of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (separatethreevectorcomponents:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 3, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-17, latex: 'Separate three vector components in Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2} and Eq.~\ref{eq:#3} and Eq.~\ref{eq:#4}.'}) CREATE (separatetwovectorcomponents:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 2, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-17, latex: 'Separate two vector components in Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2} and Eq.~\ref{eq:#3}'}) CREATE (separatevectorintotwotrigonometricratios:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 2, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-17, latex: 'Separate vector in Eq.~\ref{eq:#2} into components related by angle $#1$; yields Eq.~\ref{eq:#3} and Eq.~\ref{eq:#4}.'}) CREATE (simplify:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (solveforX:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Solve Eq.~\ref{eq:#2} for $#1$; yields Eq.~\ref{eq:#3}.'}) CREATE (squarerootbothsides:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 2, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-14, latex: 'Take the square root of both sides of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2} and Eq.~\ref{eq:#3}.'}) CREATE (substituteLHSofexpr1intoexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (substituteLHSoffiveexpressionsintoexpr:infrule { num_inputs: 6, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} and LHS of Eq.~\ref{eq:#4} and LHS of Eq.~\ref{eq:#5} into Eq.~\ref{eq:#6}; yields Eq.~\ref{eq:#7}.'}) CREATE (substituteLHSoffourexpressionsintoexpr:infrule { num_inputs: 5, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} and LHS of Eq.~\ref{eq:#4} into Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.'}) CREATE (substituteLHSofsixexpressionsintoexpr:infrule { num_inputs: 7, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} and LHS of Eq.~\ref{eq:#4} and LHS of Eq.~\ref{eq:#5} and LHS of Eq.~\ref{eq:#6} into Eq.~\ref{eq:#7}; yields Eq.~\ref{eq:#8}.'}) CREATE (substituteLHSofthreeexpressionsintoexpr:infrule { num_inputs: 4, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} into Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.'}) CREATE (substituteLHSoftwoexpressionsintoexpr:infrule { num_inputs: 3, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-05-12, latex: 'Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} into Eq.~\ref{eq:#3}; yields Eq.~\ref{eq:#4}.'}) CREATE (substituteRHSofexpr1intoexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (subtractXfrombothsides:infrule { num_inputs: 1, num_feeds: 1, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Subtract $#1$ from both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.'}) CREATE (subtractexpr1fromexpr2:infrule { num_inputs: 2, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-20, latex: 'Subtract Eq.~\ref{eq:#1} from Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#2}.'}) CREATE (sumexponents:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Sum exponents on LHS and RHS of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (sumexponentsLHS:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Sum exponents on LHS of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (sumexponentsRHS:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Sum exponents on RHS of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (swapLHSwithRHS:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.'}) CREATE (takecurlofbothsides:infrule { num_inputs: 1, num_feeds: 0, num_outputs: 1, author: 4a0987466473c589d2c328d12856760e, creation_date: 2020-04-14, latex: 'Apply curl to both sides of Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.'}) CREATE (000001:derivation { name: 'Eulerequationproof', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1029890:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1029890)<-[:linear_index {linear_index: '10}']-(id000001) CREATE (id1029890)<-[:infrule]-(makeexprpower) CREATE (id1029890)<-[:expr { local_id: '3784785'}]-(id4923339482) CREATE (id1029890)<-[:expr { local_id: '6656532'}]-(id0006656532) CREATE (id1029890)-[:expr { local_id: '9587572'}]->(id9482923849) CREATE (id1848471:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1848471)<-[:linear_index {linear_index: '7}']-(id000001) CREATE (id1848471)<-[:infrule]-(indefiniteintegrateRHSover) CREATE (id1848471)<-[:expr { local_id: '8883737'}]-(id9482113948) CREATE (id1848471)<-[:expr { local_id: '4264724'}]-(id0004264724) CREATE (id1848471)-[:expr { local_id: '9984877'}]->(id9482943948) CREATE (id2741906:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2741906)<-[:linear_index {linear_index: '5}']-(id000001) CREATE (id2741906)<-[:infrule]-(multiplybothsidesby) CREATE (id2741906)<-[:expr { local_id: '9038289'}]-(id9848294829) CREATE (id2741906)<-[:expr { local_id: '3954314'}]-(id0003954314) CREATE (id2741906)-[:expr { local_id: '1111289'}]->(id9848292229) CREATE (id4614728:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4614728)<-[:linear_index {linear_index: '3}']-(id000001) CREATE (id4614728)<-[:infrule]-(factoroutXfromRHS) CREATE (id4614728)<-[:expr { local_id: '1838300'}]-(id9429829482) CREATE (id4614728)<-[:expr { local_id: '7563791'}]-(id0007563791) CREATE (id4614728)-[:expr { local_id: '2948271'}]->(id9482984922) CREATE (id6462728:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6462728)<-[:linear_index {linear_index: '8}']-(id000001) CREATE (id6462728)<-[:infrule]-(indefiniteintegrateRHSover) CREATE (id6462728)<-[:expr { local_id: '9984877'}]-(id9482943948) CREATE (id6462728)<-[:expr { local_id: '6563727'}]-(id0006563727) CREATE (id6462728)-[:expr { local_id: '3747585'}]->(id4928239482) CREATE (id6463728:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6463728)<-[:linear_index {linear_index: '2}']-(id000001) CREATE (id6463728)<-[:infrule]-(differentiatewithrespectto) CREATE (id6463728)<-[:expr { local_id: '1029383'}]-(id9492920340) CREATE (id6463728)<-[:expr { local_id: '7636749'}]-(id0007636749) CREATE (id6463728)-[:expr { local_id: '1838300'}]->(id9429829482) CREATE (id6466378:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6466378)<-[:linear_index {linear_index: '6}']-(id000001) CREATE (id6466378)<-[:infrule]-(dividebothsidesby) CREATE (id6466378)<-[:expr { local_id: '1111289'}]-(id9848292229) CREATE (id6466378)<-[:expr { local_id: '9877781'}]-(id0009877781) CREATE (id6466378)-[:expr { local_id: '8883737'}]->(id9482113948) CREATE (id7364656:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7364656)<-[:linear_index {linear_index: '1}']-(id000001) CREATE (id7364656)<-[:infrule]-(declareinitialexpr) CREATE (id7364656)-[:expr { local_id: '1029383'}]->(id9492920340) CREATE (id7466748:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7466748)<-[:linear_index {linear_index: '4}']-(id000001) CREATE (id7466748)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id7466748)<-[:expr { local_id: '1029383'}]-(id9492920340) CREATE (id7466748)<-[:expr { local_id: '2948271'}]-(id9482984922) CREATE (id7466748)-[:expr { local_id: '9038289'}]->(id9848294829) CREATE (id7561612:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7561612)<-[:linear_index {linear_index: '12}']-(id000001) CREATE (id7561612)<-[:infrule]-(declarefinalexpr) CREATE (id7561612)<-[:expr { local_id: '8888888'}]-(id4938429483) CREATE (id7563728:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7563728)<-[:linear_index {linear_index: '9}']-(id000001) CREATE (id7563728)<-[:infrule]-(swapLHSwithRHS) CREATE (id7563728)<-[:expr { local_id: '3747585'}]-(id4928239482) CREATE (id7563728)-[:expr { local_id: '3784785'}]->(id4923339482) CREATE (id7566272:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7566272)<-[:linear_index {linear_index: '11}']-(id000001) CREATE (id7566272)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id7566272)<-[:expr { local_id: '9587572'}]-(id9482923849) CREATE (id7566272)<-[:expr { local_id: '1029383'}]-(id9492920340) CREATE (id7566272)-[:expr { local_id: '8888888'}]->(id4938429483) CREATE (000002:derivation { name: 'Eulerequationtrigsquareroot', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1383414:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1383414)<-[:linear_index {linear_index: '16}']-(id000002) CREATE (id1383414)<-[:infrule]-(declarefinalexpr) CREATE (id1383414)<-[:expr { local_id: '1231131'}]-(id9988949211) CREATE (id3040493:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3040493)<-[:linear_index {linear_index: '8}']-(id000002) CREATE (id3040493)<-[:infrule]-(declareidentity) CREATE (id3040493)-[:expr { local_id: '9385720'}]->(id5832984291) CREATE (id3841414:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3841414)<-[:linear_index {linear_index: '15}']-(id000002) CREATE (id3841414)<-[:infrule]-(dividebothsidesby) CREATE (id3841414)<-[:expr { local_id: '7472666'}]-(id9889984281) CREATE (id3841414)<-[:expr { local_id: '3838111'}]-(id0003838111) CREATE (id3841414)-[:expr { local_id: '1231131'}]->(id9988949211) CREATE (id3984721:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3984721)<-[:linear_index {linear_index: '10}']-(id000002) CREATE (id3984721)<-[:infrule]-(swapLHSwithRHS) CREATE (id3984721)<-[:expr { local_id: '4890284'}]-(id9482928243) CREATE (id3984721)-[:expr { local_id: '2936550'}]->(id9482438243) CREATE (id5832058:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5832058)<-[:linear_index {linear_index: '5}']-(id000002) CREATE (id5832058)<-[:infrule]-(expandRHS) CREATE (id5832058)<-[:expr { local_id: '3333333'}]-(id4638429483) CREATE (id5832058)-[:expr { local_id: '4444444'}]->(id4598294821) CREATE (id6839583:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6839583)<-[:linear_index {linear_index: '2}']-(id000002) CREATE (id6839583)<-[:infrule]-(changevariableXtoY) CREATE (id6839583)<-[:expr { local_id: '8888888'}]-(id4938429483) CREATE (id6839583)<-[:expr { local_id: '4089571'}]-(id0004089571) CREATE (id6839583)<-[:expr { local_id: '4582412'}]-(id0004582412) CREATE (id6839583)-[:expr { local_id: '9999999'}]->(id4838429483) CREATE (id7563628:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7563628)<-[:linear_index {linear_index: '12}']-(id000002) CREATE (id7563628)<-[:infrule]-(subtractXfrombothsides) CREATE (id7563628)<-[:expr { local_id: '9481000'}]-(id4827492911) CREATE (id7563628)<-[:expr { local_id: '6466214'}]-(id0006466214) CREATE (id7563628)-[:expr { local_id: '7472641'}]->(id1248277773) CREATE (id7566277:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7566277)<-[:linear_index {linear_index: '14}']-(id000002) CREATE (id7566277)<-[:infrule]-(subtractXfrombothsides) CREATE (id7566277)<-[:expr { local_id: '1029911'}]-(id7572664728) CREATE (id7566277)<-[:expr { local_id: '8842811'}]-(id0008842811) CREATE (id7566277)-[:expr { local_id: '7472666'}]->(id9889984281) CREATE (id7572728:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7572728)<-[:linear_index {linear_index: '13}']-(id000002) CREATE (id7572728)<-[:infrule]-(addXtobothsides) CREATE (id7572728)<-[:expr { local_id: '7472641'}]-(id1248277773) CREATE (id7572728)<-[:expr { local_id: '7471778'}]-(id0007471778) CREATE (id7572728)-[:expr { local_id: '1029911'}]->(id7572664728) CREATE (id7663728:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7663728)<-[:linear_index {linear_index: '1}']-(id000002) CREATE (id7663728)<-[:infrule]-(declareinitialexpr) CREATE (id7663728)-[:expr { local_id: '8888888'}]->(id4938429483) CREATE (id8374590:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8374590)<-[:linear_index {linear_index: '6}']-(id000002) CREATE (id8374590)<-[:infrule]-(selectrealparts) CREATE (id8374590)<-[:expr { local_id: '2222222'}]-(id9483928192) CREATE (id8374590)-[:expr { local_id: '5828294'}]->(id9482928242) CREATE (id8374625:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8374625)<-[:linear_index {linear_index: '7}']-(id000002) CREATE (id8374625)<-[:infrule]-(addXtobothsides) CREATE (id8374625)<-[:expr { local_id: '5828294'}]-(id9482928242) CREATE (id8374625)<-[:expr { local_id: '7894942'}]-(id0007894942) CREATE (id8374625)-[:expr { local_id: '4890284'}]->(id9482928243) CREATE (id8492847:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8492847)<-[:linear_index {linear_index: '4}']-(id000002) CREATE (id8492847)<-[:infrule]-(multiplyexpr1byexpr2) CREATE (id8492847)<-[:expr { local_id: '8888888'}]-(id4938429483) CREATE (id8492847)<-[:expr { local_id: '8888888'}]-(id4938429483) CREATE (id8492847)-[:expr { local_id: '3333333'}]->(id4638429483) CREATE (id9483240:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9483240)<-[:linear_index {linear_index: '11}']-(id000002) CREATE (id9483240)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id9483240)<-[:expr { local_id: '2936550'}]-(id9482438243) CREATE (id9483240)<-[:expr { local_id: '9123670'}]-(id3285732911) CREATE (id9483240)-[:expr { local_id: '9481000'}]->(id4827492911) CREATE (id9582956:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9582956)<-[:linear_index {linear_index: '3}']-(id000002) CREATE (id9582956)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id9582956)<-[:expr { local_id: '4444444'}]-(id4598294821) CREATE (id9582956)<-[:expr { local_id: '9999999'}]-(id4838429483) CREATE (id9582956)-[:expr { local_id: '2222222'}]->(id9483928192) CREATE (id9832430:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9832430)<-[:linear_index {linear_index: '9}']-(id000002) CREATE (id9832430)<-[:infrule]-(subtractXfrombothsides) CREATE (id9832430)<-[:expr { local_id: '9385720'}]-(id5832984291) CREATE (id9832430)<-[:expr { local_id: '1111111'}]-(id0001111111) CREATE (id9832430)-[:expr { local_id: '9123670'}]->(id3285732911) CREATE (000003:derivation { name: 'Eulerequationtrigonometricrelations', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1928392:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1928392)<-[:linear_index {linear_index: '6}']-(id000003) CREATE (id1928392)<-[:infrule]-(dividebothsidesby) CREATE (id1928392)<-[:expr { local_id: '2939484'}]-(id4742644828) CREATE (id1928392)<-[:expr { local_id: '4829194'}]-(id0004829194) CREATE (id1928392)-[:expr { local_id: '4383592'}]->(id3829492824) CREATE (id2384942:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2384942)<-[:linear_index {linear_index: '8}']-(id000003) CREATE (id2384942)<-[:infrule]-(declarefinalexpr) CREATE (id2384942)<-[:expr { local_id: '4849888'}]-(id4585932229) CREATE (id2384942)<-[:expr { local_id: '4849959'}]-(id2103023049) CREATE (id2849492:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2849492)<-[:linear_index {linear_index: '11}']-(id000003) CREATE (id2849492)<-[:infrule]-(dividebothsidesby) CREATE (id2849492)<-[:expr { local_id: '4825483'}]-(id3942849294) CREATE (id2849492)<-[:expr { local_id: '1921933'}]-(id0001921933) CREATE (id2849492)-[:expr { local_id: '1133483'}]->(id4843995999) CREATE (id2939404:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2939404)<-[:linear_index {linear_index: '10}']-(id000003) CREATE (id2939404)<-[:infrule]-(addexpr1toexpr2) CREATE (id2939404)<-[:expr { local_id: '8888888'}]-(id4938429483) CREATE (id2939404)<-[:expr { local_id: '3194924'}]-(id2123139121) CREATE (id2939404)-[:expr { local_id: '4825483'}]->(id3942849294) CREATE (id2949492:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2949492)<-[:linear_index {linear_index: '7}']-(id000003) CREATE (id2949492)<-[:infrule]-(swapLHSwithRHS) CREATE (id2949492)<-[:expr { local_id: '4383592'}]-(id3829492824) CREATE (id2949492)-[:expr { local_id: '4849888'}]->(id4585932229) CREATE (id3848592:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3848592)<-[:linear_index {linear_index: '5}']-(id000003) CREATE (id3848592)<-[:infrule]-(addexpr1toexpr2) CREATE (id3848592)<-[:expr { local_id: '8888888'}]-(id4938429483) CREATE (id3848592)<-[:expr { local_id: '8888883'}]-(id4938429484) CREATE (id3848592)-[:expr { local_id: '2939484'}]->(id4742644828) CREATE (id3848924:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3848924)<-[:linear_index {linear_index: '9}']-(id000003) CREATE (id3848924)<-[:infrule]-(multiplybothsidesby) CREATE (id3848924)<-[:expr { local_id: '8888883'}]-(id4938429484) CREATE (id3848924)<-[:expr { local_id: '3747849'}]-(id0003747849) CREATE (id3848924)-[:expr { local_id: '3194924'}]->(id2123139121) CREATE (id3848927:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3848927)<-[:linear_index {linear_index: '2}']-(id000003) CREATE (id3848927)<-[:infrule]-(changevariableXtoY) CREATE (id3848927)<-[:expr { local_id: '8888888'}]-(id4938429483) CREATE (id3848927)<-[:expr { local_id: '2393922'}]-(id0002393922) CREATE (id3848927)<-[:expr { local_id: '3949052'}]-(id0003949052) CREATE (id3848927)-[:expr { local_id: '8888881'}]->(id2394853829) CREATE (id4294921:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4294921)<-[:linear_index {linear_index: '12}']-(id000003) CREATE (id4294921)<-[:infrule]-(swapLHSwithRHS) CREATE (id4294921)<-[:expr { local_id: '1133483'}]-(id4843995999) CREATE (id4294921)-[:expr { local_id: '4849959'}]->(id2103023049) CREATE (id4747288:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4747288)<-[:linear_index {linear_index: '4}']-(id000003) CREATE (id4747288)<-[:infrule]-(functionisodd) CREATE (id4747288)<-[:expr { local_id: '8888882'}]-(id4938429482) CREATE (id4747288)<-[:expr { local_id: '3919391'}]-(id0003919391) CREATE (id4747288)<-[:expr { local_id: '3981813'}]-(id0003981813) CREATE (id4747288)<-[:expr { local_id: '2919191'}]-(id0002919191) CREATE (id4747288)-[:expr { local_id: '8888883'}]->(id4938429484) CREATE (id7473895:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7473895)<-[:linear_index {linear_index: '1}']-(id000003) CREATE (id7473895)<-[:infrule]-(declareinitialexpr) CREATE (id7473895)-[:expr { local_id: '8888888'}]->(id4938429483) CREATE (id9595949:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9595949)<-[:linear_index {linear_index: '3}']-(id000003) CREATE (id9595949)<-[:infrule]-(functioniseven) CREATE (id9595949)<-[:expr { local_id: '8888881'}]-(id2394853829) CREATE (id9595949)<-[:expr { local_id: '4849392'}]-(id0004849392) CREATE (id9595949)<-[:expr { local_id: '1030901'}]-(id0001030901) CREATE (id9595949)<-[:expr { local_id: '3413423'}]-(id0003413423) CREATE (id9595949)-[:expr { local_id: '8888882'}]->(id4938429482) CREATE (000004:derivation { name: 'Maxwellequationstoelectricfieldwaveequation', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1010301:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1010301)<-[:linear_index {linear_index: '3}']-(id000004) CREATE (id1010301)<-[:infrule]-(partiallydifferentiatewithrespectto) CREATE (id1010301)<-[:expr { local_id: '1199299'}]-(id1314864131) CREATE (id1010301)<-[:expr { local_id: '5626421'}]-(id0005626421) CREATE (id1010301)-[:expr { local_id: '4642245'}]->(id1314464131) CREATE (id1939442:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1939442)<-[:linear_index {linear_index: '5}']-(id000004) CREATE (id1939442)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1939442)<-[:expr { local_id: '2392932'}]-(id9291999979) CREATE (id1939442)<-[:expr { local_id: '4642245'}]-(id1314464131) CREATE (id1939442)-[:expr { local_id: '2962831'}]->(id3947269979) CREATE (id2932848:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2932848)<-[:linear_index {linear_index: '1}']-(id000004) CREATE (id2932848)<-[:infrule]-(declareinitialexpr) CREATE (id2932848)-[:expr { local_id: '4757562'}]->(id9991999979) CREATE (id2932849:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2932849)<-[:linear_index {linear_index: '1.3}']-(id000004) CREATE (id2932849)<-[:infrule]-(declareinitialexpr) CREATE (id2932849)-[:expr { local_id: '1199299'}]->(id1314864131) CREATE (id2932850:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2932850)<-[:linear_index {linear_index: '1.6}']-(id000004) CREATE (id2932850)<-[:infrule]-(declareinitialexpr) CREATE (id2932850)-[:expr { local_id: '4857731'}]->(id9999999981) CREATE (id3737384:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3737384)<-[:linear_index {linear_index: '11}']-(id000004) CREATE (id3737384)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3737384)<-[:expr { local_id: '3738373'}]-(id1636453295) CREATE (id3737384)<-[:expr { local_id: '2962831'}]-(id3947269979) CREATE (id3737384)-[:expr { local_id: '4758592'}]->(id8494839423) CREATE (id3837471:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3837471)<-[:linear_index {linear_index: '7}']-(id000004) CREATE (id3837471)<-[:infrule]-(declareassumption) CREATE (id3837471)-[:expr { local_id: '3984852'}]->(id9919999981) CREATE (id3948573:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3948573)<-[:linear_index {linear_index: '9}']-(id000004) CREATE (id3948573)<-[:infrule]-(declareidentity) CREATE (id3948573)-[:expr { local_id: '1939485'}]->(id7575859295) CREATE (id3948584:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3948584)<-[:linear_index {linear_index: '12}']-(id000004) CREATE (id3948584)<-[:infrule]-(declarefinalexpr) CREATE (id3948584)<-[:expr { local_id: '4758592'}]-(id8494839423) CREATE (id4224853:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4224853)<-[:linear_index {linear_index: '4}']-(id000004) CREATE (id4224853)<-[:infrule]-(takecurlofbothsides) CREATE (id4224853)<-[:expr { local_id: '4757562'}]-(id9991999979) CREATE (id4224853)-[:expr { local_id: '2392932'}]->(id9291999979) CREATE (id4655746:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4655746)<-[:linear_index {linear_index: '10}']-(id000004) CREATE (id4655746)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id4655746)<-[:expr { local_id: '1939485'}]-(id7575859295) CREATE (id4655746)<-[:expr { local_id: '2837471'}]-(id7466829492) CREATE (id4655746)-[:expr { local_id: '3738373'}]->(id1636453295) CREATE (id5656372:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5656372)<-[:linear_index {linear_index: '8}']-(id000004) CREATE (id5656372)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5656372)<-[:expr { local_id: '4857731'}]-(id9999999981) CREATE (id5656372)<-[:expr { local_id: '3984852'}]-(id9919999981) CREATE (id5656372)-[:expr { local_id: '2837471'}]->(id7466829492) CREATE (000005:derivation { name: 'curlcurlidentity', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1393411:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1393411)<-[:linear_index {linear_index: '8}']-(id000005) CREATE (id1393411)<-[:infrule]-(replacesummationnotationwithvectornotation) CREATE (id1393411)<-[:expr { local_id: '3948472'}]-(id7575859310) CREATE (id1393411)-[:expr { local_id: '2109231'}]->(id7575859312) CREATE (id2339482:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2339482)<-[:linear_index {linear_index: '2}']-(id000005) CREATE (id2339482)<-[:infrule]-(replacecurlwithLeviCevitasummationcontravariant) CREATE (id2339482)<-[:expr { local_id: '1939485'}]-(id7575859295) CREATE (id2339482)-[:expr { local_id: '9485482'}]->(id7575859300) CREATE (id2930454:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2930454)<-[:linear_index {linear_index: '5}']-(id000005) CREATE (id2930454)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2930454)<-[:expr { local_id: '2934842'}]-(id7575859304) CREATE (id2930454)<-[:expr { local_id: '2941319'}]-(id7575859302) CREATE (id2930454)-[:expr { local_id: '3949292'}]->(id7575859306) CREATE (id3838233:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3838233)<-[:linear_index {linear_index: '7}']-(id000005) CREATE (id3838233)<-[:infrule]-(simplify) CREATE (id3838233)<-[:expr { local_id: '3844221'}]-(id7575859308) CREATE (id3838233)-[:expr { local_id: '3948472'}]->(id7575859310) CREATE (id3848292:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3848292)<-[:linear_index {linear_index: '6}']-(id000005) CREATE (id3848292)<-[:infrule]-(simplify) CREATE (id3848292)<-[:expr { local_id: '3949292'}]-(id7575859306) CREATE (id3848292)-[:expr { local_id: '3844221'}]->(id7575859308) CREATE (id3948552:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3948552)<-[:linear_index {linear_index: '3}']-(id000005) CREATE (id3948552)<-[:infrule]-(replacecurlwithLeviCevitasummationcontravariant) CREATE (id3948552)<-[:expr { local_id: '9485482'}]-(id7575859300) CREATE (id3948552)-[:expr { local_id: '2941319'}]->(id7575859302) CREATE (id3948572:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3948572)<-[:linear_index {linear_index: '1}']-(id000005) CREATE (id3948572)<-[:infrule]-(declareidentity) CREATE (id3948572)-[:expr { local_id: '1939485'}]->(id7575859295) CREATE (id3949211:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3949211)<-[:linear_index {linear_index: '9}']-(id000005) CREATE (id3949211)<-[:infrule]-(claimLHSequalsRHS) CREATE (id3949211)<-[:expr { local_id: '2109231'}]-(id7575859312) CREATE (id4295822:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4295822)<-[:linear_index {linear_index: '4}']-(id000005) CREATE (id4295822)<-[:infrule]-(declareidentity) CREATE (id4295822)-[:expr { local_id: '2934842'}]->(id7575859304) CREATE (000006:derivation { name: 'derivationofSchrodingerEquation', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1039774:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1039774)<-[:linear_index {linear_index: '14}']-(id000006) CREATE (id1039774)<-[:infrule]-(replacescalarwithvector) CREATE (id1039774)<-[:expr { local_id: '4948325'}]-(id9999999870) CREATE (id1039774)-[:expr { local_id: '2948487'}]->(id9999998870) CREATE (id1203100:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1203100)<-[:linear_index {linear_index: '17}']-(id000006) CREATE (id1203100)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id1203100)<-[:expr { local_id: '2100421'}]-(id3948574226) CREATE (id1203100)<-[:expr { local_id: '4499582'}]-(id9999999961) CREATE (id1203100)-[:expr { local_id: '1291313'}]->(id3948574228) CREATE (id1204921:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1204921)<-[:linear_index {linear_index: '1}']-(id000006) CREATE (id1204921)<-[:infrule]-(declareinitialexpr) CREATE (id1204921)-[:expr { local_id: '2934848'}]->(id3121513111) CREATE (id1204929:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1204929)<-[:linear_index {linear_index: '19}']-(id000006) CREATE (id1204929)<-[:infrule]-(declareinitialexpr) CREATE (id1204929)-[:expr { local_id: '1039948'}]->(id1029039903) CREATE (id1204945:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1204945)<-[:linear_index {linear_index: '11}']-(id000006) CREATE (id1204945)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id1204945)<-[:expr { local_id: '1203491'}]-(id1020394900) CREATE (id1204945)<-[:expr { local_id: '1039485'}]-(id3121234211) CREATE (id1204945)-[:expr { local_id: '2901049'}]->(id3121234212) CREATE (id1294844:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1294844)<-[:linear_index {linear_index: '3}']-(id000006) CREATE (id1294844)<-[:infrule]-(declareinitialexpr) CREATE (id1294844)-[:expr { local_id: '2949002'}]->(id9999999960) CREATE (id1294945:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1294945)<-[:linear_index {linear_index: '7}']-(id000006) CREATE (id1294945)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id1294945)<-[:expr { local_id: '2939402'}]-(id3147472131) CREATE (id1294945)<-[:expr { local_id: '3499522'}]-(id1020394902) CREATE (id1294945)-[:expr { local_id: '2949821'}]->(id4147472132) CREATE (id1341141:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1341141)<-[:linear_index {linear_index: '18}']-(id000006) CREATE (id1341141)<-[:infrule]-(simplify) CREATE (id1341141)<-[:expr { local_id: '1291313'}]-(id3948574228) CREATE (id1341141)-[:expr { local_id: '1305534'}]->(id3948574230) CREATE (id1347587:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1347587)<-[:linear_index {linear_index: '24}']-(id000006) CREATE (id1347587)<-[:infrule]-(partiallydifferentiatewithrespectto) CREATE (id1347587)<-[:expr { local_id: '1305534'}]-(id3948574230) CREATE (id1347587)<-[:expr { local_id: '6544644'}]-(id0006544644) CREATE (id1347587)-[:expr { local_id: '2364546'}]->(id3948574233) CREATE (id1395335:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1395335)<-[:linear_index {linear_index: '20}']-(id000006) CREATE (id1395335)<-[:infrule]-(declareinitialexpr) CREATE (id1395335)-[:expr { local_id: '1353583'}]->(id4298359835) CREATE (id1923945:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1923945)<-[:linear_index {linear_index: '15}']-(id000006) CREATE (id1923945)<-[:infrule]-(declareinitialexpr) CREATE (id1923945)-[:expr { local_id: '3940505'}]->(id3948574224) CREATE (id2030624:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2030624)<-[:linear_index {linear_index: '13}']-(id000006) CREATE (id2030624)<-[:infrule]-(dividebothsidesby) CREATE (id2030624)<-[:expr { local_id: '1039013'}]-(id9999999962) CREATE (id2030624)<-[:expr { local_id: '1304952'}]-(id0001304952) CREATE (id2030624)-[:expr { local_id: '4948325'}]->(id9999999870) CREATE (id2322434:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2322434)<-[:linear_index {linear_index: '22}']-(id000006) CREATE (id2322434)<-[:infrule]-(multiplyRHSbyunity) CREATE (id2322434)<-[:expr { local_id: '1353583'}]-(id4298359835) CREATE (id2322434)<-[:expr { local_id: '2342425'}]-(id0002342425) CREATE (id2322434)-[:expr { local_id: '2326309'}]->(id4298359845) CREATE (id2394495:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2394495)<-[:linear_index {linear_index: '32}']-(id000006) CREATE (id2394495)<-[:infrule]-(simplify) CREATE (id2394495)<-[:expr { local_id: '4938589'}]-(id4394958389) CREATE (id2394495)-[:expr { local_id: '1495034'}]->(id1648958381) CREATE (id2422434:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2422434)<-[:linear_index {linear_index: '21}']-(id000006) CREATE (id2422434)<-[:infrule]-(raisebothsidestopower) CREATE (id2422434)<-[:expr { local_id: '1039948'}]-(id1029039903) CREATE (id2422434)<-[:expr { local_id: '2239424'}]-(id0002239424) CREATE (id2422434)-[:expr { local_id: '1432042'}]->(id1029039904) CREATE (id2449858:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2449858)<-[:linear_index {linear_index: '23}']-(id000006) CREATE (id2449858)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2449858)<-[:expr { local_id: '1432042'}]-(id1029039904) CREATE (id2449858)<-[:expr { local_id: '2326309'}]-(id4298359845) CREATE (id2449858)-[:expr { local_id: '3576787'}]->(id4298359851) CREATE (id2454535:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2454535)<-[:linear_index {linear_index: '28}']-(id000006) CREATE (id2454535)<-[:infrule]-(applygradienttoscalarfunction) CREATE (id2454535)<-[:expr { local_id: '1305534'}]-(id3948574230) CREATE (id2454535)-[:expr { local_id: '5577584'}]->(id3948574230) CREATE (id2455452:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2455452)<-[:linear_index {linear_index: '37}']-(id000006) CREATE (id2455452)<-[:infrule]-(declareinitialexpr) CREATE (id2455452)-[:expr { local_id: '2344324'}]->(id1158485859) CREATE (id2464445:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2464445)<-[:linear_index {linear_index: '25}']-(id000006) CREATE (id2464445)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2464445)<-[:expr { local_id: '2364546'}]-(id3948574233) CREATE (id2464445)<-[:expr { local_id: '1305534'}]-(id3948574230) CREATE (id2464445)-[:expr { local_id: '5345567'}]->(id3948571256) CREATE (id2900428:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2900428)<-[:linear_index {linear_index: '10}']-(id000006) CREATE (id2900428)<-[:infrule]-(dividebothsidesby) CREATE (id2900428)<-[:expr { local_id: '2934848'}]-(id3121513111) CREATE (id2900428)<-[:expr { local_id: '1209482'}]-(id0001209482) CREATE (id2900428)-[:expr { local_id: '1039485'}]->(id3121234211) CREATE (id2919311:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2919311)<-[:linear_index {linear_index: '2}']-(id000006) CREATE (id2919311)<-[:infrule]-(declareinitialexpr) CREATE (id2919311)-[:expr { local_id: '9214650'}]->(id3131211131) CREATE (id2930492:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2930492)<-[:linear_index {linear_index: '8}']-(id000006) CREATE (id2930492)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2930492)<-[:expr { local_id: '2949002'}]-(id9999999960) CREATE (id2930492)<-[:expr { local_id: '2949821'}]-(id4147472132) CREATE (id2930492)-[:expr { local_id: '3741728'}]->(id9999999965) CREATE (id2938341:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2938341)<-[:linear_index {linear_index: '16}']-(id000006) CREATE (id2938341)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2938341)<-[:expr { local_id: '3940505'}]-(id3948574224) CREATE (id2938341)<-[:expr { local_id: '2948487'}]-(id9999998870) CREATE (id2938341)-[:expr { local_id: '2100421'}]->(id3948574226) CREATE (id2939400:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2939400)<-[:linear_index {linear_index: '12}']-(id000006) CREATE (id2939400)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2939400)<-[:expr { local_id: '2901049'}]-(id3121234212) CREATE (id2939400)<-[:expr { local_id: '2949002'}]-(id9999999960) CREATE (id2939400)-[:expr { local_id: '1039013'}]->(id9999999962) CREATE (id2954835:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2954835)<-[:linear_index {linear_index: '38}']-(id000006) CREATE (id2954835)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id2954835)<-[:expr { local_id: '2344324'}]-(id1158485859) CREATE (id2954835)<-[:expr { local_id: '1304924'}]-(id9958485859) CREATE (id2954835)-[:expr { local_id: '2456546'}]->(id2258485859) CREATE (id3294932:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3294932)<-[:linear_index {linear_index: '31}']-(id000006) CREATE (id3294932)<-[:infrule]-(applydivergence) CREATE (id3294932)<-[:expr { local_id: '5535257'}]-(id5985371230) CREATE (id3294932)-[:expr { local_id: '4938589'}]->(id4394958389) CREATE (id3454353:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3454353)<-[:linear_index {linear_index: '26}']-(id000006) CREATE (id3454353)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id3454353)<-[:expr { local_id: '3576787'}]-(id4298359851) CREATE (id3454353)<-[:expr { local_id: '5345567'}]-(id3948571256) CREATE (id3454353)-[:expr { local_id: '2495835'}]->(id4348571256) CREATE (id3919384:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3919384)<-[:linear_index {linear_index: '9}']-(id000006) CREATE (id3919384)<-[:infrule]-(dividebothsidesby) CREATE (id3919384)<-[:expr { local_id: '3741728'}]-(id9999999965) CREATE (id3919384)<-[:expr { local_id: '3949921'}]-(id0003949921) CREATE (id3919384)-[:expr { local_id: '4499582'}]->(id9999999961) CREATE (id3934948:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3934948)<-[:linear_index {linear_index: '5}']-(id000006) CREATE (id3934948)<-[:infrule]-(declareinitialexpr) CREATE (id3934948)-[:expr { local_id: '3499522'}]->(id1020394902) CREATE (id3949482:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3949482)<-[:linear_index {linear_index: '6}']-(id000006) CREATE (id3949482)<-[:infrule]-(dividebothsidesby) CREATE (id3949482)<-[:expr { local_id: '9214650'}]-(id3131211131) CREATE (id3949482)<-[:expr { local_id: '2940021'}]-(id0002940021) CREATE (id3949482)-[:expr { local_id: '2939402'}]->(id3147472131) CREATE (id4059592:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4059592)<-[:linear_index {linear_index: '33}']-(id000006) CREATE (id4059592)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id4059592)<-[:expr { local_id: '5535257'}]-(id5985371230) CREATE (id4059592)<-[:expr { local_id: '1495034'}]-(id1648958381) CREATE (id4059592)-[:expr { local_id: '1049553'}]->(id2648958382) CREATE (id4305953:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4305953)<-[:linear_index {linear_index: '34}']-(id000006) CREATE (id4305953)<-[:infrule]-(simplify) CREATE (id4305953)<-[:expr { local_id: '1049553'}]-(id2648958382) CREATE (id4305953)-[:expr { local_id: '4959593'}]->(id2395958385) CREATE (id4358635:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4358635)<-[:linear_index {linear_index: '27}']-(id000006) CREATE (id4358635)<-[:infrule]-(multiplybothsidesby) CREATE (id4358635)<-[:expr { local_id: '2495835'}]-(id4348571256) CREATE (id4358635)<-[:expr { local_id: '2436656'}]-(id0002436656) CREATE (id4358635)-[:expr { local_id: '3429538'}]->(id4341171256) CREATE (id4939459:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4939459)<-[:linear_index {linear_index: '35}']-(id000006) CREATE (id4939459)<-[:infrule]-(multiplybothsidesby) CREATE (id4939459)<-[:expr { local_id: '4959593'}]-(id2395958385) CREATE (id4939459)<-[:expr { local_id: '5938585'}]-(id0005938585) CREATE (id4939459)-[:expr { local_id: '4349493'}]->(id5868688585) CREATE (id5354635:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5354635)<-[:linear_index {linear_index: '30}']-(id000006) CREATE (id5354635)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id5354635)<-[:expr { local_id: '3454565'}]-(id4943571230) CREATE (id5354635)<-[:expr { local_id: '1305534'}]-(id3948574230) CREATE (id5354635)-[:expr { local_id: '5535257'}]->(id5985371230) CREATE (id5858694:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5858694)<-[:linear_index {linear_index: '29}']-(id000006) CREATE (id5858694)<-[:infrule]-(simplify) CREATE (id5858694)<-[:expr { local_id: '5577584'}]-(id3948574230) CREATE (id5858694)-[:expr { local_id: '3454565'}]->(id4943571230) CREATE (id6756574:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6756574)<-[:linear_index {linear_index: '39}']-(id000006) CREATE (id6756574)<-[:infrule]-(declarefinalexpr) CREATE (id6756574)<-[:expr { local_id: '2456546'}]-(id2258485859) CREATE (id9394834:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9394834)<-[:linear_index {linear_index: '36}']-(id000006) CREATE (id9394834)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id9394834)<-[:expr { local_id: '3429538'}]-(id4341171256) CREATE (id9394834)<-[:expr { local_id: '4349493'}]-(id5868688585) CREATE (id9394834)-[:expr { local_id: '1304924'}]->(id9958485859) CREATE (id9394842:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9394842)<-[:linear_index {linear_index: '4}']-(id000006) CREATE (id9394842)<-[:infrule]-(declareinitialexpr) CREATE (id9394842)-[:expr { local_id: '1203491'}]->(id1020394900) CREATE (000007:derivation { name: 'electricfieldwaveequationfromtimedependenttotimeindependent', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1002928:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1002928)<-[:linear_index {linear_index: '5}']-(id000007) CREATE (id1002928)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1002928)<-[:expr { local_id: '3994928'}]-(id9499428242) CREATE (id1002928)<-[:expr { local_id: '3839493'}]-(id9394939493) CREATE (id1002928)-[:expr { local_id: '1029393'}]->(id2029293929) CREATE (id2319391:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2319391)<-[:linear_index {linear_index: '6}']-(id000007) CREATE (id2319391)<-[:infrule]-(differentiatewithrespectto) CREATE (id2319391)<-[:expr { local_id: '1029393'}]-(id2029293929) CREATE (id2319391)<-[:expr { local_id: '3232241'}]-(id0003232242) CREATE (id2319391)-[:expr { local_id: '2939392'}]->(id4985825552) CREATE (id3568093:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3568093)<-[:linear_index {linear_index: '2}']-(id000007) CREATE (id3568093)<-[:infrule]-(declareinitialexpr) CREATE (id3568093)-[:expr { local_id: '9393848'}]->(id8572852424) CREATE (id4585829:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4585829)<-[:linear_index {linear_index: '3}']-(id000007) CREATE (id4585829)<-[:infrule]-(declareguesssolution) CREATE (id4585829)<-[:expr { local_id: '4758592'}]-(id8494839423) CREATE (id4585829)-[:expr { local_id: '3994928'}]->(id9499428242) CREATE (id4858282:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4858282)<-[:linear_index {linear_index: '4}']-(id000007) CREATE (id4858282)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id4858282)<-[:expr { local_id: '9393848'}]-(id8572852424) CREATE (id4858282)<-[:expr { local_id: '4758592'}]-(id8494839423) CREATE (id4858282)-[:expr { local_id: '3839493'}]->(id9394939493) CREATE (id4955966:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4955966)<-[:linear_index {linear_index: '7}']-(id000007) CREATE (id4955966)<-[:infrule]-(differentiatewithrespectto) CREATE (id4955966)<-[:expr { local_id: '2939392'}]-(id4985825552) CREATE (id4955966)<-[:expr { local_id: '3232242'}]-(id0003232242) CREATE (id4955966)-[:expr { local_id: '4958573'}]->(id1858578388) CREATE (id4958883:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4958883)<-[:linear_index {linear_index: '10}']-(id000007) CREATE (id4958883)<-[:infrule]-(simplify) CREATE (id4958883)<-[:expr { local_id: '9495903'}]-(id9485384858) CREATE (id4958883)-[:expr { local_id: '3949492'}]->(id3485475729) CREATE (id5495827:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5495827)<-[:linear_index {linear_index: '11}']-(id000007) CREATE (id5495827)<-[:infrule]-(declarefinalexpr) CREATE (id5495827)<-[:expr { local_id: '3949492'}]-(id3485475729) CREATE (id5839535:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5839535)<-[:linear_index {linear_index: '9}']-(id000007) CREATE (id5839535)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5839535)<-[:expr { local_id: '4958573'}]-(id1858578388) CREATE (id5839535)<-[:expr { local_id: '4949582'}]-(id4585828572) CREATE (id5839535)-[:expr { local_id: '9495903'}]->(id9485384858) CREATE (id7419980:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7419980)<-[:linear_index {linear_index: '1}']-(id000007) CREATE (id7419980)<-[:infrule]-(declareinitialexpr) CREATE (id7419980)-[:expr { local_id: '4758592'}]->(id8494839423) CREATE (id8485758:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8485758)<-[:linear_index {linear_index: '8}']-(id000007) CREATE (id8485758)<-[:infrule]-(declareinitialexpr) CREATE (id8485758)-[:expr { local_id: '4949582'}]->(id4585828572) CREATE (000008:derivation { name: 'frequencyrelations', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2303943:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2303943)<-[:linear_index {linear_index: '1}']-(id000008) CREATE (id2303943)<-[:infrule]-(declareinitialexpr) CREATE (id2303943)-[:expr { local_id: '3293094'}]->(id5900595848) CREATE (id2939482:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2939482)<-[:linear_index {linear_index: '6}']-(id000008) CREATE (id2939482)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2939482)<-[:expr { local_id: '8482459'}]-(id3131111133) CREATE (id2939482)<-[:expr { local_id: '3294004'}]-(id0404050504) CREATE (id2939482)-[:expr { local_id: '3993940'}]->(id1293923844) CREATE (id3049480:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3049480)<-[:linear_index {linear_index: '2}']-(id000008) CREATE (id3049480)<-[:infrule]-(declareinitialexpr) CREATE (id3049480)-[:expr { local_id: '3294004'}]->(id0404050504) CREATE (id3832748:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3832748)<-[:linear_index {linear_index: '5}']-(id000008) CREATE (id3832748)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id3832748)<-[:expr { local_id: '8374556'}]-(id3132131132) CREATE (id3832748)<-[:expr { local_id: '3293094'}]-(id5900595848) CREATE (id3832748)-[:expr { local_id: '8394853'}]->(id0934990943) CREATE (id6822583:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6822583)<-[:linear_index {linear_index: '8}']-(id000008) CREATE (id6822583)<-[:infrule]-(multiplybothsidesby) CREATE (id6822583)<-[:expr { local_id: '8482459'}]-(id3131111133) CREATE (id6822583)<-[:expr { local_id: '5749291'}]-(id0005749291) CREATE (id6822583)-[:expr { local_id: '8341200'}]->(id2131616531) CREATE (id8332941:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8332941)<-[:linear_index {linear_index: '3}']-(id000008) CREATE (id8332941)<-[:infrule]-(declareinitialexpr) CREATE (id8332941)-[:expr { local_id: '9214650'}]->(id3131211131) CREATE (id8345721:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8345721)<-[:linear_index {linear_index: '11}']-(id000008) CREATE (id8345721)<-[:infrule]-(declarefinalexpr) CREATE (id8345721)<-[:expr { local_id: '2934848'}]-(id3121513111) CREATE (id8946983:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8946983)<-[:linear_index {linear_index: '7}']-(id000008) CREATE (id8946983)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id8946983)<-[:expr { local_id: '3993940'}]-(id1293923844) CREATE (id8946983)<-[:expr { local_id: '8394853'}]-(id0934990943) CREATE (id8946983)-[:expr { local_id: '2934848'}]->(id3121513111) CREATE (id9103516:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9103516)<-[:linear_index {linear_index: '4}']-(id000008) CREATE (id9103516)<-[:infrule]-(declareinitialexpr) CREATE (id9103516)-[:expr { local_id: '8482459'}]->(id3131111133) CREATE (id9483715:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9483715)<-[:linear_index {linear_index: '9}']-(id000008) CREATE (id9483715)<-[:infrule]-(dividebothsidesby) CREATE (id9483715)<-[:expr { local_id: '8341200'}]-(id2131616531) CREATE (id9483715)<-[:expr { local_id: '8837284'}]-(id0008837284) CREATE (id9483715)-[:expr { local_id: '9380032'}]->(id2113211456) CREATE (id9483843:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9483843)<-[:linear_index {linear_index: '10}']-(id000008) CREATE (id9483843)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id9483843)<-[:expr { local_id: '9380032'}]-(id2113211456) CREATE (id9483843)<-[:expr { local_id: '9214650'}]-(id3131211131) CREATE (id9483843)-[:expr { local_id: '8374556'}]->(id3132131132) CREATE (000009:derivation { name: 'integrationbyparts', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2839422:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2839422)<-[:linear_index {linear_index: '5}']-(id000009) CREATE (id2839422)<-[:infrule]-(declarefinalexpr) CREATE (id2839422)<-[:expr { local_id: '3848329'}]-(id8489593964) CREATE (id4842942:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4842942)<-[:linear_index {linear_index: '2}']-(id000009) CREATE (id4842942)<-[:infrule]-(subtractXfrombothsides) CREATE (id4842942)<-[:expr { local_id: '3494854'}]-(id8489593958) CREATE (id4842942)<-[:expr { local_id: '9492929'}]-(id0009492929) CREATE (id4842942)-[:expr { local_id: '2938188'}]->(id8489593960) CREATE (id4848592:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4848592)<-[:linear_index {linear_index: '3}']-(id000009) CREATE (id4848592)<-[:infrule]-(swapLHSwithRHS) CREATE (id4848592)<-[:expr { local_id: '2938188'}]-(id8489593960) CREATE (id4848592)-[:expr { local_id: '2938190'}]->(id8489593962) CREATE (id4952082:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4952082)<-[:linear_index {linear_index: '1}']-(id000009) CREATE (id4952082)<-[:infrule]-(declareidentity) CREATE (id4952082)-[:expr { local_id: '3494854'}]->(id8489593958) CREATE (id8483953:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8483953)<-[:linear_index {linear_index: '4}']-(id000009) CREATE (id8483953)<-[:infrule]-(indefiniteintegration) CREATE (id8483953)<-[:expr { local_id: '2938190'}]-(id8489593962) CREATE (id8483953)-[:expr { local_id: '3848329'}]->(id8489593964) CREATE (000010:derivation { name: 'particleina1Dbox', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1003049:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1003049)<-[:linear_index {linear_index: '20}']-(id000010) CREATE (id1003049)<-[:infrule]-(changevariableXtoY) CREATE (id1003049)<-[:expr { local_id: '1231131'}]-(id9988949211) CREATE (id1003049)<-[:expr { local_id: '9484724'}]-(id0009484724) CREATE (id1003049)<-[:expr { local_id: '4934845'}]-(id0004934845) CREATE (id1003049)-[:expr { local_id: '0100404'}]->(id7575738420) CREATE (id1293948:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1293948)<-[:linear_index {linear_index: '32}']-(id000010) CREATE (id1293948)<-[:infrule]-(squarerootbothsides) CREATE (id1293948)<-[:expr { local_id: '1029384'}]-(id8485867742) CREATE (id1293948)-[:expr { local_id: '9394857'}]->(id9485747245) CREATE (id1293948)-[:expr { local_id: '9394858'}]->(id9485747246) CREATE (id1384011:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1384011)<-[:linear_index {linear_index: '2}']-(id000010) CREATE (id1384011)<-[:infrule]-(declareguesssolution) CREATE (id1384011)<-[:expr { local_id: '7572748'}]-(id5727578862) CREATE (id1384011)-[:expr { local_id: '7572118'}]->(id8582885111) CREATE (id1384935:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1384935)<-[:linear_index {linear_index: '33}']-(id000010) CREATE (id1384935)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1384935)<-[:expr { local_id: '9394857'}]-(id9485747245) CREATE (id1384935)<-[:expr { local_id: '3452131'}]-(id2944838499) CREATE (id1384935)-[:expr { local_id: '8474766'}]->(id9393939991) CREATE (id1911919:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1911919)<-[:linear_index {linear_index: '27}']-(id000010) CREATE (id1911919)<-[:infrule]-(changevariableXtoY) CREATE (id1911919)<-[:expr { local_id: '0021030'}]-(id5857434758) CREATE (id1911919)<-[:expr { local_id: '2929944'}]-(id0002929944) CREATE (id1911919)<-[:expr { local_id: '4948585'}]-(id0004948585) CREATE (id1911919)-[:expr { local_id: '9339495'}]->(id8575746378) CREATE (id2029394:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2029394)<-[:linear_index {linear_index: '38}']-(id000010) CREATE (id2029394)<-[:infrule]-(simplify) CREATE (id2029394)<-[:expr { local_id: '2838288'}]-(id8575748999) CREATE (id2029394)-[:expr { local_id: '8474762'}]->(id8485757728) CREATE (id3048100:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3048100)<-[:linear_index {linear_index: '26}']-(id000010) CREATE (id3048100)<-[:infrule]-(declareidentity) CREATE (id3048100)-[:expr { local_id: '0021030'}]->(id5857434758) CREATE (id3048800:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3048800)<-[:linear_index {linear_index: '24}']-(id000010) CREATE (id3048800)<-[:infrule]-(declareidentity) CREATE (id3048800)-[:expr { local_id: '3992939'}]->(id0948572140) CREATE (id3329831:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3329831)<-[:linear_index {linear_index: '28}']-(id000010) CREATE (id3329831)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3329831)<-[:expr { local_id: '9339495'}]-(id8575746378) CREATE (id3329831)<-[:expr { local_id: '0203020'}]-(id1202310110) CREATE (id3329831)-[:expr { local_id: '8584733'}]->(id1202312210) CREATE (id3847567:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3847567)<-[:linear_index {linear_index: '34}']-(id000010) CREATE (id3847567)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3847567)<-[:expr { local_id: '9394858'}]-(id9485747246) CREATE (id3847567)<-[:expr { local_id: '3452131'}]-(id2944838499) CREATE (id3847567)-[:expr { local_id: '8474765'}]->(id9393939992) CREATE (id3949284:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3949284)<-[:linear_index {linear_index: '23}']-(id000010) CREATE (id3949284)<-[:infrule]-(expandintegrand) CREATE (id3949284)<-[:expr { local_id: '0495054'}]-(id9858028950) CREATE (id3949284)-[:expr { local_id: '0203020'}]->(id1202310110) CREATE (id4434559:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4434559)<-[:linear_index {linear_index: '13}']-(id000010) CREATE (id4434559)<-[:infrule]-(normalizationcondition) CREATE (id4434559)-[:expr { local_id: '7575626'}]->(id1934748140) CREATE (id4455453:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4455453)<-[:linear_index {linear_index: '17}']-(id000010) CREATE (id4455453)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id4455453)<-[:expr { local_id: '3452131'}]-(id2944838499) CREATE (id4455453)<-[:expr { local_id: '0595847'}]-(id4857472413) CREATE (id4455453)-[:expr { local_id: '0495950'}]->(id0203024440) CREATE (id4485722:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4485722)<-[:linear_index {linear_index: '25}']-(id000010) CREATE (id4485722)<-[:infrule]-(changevariableXtoY) CREATE (id4485722)<-[:expr { local_id: '3992939'}]-(id0948572140) CREATE (id4485722)<-[:expr { local_id: '9485858'}]-(id0009485858) CREATE (id4485722)<-[:expr { local_id: '4831494'}]-(id0004831494) CREATE (id4485722)-[:expr { local_id: '4948377'}]->(id7564894985) CREATE (id4757567:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4757567)<-[:linear_index {linear_index: '15}']-(id000010) CREATE (id4757567)<-[:infrule]-(swapLHSwithRHS) CREATE (id4757567)<-[:expr { local_id: '7575626'}]-(id1934748140) CREATE (id4757567)-[:expr { local_id: '5577567'}]->(id8572657110) CREATE (id4757743:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4757743)<-[:linear_index {linear_index: '37}']-(id000010) CREATE (id4757743)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id4757743)<-[:expr { local_id: '7572748'}]-(id5727578862) CREATE (id4757743)<-[:expr { local_id: '7572118'}]-(id8582885111) CREATE (id4757743)-[:expr { local_id: '2838288'}]->(id8575748999) CREATE (id4948339:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4948339)<-[:linear_index {linear_index: '18}']-(id000010) CREATE (id4948339)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id4948339)<-[:expr { local_id: '3452132'}]-(id8849289982) CREATE (id4948339)<-[:expr { local_id: '0495950'}]-(id0203024440) CREATE (id4948339)-[:expr { local_id: '8478550'}]->(id8889444440) CREATE (id5751725:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5751725)<-[:linear_index {linear_index: '14}']-(id000010) CREATE (id5751725)<-[:infrule]-(conjugatefunctionX) CREATE (id5751725)<-[:expr { local_id: '3452131'}]-(id2944838499) CREATE (id5751725)<-[:expr { local_id: '9587738'}]-(id0009587738) CREATE (id5751725)-[:expr { local_id: '3452132'}]->(id8849289982) CREATE (id5859994:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5859994)<-[:linear_index {linear_index: '31}']-(id000010) CREATE (id5859994)<-[:infrule]-(multiplybothsidesby) CREATE (id5859994)<-[:expr { local_id: '9493949'}]-(id4857475848) CREATE (id5859994)<-[:expr { local_id: '9485857'}]-(id0009485857) CREATE (id5859994)-[:expr { local_id: '1029384'}]->(id8485867742) CREATE (id5940300:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5940300)<-[:linear_index {linear_index: '22}']-(id000010) CREATE (id5940300)<-[:infrule]-(dividebothsidesby) CREATE (id5940300)<-[:expr { local_id: '9485800'}]-(id8576785890) CREATE (id5940300)<-[:expr { local_id: '0040490'}]-(id0000040490) CREATE (id5940300)-[:expr { local_id: '0495054'}]->(id9858028950) CREATE (id7374289:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7374289)<-[:linear_index {linear_index: '40}']-(id000010) CREATE (id7374289)<-[:infrule]-(claimLHSequalsRHS) CREATE (id7374289)<-[:expr { local_id: '1214762'}]-(id8484544728) CREATE (id7455643:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7455643)<-[:linear_index {linear_index: '16}']-(id000010) CREATE (id7455643)<-[:infrule]-(expandmagnitudetoconjugate) CREATE (id7455643)<-[:expr { local_id: '5577567'}]-(id8572657110) CREATE (id7455643)<-[:expr { local_id: '9458842'}]-(id0009458842) CREATE (id7455643)-[:expr { local_id: '0595847'}]->(id4857472413) CREATE (id7474753:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7474753)<-[:linear_index {linear_index: '35}']-(id000010) CREATE (id7474753)<-[:infrule]-(declarefinalexpr) CREATE (id7474753)<-[:expr { local_id: '8474765'}]-(id9393939992) CREATE (id8373472:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8373472)<-[:linear_index {linear_index: '30}']-(id000010) CREATE (id8373472)<-[:infrule]-(simplify) CREATE (id8373472)<-[:expr { local_id: '0405049'}]-(id0439492440) CREATE (id8373472)-[:expr { local_id: '9493949'}]->(id4857475848) CREATE (id8485725:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8485725)<-[:linear_index {linear_index: '19}']-(id000010) CREATE (id8485725)<-[:infrule]-(declareidentity) CREATE (id8485725)-[:expr { local_id: '1231131'}]->(id9988949211) CREATE (id8485747:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8485747)<-[:linear_index {linear_index: '29}']-(id000010) CREATE (id8485747)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id8485747)<-[:expr { local_id: '4948377'}]-(id7564894985) CREATE (id8485747)<-[:expr { local_id: '8584733'}]-(id1202312210) CREATE (id8485747)-[:expr { local_id: '0405049'}]->(id0439492440) CREATE (id8571277:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8571277)<-[:linear_index {linear_index: '5}']-(id000010) CREATE (id8571277)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id8571277)<-[:expr { local_id: '8577781'}]-(id9585727710) CREATE (id8571277)<-[:expr { local_id: '7572118'}]-(id8582885111) CREATE (id8571277)-[:expr { local_id: '7547581'}]->(id8577275751) CREATE (id8572265:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8572265)<-[:linear_index {linear_index: '7}']-(id000010) CREATE (id8572265)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id8572265)<-[:expr { local_id: '7572859'}]-(id1293913110) CREATE (id8572265)<-[:expr { local_id: '7572118'}]-(id8582885111) CREATE (id8572265)-[:expr { local_id: '7562671'}]->(id9059289981) CREATE (id8572771:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8572771)<-[:linear_index {linear_index: '3}']-(id000010) CREATE (id8572771)<-[:infrule]-(boundaryconditionforexpr) CREATE (id8572771)<-[:expr { local_id: '7572748'}]-(id5727578862) CREATE (id8572771)-[:expr { local_id: '8577781'}]->(id9585727710) CREATE (id8572778:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8572778)<-[:linear_index {linear_index: '4}']-(id000010) CREATE (id8572778)<-[:infrule]-(boundaryconditionforexpr) CREATE (id8572778)<-[:expr { local_id: '7572748'}]-(id5727578862) CREATE (id8572778)-[:expr { local_id: '8585727'}]->(id9495857278) CREATE (id8575627:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8575627)<-[:linear_index {linear_index: '10}']-(id000010) CREATE (id8575627)<-[:infrule]-(expr1istrueunderconditionexpr2) CREATE (id8575627)<-[:expr { local_id: '8577672'}]-(id1020010291) CREATE (id8575627)<-[:expr { local_id: '8577711'}]-(id1857710291) CREATE (id8575627)-[:expr { local_id: '9847600'}]->(id1010923823) CREATE (id8575717:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8575717)<-[:linear_index {linear_index: '9}']-(id000010) CREATE (id8575717)<-[:infrule]-(declareidentity) CREATE (id8575717)-[:expr { local_id: '8577711'}]->(id1857710291) CREATE (id8575761:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8575761)<-[:linear_index {linear_index: '12}']-(id000010) CREATE (id8575761)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id8575761)<-[:expr { local_id: '9495882'}]-(id1858772113) CREATE (id8575761)<-[:expr { local_id: '7562671'}]-(id9059289981) CREATE (id8575761)-[:expr { local_id: '3452131'}]->(id2944838499) CREATE (id8576571:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8576571)<-[:linear_index {linear_index: '6}']-(id000010) CREATE (id8576571)<-[:infrule]-(simplify) CREATE (id8576571)<-[:expr { local_id: '7547581'}]-(id8577275751) CREATE (id8576571)-[:expr { local_id: '7572859'}]->(id1293913110) CREATE (id8576627:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8576627)<-[:linear_index {linear_index: '1}']-(id000010) CREATE (id8576627)<-[:infrule]-(declareinitialexpr) CREATE (id8576627)-[:expr { local_id: '7572748'}]->(id5727578862) CREATE (id8576741:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8576741)<-[:linear_index {linear_index: '21}']-(id000010) CREATE (id8576741)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id8576741)<-[:expr { local_id: '0100404'}]-(id7575738420) CREATE (id8576741)<-[:expr { local_id: '8478550'}]-(id8889444440) CREATE (id8576741)-[:expr { local_id: '9485800'}]->(id8576785890) CREATE (id9114413:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9114413)<-[:linear_index {linear_index: '11}']-(id000010) CREATE (id9114413)<-[:infrule]-(dividebothsidesby) CREATE (id9114413)<-[:expr { local_id: '9847600'}]-(id1010923823) CREATE (id9114413)<-[:expr { local_id: '1334112'}]-(id0001334112) CREATE (id9114413)-[:expr { local_id: '9495882'}]->(id1858772113) CREATE (id9394948:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9394948)<-[:linear_index {linear_index: '39}']-(id000010) CREATE (id9394948)<-[:infrule]-(simplify) CREATE (id9394948)<-[:expr { local_id: '8474762'}]-(id8485757728) CREATE (id9394948)-[:expr { local_id: '1214762'}]->(id8484544728) CREATE (id9686782:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9686782)<-[:linear_index {linear_index: '8}']-(id000010) CREATE (id9686782)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id9686782)<-[:expr { local_id: '8585727'}]-(id9495857278) CREATE (id9686782)<-[:expr { local_id: '7562671'}]-(id9059289981) CREATE (id9686782)-[:expr { local_id: '8577672'}]->(id1020010291) CREATE (000011:derivation { name: 'quadraticequationderivation', notes: 'https://en.wikipedia.org/wiki/Quadratic_formula#Derivations_of_the_formula', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2200910:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2200910)<-[:linear_index {linear_index: '10}']-(id000011) CREATE (id2200910)<-[:infrule]-(subtractXfrombothsides) CREATE (id2200910)<-[:expr { local_id: '6608123'}]-(id5982958249) CREATE (id2200910)<-[:expr { local_id: '2838490'}]-(id0002838490) CREATE (id2200910)-[:expr { local_id: '4433112'}]->(id9582958293) CREATE (id2200911:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2200911)<-[:linear_index {linear_index: '10.5}']-(id000011) CREATE (id2200911)<-[:infrule]-(subtractXfrombothsides) CREATE (id2200911)<-[:expr { local_id: '6608102'}]-(id9582958294) CREATE (id2200911)<-[:expr { local_id: '2449291'}]-(id0002449291) CREATE (id2200911)-[:expr { local_id: '2657355'}]->(id5982958248) CREATE (id2211910:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2211910)<-[:linear_index {linear_index: '11}']-(id000011) CREATE (id2211910)<-[:infrule]-(simplify) CREATE (id2211910)<-[:expr { local_id: '2657355'}]-(id5982958248) CREATE (id2211910)-[:expr { local_id: '8811221'}]->(id9999999968) CREATE (id2211911:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2211911)<-[:linear_index {linear_index: '11.5}']-(id000011) CREATE (id2211911)<-[:infrule]-(simplify) CREATE (id2211911)<-[:expr { local_id: '4433112'}]-(id9582958293) CREATE (id2211911)-[:expr { local_id: '8761200'}]->(id9999999969) CREATE (id2500423:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2500423)<-[:linear_index {linear_index: '5}']-(id000011) CREATE (id2500423)<-[:infrule]-(addXtobothsides) CREATE (id2500423)<-[:expr { local_id: '1212129'}]-(id5938459282) CREATE (id2500423)<-[:expr { local_id: '4307451'}]-(id0004307451) CREATE (id2500423)-[:expr { local_id: '1120000'}]->(id5928292841) CREATE (id5829110:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5829110)<-[:linear_index {linear_index: '4}']-(id000011) CREATE (id5829110)<-[:infrule]-(subtractXfrombothsides) CREATE (id5829110)<-[:expr { local_id: '7777621'}]-(id5958392859) CREATE (id5829110)<-[:expr { local_id: '6644853'}]-(id0006644853) CREATE (id5829110)-[:expr { local_id: '1212129'}]->(id5938459282) CREATE (id7487443:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7487443)<-[:linear_index {linear_index: '9}']-(id000011) CREATE (id7487443)<-[:infrule]-(squarerootbothsides) CREATE (id7487443)<-[:expr { local_id: '2985412'}]-(id9385938295) CREATE (id7487443)-[:expr { local_id: '6608123'}]->(id5982958249) CREATE (id7487443)-[:expr { local_id: '6608102'}]->(id9582958294) CREATE (id7777777:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7777777)<-[:linear_index {linear_index: '8}']-(id000011) CREATE (id7777777)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id7777777)<-[:expr { local_id: '1120000'}]-(id5928292841) CREATE (id7777777)<-[:expr { local_id: '1734000'}]-(id5959282914) CREATE (id7777777)-[:expr { local_id: '2985412'}]->(id9385938295) CREATE (id7996484:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7996484)<-[:linear_index {linear_index: '7}']-(id000011) CREATE (id7996484)<-[:infrule]-(simplify) CREATE (id7996484)<-[:expr { local_id: '1239010'}]-(id5928285821) CREATE (id7996484)-[:expr { local_id: '1734000'}]->(id5959282914) CREATE (id8321038:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8321038)<-[:linear_index {linear_index: '6}']-(id000011) CREATE (id8321038)<-[:infrule]-(changevariableXtoY) CREATE (id8321038)<-[:expr { local_id: '9091270'}]-(id8582954722) CREATE (id8321038)<-[:expr { local_id: '4858592'}]-(id0004858592) CREATE (id8321038)<-[:expr { local_id: '0999900'}]-(id0000999900) CREATE (id8321038)-[:expr { local_id: '1239010'}]->(id5928285821) CREATE (id8359402:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8359402)<-[:linear_index {linear_index: '14}']-(id000011) CREATE (id8359402)<-[:infrule]-(declarefinalexpr) CREATE (id8359402)<-[:expr { local_id: '8811221'}]-(id9999999968) CREATE (id8359403:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8359403)<-[:linear_index {linear_index: '15}']-(id000011) CREATE (id8359403)<-[:infrule]-(declarefinalexpr) CREATE (id8359403)<-[:expr { local_id: '8761200'}]-(id9999999969) CREATE (id8492932:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8492932)<-[:linear_index {linear_index: '3}']-(id000011) CREATE (id8492932)<-[:infrule]-(dividebothsidesby) CREATE (id8492932)<-[:expr { local_id: '8882098'}]-(id9285928292) CREATE (id8492932)<-[:expr { local_id: '2424922'}]-(id0002424922) CREATE (id8492932)-[:expr { local_id: '7777621'}]->(id5958392859) CREATE (id8494551:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8494551)<-[:linear_index {linear_index: '1}']-(id000011) CREATE (id8494551)<-[:infrule]-(declareinitialexpr) CREATE (id8494551)-[:expr { local_id: '8882098'}]->(id9285928292) CREATE (id8494552:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8494552)<-[:linear_index {linear_index: '7.5}']-(id000011) CREATE (id8494552)<-[:infrule]-(declareinitialexpr) CREATE (id8494552)-[:expr { local_id: '9091270'}]->(id8582954722) CREATE (000012:derivation { name: 'quantumbasicsHermitianoperatorshaverealvaluedobservables', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1294984:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1294984)<-[:linear_index {linear_index: '4}']-(id000012) CREATE (id1294984)<-[:infrule]-(declareassumption) CREATE (id1294984)-[:expr { local_id: '2484892'}]->(id9294858532) CREATE (id2394942:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2394942)<-[:linear_index {linear_index: '3}']-(id000012) CREATE (id2394942)<-[:infrule]-(distributeconjugatetransposetofactors) CREATE (id2394942)<-[:expr { local_id: '2495954'}]-(id2394935835) CREATE (id2394942)-[:expr { local_id: '2390094'}]->(id1010393913) CREATE (id2485909:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2485909)<-[:linear_index {linear_index: '5}']-(id000012) CREATE (id2485909)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2485909)<-[:expr { local_id: '2484892'}]-(id9294858532) CREATE (id2485909)<-[:expr { local_id: '2390094'}]-(id1010393913) CREATE (id2485909)-[:expr { local_id: '2494040'}]->(id4948934890) CREATE (id2490098:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2490098)<-[:linear_index {linear_index: '6}']-(id000012) CREATE (id2490098)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id2490098)<-[:expr { local_id: '2494040'}]-(id4948934890) CREATE (id2490098)<-[:expr { local_id: '3402919'}]-(id9999999975) CREATE (id2490098)-[:expr { local_id: '4930585'}]->(id2848934890) CREATE (id2939493:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2939493)<-[:linear_index {linear_index: '7}']-(id000012) CREATE (id2939493)<-[:infrule]-(declarefinalexpr) CREATE (id2939493)<-[:expr { local_id: '4930585'}]-(id2848934890) CREATE (id3403595:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3403595)<-[:linear_index {linear_index: '1}']-(id000012) CREATE (id3403595)<-[:infrule]-(declareinitialexpr) CREATE (id3403595)-[:expr { local_id: '3402919'}]->(id9999999975) CREATE (id9538385:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9538385)<-[:linear_index {linear_index: '2}']-(id000012) CREATE (id9538385)<-[:infrule]-(conjugatetransposebothsides) CREATE (id9538385)<-[:expr { local_id: '3402919'}]-(id9999999975) CREATE (id9538385)-[:expr { local_id: '2495954'}]->(id2394935835) CREATE (000013:derivation { name: 'quantumbasicsorthogonality', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1301442:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1301442)<-[:linear_index {linear_index: '3}']-(id000013) CREATE (id1301442)<-[:infrule]-(applyoperatortobra) CREATE (id1301442)<-[:expr { local_id: '3849595'}]-(id9596004948) CREATE (id1301442)-[:expr { local_id: '4349300'}]->(id1395858355) CREATE (id2304934:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2304934)<-[:linear_index {linear_index: '4}']-(id000013) CREATE (id2304934)<-[:infrule]-(simplify) CREATE (id2304934)<-[:expr { local_id: '4940359'}]-(id1010393944) CREATE (id2304934)-[:expr { local_id: '2409402'}]->(id2394240499) CREATE (id2384852:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2384852)<-[:linear_index {linear_index: '9}']-(id000013) CREATE (id2384852)<-[:infrule]-(declarefinalexpr) CREATE (id2384852)<-[:expr { local_id: '3494855'}]-(id2394935831) CREATE (id2455366:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2455366)<-[:linear_index {linear_index: '1}']-(id000013) CREATE (id2455366)<-[:infrule]-(declareinitialexpr) CREATE (id2455366)-[:expr { local_id: '3849595'}]->(id9596004948) CREATE (id3848591:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3848591)<-[:linear_index {linear_index: '2}']-(id000013) CREATE (id3848591)<-[:infrule]-(applyoperatortoket) CREATE (id3848591)<-[:expr { local_id: '3849595'}]-(id9596004948) CREATE (id3848591)-[:expr { local_id: '4940359'}]->(id1010393944) CREATE (id4838499:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4838499)<-[:linear_index {linear_index: '7}']-(id000013) CREATE (id4838499)<-[:infrule]-(subtractXfrombothsides) CREATE (id4838499)<-[:expr { local_id: '3495045'}]-(id1203938249) CREATE (id4838499)<-[:expr { local_id: '5395034'}]-(id0005395034) CREATE (id4838499)-[:expr { local_id: '4939583'}]->(id3924948349) CREATE (id4938400:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4938400)<-[:linear_index {linear_index: '5}']-(id000013) CREATE (id4938400)<-[:infrule]-(simplify) CREATE (id4938400)<-[:expr { local_id: '4349300'}]-(id1395858355) CREATE (id4938400)-[:expr { local_id: '4934893'}]->(id3943939590) CREATE (id9878900:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9878900)<-[:linear_index {linear_index: '6}']-(id000013) CREATE (id9878900)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id9878900)<-[:expr { local_id: '2409402'}]-(id2394240499) CREATE (id9878900)<-[:expr { local_id: '4934893'}]-(id3943939590) CREATE (id9878900)-[:expr { local_id: '3495045'}]->(id1203938249) CREATE (id9888730:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9888730)<-[:linear_index {linear_index: '8}']-(id000013) CREATE (id9888730)<-[:infrule]-(combineliketerms) CREATE (id9888730)<-[:expr { local_id: '4939583'}]-(id3924948349) CREATE (id9888730)-[:expr { local_id: '3494855'}]->(id2394935831) CREATE (000014:derivation { name: 'variancerelation', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2004989:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2004989)<-[:linear_index {linear_index: '1}']-(id000014) CREATE (id2004989)<-[:infrule]-(declareidentity) CREATE (id2004989)-[:expr { local_id: '3493498'}]->(id3585845894) CREATE (id2349059:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2349059)<-[:linear_index {linear_index: '2}']-(id000014) CREATE (id2349059)<-[:infrule]-(simplify) CREATE (id2349059)<-[:expr { local_id: '3493498'}]-(id3585845894) CREATE (id2349059)-[:expr { local_id: '5049530'}]->(id8399484849) CREATE (id2390498:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2390498)<-[:linear_index {linear_index: '3}']-(id000014) CREATE (id2390498)<-[:infrule]-(simplify) CREATE (id2390498)<-[:expr { local_id: '5049530'}]-(id8399484849) CREATE (id2390498)-[:expr { local_id: '6757584'}]->(id2404934990) CREATE (id3848494:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3848494)<-[:linear_index {linear_index: '4}']-(id000014) CREATE (id3848494)<-[:infrule]-(simplify) CREATE (id3848494)<-[:expr { local_id: '6757584'}]-(id2404934990) CREATE (id3848494)-[:expr { local_id: '3294824'}]->(id4949359835) CREATE (id4948384:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4948384)<-[:linear_index {linear_index: '5}']-(id000014) CREATE (id4948384)<-[:infrule]-(simplify) CREATE (id4948384)<-[:expr { local_id: '3294824'}]-(id4949359835) CREATE (id4948384)-[:expr { local_id: '5949484'}]->(id2494533900) CREATE (id4948955:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4948955)<-[:linear_index {linear_index: '6}']-(id000014) CREATE (id4948955)<-[:infrule]-(claimLHSequalsRHS) CREATE (id4948955)<-[:expr { local_id: '5949484'}]-(id2494533900) CREATE (000015:derivation { name: 'Comptonsequationforscattering', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3445641:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3445641)<-[:linear_index {linear_index: '2}']-(id000015) CREATE (id3445641)<-[:infrule]-(declareinitialexpr) CREATE (id3445641)-[:expr { local_id: '2840008'}]->(id8257621077) CREATE (id3667395:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3667395)<-[:linear_index {linear_index: '5}']-(id000015) CREATE (id3667395)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3667395)<-[:expr { local_id: '2491904'}]-(id3951205425) CREATE (id3667395)<-[:expr { local_id: '1209604'}]-(id8311458118) CREATE (id3667395)-[:expr { local_id: '5610925'}]->(id8139187332) CREATE (id3871228:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3871228)<-[:linear_index {linear_index: '7}']-(id000015) CREATE (id3871228)<-[:infrule]-(swapLHSwithRHS) CREATE (id3871228)<-[:expr { local_id: '4068150'}]-(id5530148480) CREATE (id3871228)-[:expr { local_id: '4200334'}]->(id7917051060) CREATE (id4733986:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4733986)<-[:linear_index {linear_index: '3}']-(id000015) CREATE (id4733986)<-[:infrule]-(declareinitialexpr) CREATE (id4733986)-[:expr { local_id: '1209604'}]->(id8311458118) CREATE (id4738354:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4738354)<-[:linear_index {linear_index: '8}']-(id000015) CREATE (id4738354)<-[:infrule]-(multiplyexpr1byexpr2) CREATE (id4738354)<-[:expr { local_id: '4200334'}]-(id7917051060) CREATE (id4738354)<-[:expr { local_id: '4200334'}]-(id7917051060) CREATE (id4738354)-[:expr { local_id: '4218805'}]->(id6742123016) CREATE (id7952658:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7952658)<-[:linear_index {linear_index: '6}']-(id000015) CREATE (id7952658)<-[:infrule]-(subtractXfrombothsides) CREATE (id7952658)<-[:expr { local_id: '5610925'}]-(id8139187332) CREATE (id7952658)<-[:expr { local_id: '2338514'}]-(id0002338514) CREATE (id7952658)-[:expr { local_id: '4068150'}]->(id5530148480) CREATE (id7958085:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7958085)<-[:linear_index {linear_index: '4}']-(id000015) CREATE (id7958085)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7958085)<-[:expr { local_id: '2840008'}]-(id8257621077) CREATE (id7958085)<-[:expr { local_id: '4978059'}]-(id1638282134) CREATE (id7958085)-[:expr { local_id: '2491904'}]->(id3951205425) CREATE (id8668018:step { creation_date: '2020-04-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8668018)<-[:linear_index {linear_index: '1}']-(id000015) CREATE (id8668018)<-[:infrule]-(declareinitialexpr) CREATE (id8668018)-[:expr { local_id: '4978059'}]->(id1638282134) CREATE (000016:derivation { name: 'identitysin2x2sinxcosxusingEulersequation', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1541045:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1541045)<-[:linear_index {linear_index: '4}']-(id000016) CREATE (id1541045)<-[:infrule]-(multiplyexpr1byexpr2) CREATE (id1541045)<-[:expr { local_id: '6060683'}]-(id2103023049) CREATE (id1541045)<-[:expr { local_id: '5011637'}]-(id4585932229) CREATE (id1541045)-[:expr { local_id: '6350246'}]->(id3470587782) CREATE (id2750343:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2750343)<-[:linear_index {linear_index: '8}']-(id000016) CREATE (id2750343)<-[:infrule]-(RHSofexpr1equalsRHSofexpr2) CREATE (id2750343)<-[:expr { local_id: '6229292'}]-(id9180861128) CREATE (id2750343)<-[:expr { local_id: '1414263'}]-(id8483686863) CREATE (id2750343)-[:expr { local_id: '7647794'}]->(id2405307372) CREATE (id5887774:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5887774)<-[:linear_index {linear_index: '1}']-(id000016) CREATE (id5887774)<-[:infrule]-(declareinitialexpr) CREATE (id5887774)-[:expr { local_id: '6060683'}]->(id2103023049) CREATE (id6131891:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6131891)<-[:linear_index {linear_index: '3}']-(id000016) CREATE (id6131891)<-[:infrule]-(declareinitialexpr) CREATE (id6131891)-[:expr { local_id: '5011637'}]->(id4585932229) CREATE (id6240603:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6240603)<-[:linear_index {linear_index: '2}']-(id000016) CREATE (id6240603)<-[:infrule]-(changevariableXtoY) CREATE (id6240603)<-[:expr { local_id: '6060683'}]-(id2103023049) CREATE (id6240603)<-[:expr { local_id: '2597988'}]-(id4961662865) CREATE (id6240603)<-[:expr { local_id: '7992949'}]-(id9110536742) CREATE (id6240603)-[:expr { local_id: '1414263'}]->(id8483686863) CREATE (id6790653:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6790653)<-[:linear_index {linear_index: '7}']-(id000016) CREATE (id6790653)<-[:infrule]-(simplify) CREATE (id6790653)<-[:expr { local_id: '5714636'}]-(id8699789241) CREATE (id6790653)-[:expr { local_id: '6229292'}]->(id9180861128) CREATE (id7763037:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7763037)<-[:linear_index {linear_index: '9}']-(id000016) CREATE (id7763037)<-[:infrule]-(declarefinalexpr) CREATE (id7763037)<-[:expr { local_id: '7647794'}]-(id2405307372) CREATE (id8636739:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8636739)<-[:linear_index {linear_index: '5}']-(id000016) CREATE (id8636739)<-[:infrule]-(multiplybothsidesby) CREATE (id8636739)<-[:expr { local_id: '6350246'}]-(id3470587782) CREATE (id8636739)<-[:expr { local_id: '8830175'}]-(id8642992037) CREATE (id8636739)-[:expr { local_id: '7867574'}]->(id9894826550) CREATE (id9916897:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9916897)<-[:linear_index {linear_index: '6}']-(id000016) CREATE (id9916897)<-[:infrule]-(simplify) CREATE (id9916897)<-[:expr { local_id: '7867574'}]-(id9894826550) CREATE (id9916897)-[:expr { local_id: '5714636'}]->(id8699789241) CREATE (000017:derivation { name: 'Eulerequationtoeipi10', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1530591:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1530591)<-[:linear_index {linear_index: '3}']-(id000017) CREATE (id1530591)<-[:infrule]-(simplify) CREATE (id1530591)<-[:expr { local_id: '1148677'}]-(id8332931442) CREATE (id1530591)-[:expr { local_id: '8524301'}]->(id6885625907) CREATE (id5103914:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5103914)<-[:linear_index {linear_index: '2}']-(id000017) CREATE (id5103914)<-[:infrule]-(changevariableXtoY) CREATE (id5103914)<-[:expr { local_id: '1580045'}]-(id4938429483) CREATE (id5103914)<-[:expr { local_id: '9050111'}]-(id3268645065) CREATE (id5103914)<-[:expr { local_id: '9850626'}]-(id9350663581) CREATE (id5103914)-[:expr { local_id: '1148677'}]->(id8332931442) CREATE (id6831079:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6831079)<-[:linear_index {linear_index: '1}']-(id000017) CREATE (id6831079)<-[:infrule]-(declareinitialexpr) CREATE (id6831079)-[:expr { local_id: '1580045'}]->(id4938429483) CREATE (id8465659:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8465659)<-[:linear_index {linear_index: '5}']-(id000017) CREATE (id8465659)<-[:infrule]-(addXtobothsides) CREATE (id8465659)<-[:expr { local_id: '9610540'}]-(id3331824625) CREATE (id8465659)<-[:expr { local_id: '2097240'}]-(id4901237716) CREATE (id8465659)-[:expr { local_id: '9472905'}]->(id2501591100) CREATE (id8755752:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8755752)<-[:linear_index {linear_index: '4}']-(id000017) CREATE (id8755752)<-[:infrule]-(simplify) CREATE (id8755752)<-[:expr { local_id: '8524301'}]-(id6885625907) CREATE (id8755752)-[:expr { local_id: '9610540'}]->(id3331824625) CREATE (id9932332:step { creation_date: '2020-04-19', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9932332)<-[:linear_index {linear_index: '6}']-(id000017) CREATE (id9932332)<-[:infrule]-(declarefinalexpr) CREATE (id9932332)<-[:expr { local_id: '9472905'}]-(id2501591100) CREATE (000018:derivation { name: 'timeinvariantforceconservesenergy', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1466499:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1466499)<-[:linear_index {linear_index: '27}']-(id000018) CREATE (id1466499)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id1466499)<-[:expr { local_id: '6154610'}]-(id9337785146) CREATE (id1466499)<-[:expr { local_id: '7539016'}]-(id7267155233) CREATE (id1466499)-[:expr { local_id: '9383749'}]->(id4872970974) CREATE (id1560617:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1560617)<-[:linear_index {linear_index: '14}']-(id000018) CREATE (id1560617)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id1560617)<-[:expr { local_id: '8696678'}]-(id4648451961) CREATE (id1560617)<-[:expr { local_id: '3040361'}]-(id4270680309) CREATE (id1560617)-[:expr { local_id: '6246951'}]->(id9356924046) CREATE (id1702334:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1702334)<-[:linear_index {linear_index: '18}']-(id000018) CREATE (id1702334)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id1702334)<-[:expr { local_id: '6973462'}]-(id2857430695) CREATE (id1702334)<-[:expr { local_id: '6733685'}]-(id7735737409) CREATE (id1702334)-[:expr { local_id: '4876963'}]->(id4784793837) CREATE (id1882970:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1882970)<-[:linear_index {linear_index: '31}']-(id000018) CREATE (id1882970)<-[:infrule]-(simplify) CREATE (id1882970)<-[:expr { local_id: '5300304'}]-(id1772416655) CREATE (id1882970)-[:expr { local_id: '6495233'}]->(id1809909100) CREATE (id2343637:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2343637)<-[:linear_index {linear_index: '32}']-(id000018) CREATE (id2343637)<-[:infrule]-(multiplybothsidesby) CREATE (id2343637)<-[:expr { local_id: '6495233'}]-(id1809909100) CREATE (id2343637)<-[:expr { local_id: '8639236'}]-(id5778176146) CREATE (id2343637)-[:expr { local_id: '2075807'}]->(id3806977900) CREATE (id2410249:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2410249)<-[:linear_index {linear_index: '6}']-(id000018) CREATE (id2410249)<-[:infrule]-(declareinitialexpr) CREATE (id2410249)-[:expr { local_id: '6559987'}]->(id8357234146) CREATE (id3258083:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3258083)<-[:linear_index {linear_index: '17}']-(id000018) CREATE (id3258083)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id3258083)<-[:expr { local_id: '3484339'}]-(id9397152918) CREATE (id3258083)<-[:expr { local_id: '6246951'}]-(id9356924046) CREATE (id3258083)-[:expr { local_id: '6733685'}]->(id7735737409) CREATE (id4729245:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4729245)<-[:linear_index {linear_index: '29}']-(id000018) CREATE (id4729245)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id4729245)<-[:expr { local_id: '9383749'}]-(id4872970974) CREATE (id4729245)<-[:expr { local_id: '2692856'}]-(id2770069250) CREATE (id4729245)-[:expr { local_id: '9714818'}]->(id3591237106) CREATE (id4803359:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4803359)<-[:linear_index {linear_index: '7}']-(id000018) CREATE (id4803359)<-[:infrule]-(changetwovariablesinexpr) CREATE (id4803359)<-[:expr { local_id: '6559987'}]-(id8357234146) CREATE (id4803359)<-[:expr { local_id: '7874068'}]-(id6383056612) CREATE (id4803359)<-[:expr { local_id: '5938957'}]-(id6838659900) CREATE (id4803359)<-[:expr { local_id: '3735003'}]-(id9305761407) CREATE (id4803359)<-[:expr { local_id: '6377535'}]-(id5011888122) CREATE (id4803359)-[:expr { local_id: '6632540'}]->(id7676652285) CREATE (id4909770:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4909770)<-[:linear_index {linear_index: '11}']-(id000018) CREATE (id4909770)<-[:infrule]-(dividebothsidesby) CREATE (id4909770)<-[:expr { local_id: '9602854'}]-(id5733146966) CREATE (id4909770)<-[:expr { local_id: '1633402'}]-(id6554292307) CREATE (id4909770)-[:expr { local_id: '3040361'}]->(id4270680309) CREATE (id5181988:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5181988)<-[:linear_index {linear_index: '1}']-(id000018) CREATE (id5181988)<-[:infrule]-(declareinitialexpr) CREATE (id5181988)-[:expr { local_id: '8844119'}]->(id5136652623) CREATE (id5590554:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5590554)<-[:linear_index {linear_index: '2}']-(id000018) CREATE (id5590554)<-[:infrule]-(changethreevariablesinexpr) CREATE (id5590554)<-[:expr { local_id: '8844119'}]-(id5136652623) CREATE (id5590554)<-[:expr { local_id: '9398614'}]-(id1258245373) CREATE (id5590554)<-[:expr { local_id: '2436173'}]-(id2344320475) CREATE (id5590554)<-[:expr { local_id: '7874067'}]-(id6383056612) CREATE (id5590554)<-[:expr { local_id: '1353291'}]-(id7939947931) CREATE (id5590554)<-[:expr { local_id: '7552472'}]-(id5075406409) CREATE (id5590554)<-[:expr { local_id: '6597230'}]-(id5803210729) CREATE (id5590554)-[:expr { local_id: '5642407'}]->(id7875206161) CREATE (id5826700:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5826700)<-[:linear_index {linear_index: '28}']-(id000018) CREATE (id5826700)<-[:infrule]-(dividebothsidesby) CREATE (id5826700)<-[:expr { local_id: '2443387'}]-(id5514556106) CREATE (id5826700)<-[:expr { local_id: '1092386'}]-(id2081689540) CREATE (id5826700)-[:expr { local_id: '2692856'}]->(id2770069250) CREATE (id5851086:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5851086)<-[:linear_index {linear_index: '10}']-(id000018) CREATE (id5851086)<-[:infrule]-(subtractexpr1fromexpr2) CREATE (id5851086)<-[:expr { local_id: '4208138'}]-(id4928007622) CREATE (id5851086)<-[:expr { local_id: '6632540'}]-(id7676652285) CREATE (id5851086)-[:expr { local_id: '9602854'}]->(id5733146966) CREATE (id5867939:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5867939)<-[:linear_index {linear_index: '16}']-(id000018) CREATE (id5867939)<-[:infrule]-(declareinitialexpr) CREATE (id5867939)-[:expr { local_id: '6973462'}]->(id2857430695) CREATE (id5879978:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5879978)<-[:linear_index {linear_index: '25}']-(id000018) CREATE (id5879978)<-[:infrule]-(dividebothsidesby) CREATE (id5879978)<-[:expr { local_id: '1550851'}]-(id7734996511) CREATE (id5879978)<-[:expr { local_id: '5117358'}]-(id2016063530) CREATE (id5879978)-[:expr { local_id: '7539016'}]->(id7267155233) CREATE (id5969230:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5969230)<-[:linear_index {linear_index: '23}']-(id000018) CREATE (id5969230)<-[:infrule]-(changetwovariablesinexpr) CREATE (id5969230)<-[:expr { local_id: '8497204'}]-(id6715248283) CREATE (id5969230)<-[:expr { local_id: '7978426'}]-(id3809726424) CREATE (id5969230)<-[:expr { local_id: '3017178'}]-(id6749533119) CREATE (id5969230)<-[:expr { local_id: '7633243'}]-(id4218009993) CREATE (id5969230)<-[:expr { local_id: '7396349'}]-(id1552869972) CREATE (id5969230)-[:expr { local_id: '9081932'}]->(id4669290568) CREATE (id6718378:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6718378)<-[:linear_index {linear_index: '19}']-(id000018) CREATE (id6718378)<-[:infrule]-(declareinitialexpr) CREATE (id6718378)-[:expr { local_id: '8447573'}]->(id5345738321) CREATE (id6719788:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6719788)<-[:linear_index {linear_index: '22}']-(id000018) CREATE (id6719788)<-[:infrule]-(changetwovariablesinexpr) CREATE (id6719788)<-[:expr { local_id: '8497204'}]-(id6715248283) CREATE (id6719788)<-[:expr { local_id: '7552471'}]-(id5075406409) CREATE (id6719788)<-[:expr { local_id: '7956811'}]-(id4522137851) CREATE (id6719788)<-[:expr { local_id: '7519917'}]-(id4188639044) CREATE (id6719788)<-[:expr { local_id: '3171432'}]-(id4755369593) CREATE (id6719788)-[:expr { local_id: '3988671'}]->(id2431507955) CREATE (id6886472:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6886472)<-[:linear_index {linear_index: '5}']-(id000018) CREATE (id6886472)<-[:infrule]-(subtractexpr1fromexpr2) CREATE (id6886472)<-[:expr { local_id: '1298003'}]-(id4303372136) CREATE (id6886472)<-[:expr { local_id: '5642407'}]-(id7875206161) CREATE (id6886472)-[:expr { local_id: '2443387'}]->(id5514556106) CREATE (id7014882:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7014882)<-[:linear_index {linear_index: '34}']-(id000018) CREATE (id7014882)<-[:infrule]-(declarefinalexpr) CREATE (id7014882)<-[:expr { local_id: '1781127'}]-(id8558338742) CREATE (id7067324:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7067324)<-[:linear_index {linear_index: '20}']-(id000018) CREATE (id7067324)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id7067324)<-[:expr { local_id: '8447573'}]-(id5345738321) CREATE (id7067324)<-[:expr { local_id: '4876963'}]-(id4784793837) CREATE (id7067324)-[:expr { local_id: '7034924'}]->(id2186083170) CREATE (id7085632:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7085632)<-[:linear_index {linear_index: '12}']-(id000018) CREATE (id7085632)<-[:infrule]-(declareinitialexpr) CREATE (id7085632)-[:expr { local_id: '2776565'}]->(id5781981178) CREATE (id7113502:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7113502)<-[:linear_index {linear_index: '8}']-(id000018) CREATE (id7113502)<-[:infrule]-(changetwovariablesinexpr) CREATE (id7113502)<-[:expr { local_id: '6559987'}]-(id8357234146) CREATE (id7113502)<-[:expr { local_id: '6566357'}]-(id4147101187) CREATE (id7113502)<-[:expr { local_id: '3381732'}]-(id6964468708) CREATE (id7113502)<-[:expr { local_id: '1988214'}]-(id5398681503) CREATE (id7113502)<-[:expr { local_id: '9120447'}]-(id3105350101) CREATE (id7113502)-[:expr { local_id: '4208138'}]->(id4928007622) CREATE (id7171014:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7171014)<-[:linear_index {linear_index: '21}']-(id000018) CREATE (id7171014)<-[:infrule]-(declareinitialexpr) CREATE (id7171014)-[:expr { local_id: '8497204'}]->(id6715248283) CREATE (id7184509:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7184509)<-[:linear_index {linear_index: '24}']-(id000018) CREATE (id7184509)<-[:infrule]-(subtractexpr1fromexpr2) CREATE (id7184509)<-[:expr { local_id: '9081932'}]-(id4669290568) CREATE (id7184509)<-[:expr { local_id: '3988671'}]-(id2431507955) CREATE (id7184509)-[:expr { local_id: '1550851'}]->(id7734996511) CREATE (id7511478:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7511478)<-[:linear_index {linear_index: '33}']-(id000018) CREATE (id7511478)<-[:infrule]-(addXtobothsides) CREATE (id7511478)<-[:expr { local_id: '2075807'}]-(id3806977900) CREATE (id7511478)<-[:expr { local_id: '3423567'}]-(id5960438249) CREATE (id7511478)-[:expr { local_id: '1781127'}]->(id8558338742) CREATE (id7835026:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7835026)<-[:linear_index {linear_index: '13}']-(id000018) CREATE (id7835026)<-[:infrule]-(changetwovariablesinexpr) CREATE (id7835026)<-[:expr { local_id: '2776565'}]-(id5781981178) CREATE (id7835026)<-[:expr { local_id: '4758524'}]-(id1025759423) CREATE (id7835026)<-[:expr { local_id: '9746924'}]-(id5239755033) CREATE (id7835026)<-[:expr { local_id: '3257704'}]-(id8173074178) CREATE (id7835026)<-[:expr { local_id: '9704581'}]-(id4319470443) CREATE (id7835026)-[:expr { local_id: '8696678'}]->(id4648451961) CREATE (id7965863:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7965863)<-[:linear_index {linear_index: '26}']-(id000018) CREATE (id7965863)<-[:infrule]-(declareinitialexpr) CREATE (id7965863)-[:expr { local_id: '6154610'}]->(id9337785146) CREATE (id8337849:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8337849)<-[:linear_index {linear_index: '15}']-(id000018) CREATE (id8337849)<-[:infrule]-(declareinitialexpr) CREATE (id8337849)-[:expr { local_id: '3484339'}]->(id9397152918) CREATE (id8346419:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8346419)<-[:linear_index {linear_index: '3}']-(id000018) CREATE (id8346419)<-[:infrule]-(changethreevariablesinexpr) CREATE (id8346419)<-[:expr { local_id: '8844119'}]-(id5136652623) CREATE (id8346419)<-[:expr { local_id: '8946473'}]-(id3749492596) CREATE (id8346419)<-[:expr { local_id: '5080789'}]-(id4213426349) CREATE (id8346419)<-[:expr { local_id: '6566358'}]-(id4147101187) CREATE (id8346419)<-[:expr { local_id: '4405571'}]-(id1092872200) CREATE (id8346419)<-[:expr { local_id: '7978425'}]-(id3809726424) CREATE (id8346419)<-[:expr { local_id: '6935293'}]-(id8061701434) CREATE (id8346419)-[:expr { local_id: '1298003'}]->(id4303372136) CREATE (id9646681:step { creation_date: '2020-04-20', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9646681)<-[:linear_index {linear_index: '30}']-(id000018) CREATE (id9646681)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id9646681)<-[:expr { local_id: '7034924'}]-(id2186083170) CREATE (id9646681)<-[:expr { local_id: '9714818'}]-(id3591237106) CREATE (id9646681)-[:expr { local_id: '5300304'}]->(id1772416655) CREATE (129143:derivation { name: 'escapevelocity', creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1078239:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1078239)<-[:linear_index {linear_index: '20}']-(id129143) CREATE (id1078239)<-[:infrule]-(swapLHSwithRHS) CREATE (id1078239)<-[:expr { local_id: '3358651'}]-(id2977457786) CREATE (id1078239)-[:expr { local_id: '3908344'}]->(id9412953728) CREATE (id1179540:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1179540)<-[:linear_index {linear_index: '8}']-(id129143) CREATE (id1179540)<-[:infrule]-(substituteLHSoftwoexpressionsintoexpr) CREATE (id1179540)<-[:expr { local_id: '6310702'}]-(id4303372136) CREATE (id1179540)<-[:expr { local_id: '5160388'}]-(id7875206161) CREATE (id1179540)<-[:expr { local_id: '6330719'}]-(id8558338742) CREATE (id1179540)-[:expr { local_id: '4840471'}]->(id8960645192) CREATE (id1518987:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1518987)<-[:linear_index {linear_index: '9}']-(id129143) CREATE (id1518987)<-[:infrule]-(declareassumption) CREATE (id1518987)-[:expr { local_id: '7682341'}]->(id2267521164) CREATE (id1868693:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1868693)<-[:linear_index {linear_index: '13}']-(id129143) CREATE (id1868693)<-[:infrule]-(declareinitialexpr) CREATE (id1868693)-[:expr { local_id: '6773616'}]->(id7573835180) CREATE (id3270895:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3270895)<-[:linear_index {linear_index: '19}']-(id129143) CREATE (id3270895)<-[:infrule]-(multiplybothsidesby) CREATE (id3270895)<-[:expr { local_id: '7567097'}]-(id1143343287) CREATE (id3270895)<-[:expr { local_id: '6213797'}]-(id5775658332) CREATE (id3270895)-[:expr { local_id: '3358651'}]->(id2977457786) CREATE (id3324084:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3324084)<-[:linear_index {linear_index: '4}']-(id129143) CREATE (id3324084)<-[:infrule]-(evaluatedefiniteintegral) CREATE (id3324084)<-[:expr { local_id: '4803506'}]-(id4447113478) CREATE (id3324084)-[:expr { local_id: '1089445'}]->(id5732331610) CREATE (id4165232:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4165232)<-[:linear_index {linear_index: '7}']-(id129143) CREATE (id4165232)<-[:infrule]-(simplify) CREATE (id4165232)<-[:expr { local_id: '2190752'}]-(id5978756813) CREATE (id4165232)-[:expr { local_id: '2238158'}]->(id7749253510) CREATE (id4334762:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4334762)<-[:linear_index {linear_index: '22}']-(id129143) CREATE (id4334762)<-[:infrule]-(declarefinalexpr) CREATE (id4334762)<-[:expr { local_id: '6389964'}]-(id1330874553) CREATE (id4437085:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4437085)<-[:linear_index {linear_index: '23}']-(id129143) CREATE (id4437085)<-[:infrule]-(changetwovariablesinexpr) CREATE (id4437085)<-[:expr { local_id: '6389964'}]-(id1330874553) CREATE (id4437085)<-[:expr { local_id: '3537009'}]-(id2674546234) CREATE (id4437085)<-[:expr { local_id: '3478117'}]-(id2135482543) CREATE (id4437085)<-[:expr { local_id: '9092600'}]-(id2396787389) CREATE (id4437085)<-[:expr { local_id: '4750165'}]-(id8020058613) CREATE (id4437085)-[:expr { local_id: '1619188'}]->(id5404822208) CREATE (id4505146:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4505146)<-[:linear_index {linear_index: '21}']-(id129143) CREATE (id4505146)<-[:infrule]-(squarerootbothsides) CREATE (id4505146)<-[:expr { local_id: '3908344'}]-(id9412953728) CREATE (id4505146)-[:expr { local_id: '6389964'}]->(id1330874553) CREATE (id4505146)-[:expr { local_id: '8779043'}]->(id2750380042) CREATE (id4650277:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4650277)<-[:linear_index {linear_index: '2}']-(id129143) CREATE (id4650277)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id4650277)<-[:expr { local_id: '3279838'}]-(id6935745841) CREATE (id4650277)<-[:expr { local_id: '2123766'}]-(id1590774089) CREATE (id4650277)-[:expr { local_id: '3686928'}]->(id8604483515) CREATE (id5854765:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5854765)<-[:linear_index {linear_index: '18}']-(id129143) CREATE (id5854765)<-[:infrule]-(simplify) CREATE (id5854765)<-[:expr { local_id: '6523887'}]-(id9703482302) CREATE (id5854765)-[:expr { local_id: '7567097'}]->(id1143343287) CREATE (id6008233:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6008233)<-[:linear_index {linear_index: '3}']-(id129143) CREATE (id6008233)<-[:infrule]-(integrate) CREATE (id6008233)<-[:expr { local_id: '3686928'}]-(id8604483515) CREATE (id6008233)-[:expr { local_id: '4803506'}]->(id4447113478) CREATE (id6200985:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6200985)<-[:linear_index {linear_index: '14}']-(id129143) CREATE (id6200985)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6200985)<-[:expr { local_id: '2238158'}]-(id7749253510) CREATE (id6200985)<-[:expr { local_id: '6773616'}]-(id7573835180) CREATE (id6200985)-[:expr { local_id: '9437784'}]->(id3846041519) CREATE (id6881790:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6881790)<-[:linear_index {linear_index: '1}']-(id129143) CREATE (id6881790)<-[:infrule]-(declareinitialexpr) CREATE (id6881790)-[:expr { local_id: '3279838'}]->(id6935745841) CREATE (id6988834:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6988834)<-[:linear_index {linear_index: '10}']-(id129143) CREATE (id6988834)<-[:infrule]-(declareassumption) CREATE (id6988834)-[:expr { local_id: '9324316'}]->(id1840080113) CREATE (id7320847:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7320847)<-[:linear_index {linear_index: '11}']-(id129143) CREATE (id7320847)<-[:infrule]-(substituteLHSoftwoexpressionsintoexpr) CREATE (id7320847)<-[:expr { local_id: '7682341'}]-(id2267521164) CREATE (id7320847)<-[:expr { local_id: '9324316'}]-(id1840080113) CREATE (id7320847)<-[:expr { local_id: '4840471'}]-(id8960645192) CREATE (id7320847)-[:expr { local_id: '8369684'}]->(id9749777192) CREATE (id8039319:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8039319)<-[:linear_index {linear_index: '5}']-(id129143) CREATE (id8039319)<-[:infrule]-(changetwovariablesinexpr) CREATE (id8039319)<-[:expr { local_id: '1089445'}]-(id5732331610) CREATE (id8039319)<-[:expr { local_id: '9544390'}]-(id1413137236) CREATE (id8039319)<-[:expr { local_id: '9358085'}]-(id9072369552) CREATE (id8039319)<-[:expr { local_id: '3268428'}]-(id2764966428) CREATE (id8039319)<-[:expr { local_id: '6786890'}]-(id7140470627) CREATE (id8039319)-[:expr { local_id: '2341415'}]->(id6131764194) CREATE (id8184884:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8184884)<-[:linear_index {linear_index: '16}']-(id129143) CREATE (id8184884)<-[:infrule]-(substituteLHSoftwoexpressionsintoexpr) CREATE (id8184884)<-[:expr { local_id: '5106827'}]-(id6870322215) CREATE (id8184884)<-[:expr { local_id: '9437784'}]-(id3846041519) CREATE (id8184884)<-[:expr { local_id: '9967559'}]-(id2503972039) CREATE (id8184884)-[:expr { local_id: '3493665'}]->(id2042298788) CREATE (id8498604:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8498604)<-[:linear_index {linear_index: '15}']-(id129143) CREATE (id8498604)<-[:infrule]-(changetwovariablesinexpr) CREATE (id8498604)<-[:expr { local_id: '3778087'}]-(id8357234146) CREATE (id8498604)<-[:expr { local_id: '6306015'}]-(id5021965469) CREATE (id8498604)<-[:expr { local_id: '5916018'}]-(id9370882921) CREATE (id8498604)<-[:expr { local_id: '4487753'}]-(id6681646197) CREATE (id8498604)<-[:expr { local_id: '4994113'}]-(id6498985149) CREATE (id8498604)-[:expr { local_id: '5106827'}]->(id6870322215) CREATE (id8921345:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8921345)<-[:linear_index {linear_index: '17}']-(id129143) CREATE (id8921345)<-[:infrule]-(addXtobothsides) CREATE (id8921345)<-[:expr { local_id: '3493665'}]-(id2042298788) CREATE (id8921345)<-[:expr { local_id: '7445550'}]-(id5050429607) CREATE (id8921345)-[:expr { local_id: '6523887'}]->(id9703482302) CREATE (id9534004:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9534004)<-[:linear_index {linear_index: '6}']-(id129143) CREATE (id9534004)<-[:infrule]-(simplify) CREATE (id9534004)<-[:expr { local_id: '2341415'}]-(id6131764194) CREATE (id9534004)-[:expr { local_id: '2190752'}]->(id5978756813) CREATE (id9709070:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9709070)<-[:linear_index {linear_index: '12}']-(id129143) CREATE (id9709070)<-[:infrule]-(changetwovariablesinexpr) CREATE (id9709070)<-[:expr { local_id: '8369684'}]-(id9749777192) CREATE (id9709070)<-[:expr { local_id: '7262448'}]-(id5591692598) CREATE (id9709070)<-[:expr { local_id: '9126778'}]-(id8416464049) CREATE (id9709070)<-[:expr { local_id: '6756248'}]-(id6158970683) CREATE (id9709070)<-[:expr { local_id: '7220243'}]-(id8871333437) CREATE (id9709070)-[:expr { local_id: '9967559'}]->(id2503972039) CREATE (142831:derivation { name: 'Schwarzschildradiusfornonrotatingblackhole', notes: 'https://en.wikipedia.org/wiki/Derivation_of_the_Schwarzschild_solution', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2544795:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2544795)<-[:linear_index {linear_index: '2}']-(id142831) CREATE (id2544795)<-[:infrule]-(changetwovariablesinexpr) CREATE (id2544795)<-[:expr { local_id: '2478510'}]-(id8946383937) CREATE (id2544795)<-[:expr { local_id: '8050243'}]-(id8362338572) CREATE (id2544795)<-[:expr { local_id: '2954561'}]-(id1238593037) CREATE (id2544795)<-[:expr { local_id: '8988316'}]-(id2660368546) CREATE (id2544795)<-[:expr { local_id: '2522307'}]-(id9933742680) CREATE (id2544795)-[:expr { local_id: '5459812'}]->(id4275004561) CREATE (id2775447:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2775447)<-[:linear_index {linear_index: '4}']-(id142831) CREATE (id2775447)<-[:infrule]-(dividebothsidesby) CREATE (id2775447)<-[:expr { local_id: '9932666'}]-(id2883079365) CREATE (id2775447)<-[:expr { local_id: '8824597'}]-(id7263534144) CREATE (id2775447)-[:expr { local_id: '9994959'}]->(id6800170830) CREATE (id4980032:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4980032)<-[:linear_index {linear_index: '1}']-(id142831) CREATE (id4980032)<-[:infrule]-(raisebothsidestopower) CREATE (id4980032)<-[:expr { local_id: '1044984'}]-(id5404822208) CREATE (id4980032)<-[:expr { local_id: '7891922'}]-(id3663007361) CREATE (id4980032)-[:expr { local_id: '2478510'}]->(id8946383937) CREATE (id8627172:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8627172)<-[:linear_index {linear_index: '3}']-(id142831) CREATE (id8627172)<-[:infrule]-(multiplybothsidesby) CREATE (id8627172)<-[:expr { local_id: '5459812'}]-(id4275004561) CREATE (id8627172)<-[:expr { local_id: '3067885'}]-(id7194432406) CREATE (id8627172)-[:expr { local_id: '9932666'}]->(id2883079365) CREATE (146432:derivation { name: 'coefficientofthermalexpansionusingtheequationofstateforanidealgas', notes: 'https://notendur.hi.is/hj/EE2/HD1lausn.pdf', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1997333:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1997333)<-[:linear_index {linear_index: '8}']-(id146432) CREATE (id1997333)<-[:infrule]-(simplify) CREATE (id1997333)<-[:expr { local_id: '7845152'}]-(id6925244346) CREATE (id1997333)-[:expr { local_id: '2491768'}]->(id2472653783) CREATE (id2439511:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2439511)<-[:linear_index {linear_index: '5}']-(id146432) CREATE (id2439511)<-[:infrule]-(declareinitialexpr) CREATE (id2439511)-[:expr { local_id: '5130250'}]->(id8435841627) CREATE (id3037920:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3037920)<-[:linear_index {linear_index: '2}']-(id146432) CREATE (id3037920)<-[:infrule]-(declareinitialexpr) CREATE (id3037920)-[:expr { local_id: '5927974'}]->(id3497828859) CREATE (id3078632:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3078632)<-[:linear_index {linear_index: '7}']-(id146432) CREATE (id3078632)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id3078632)<-[:expr { local_id: '8283443'}]-(id2613006036) CREATE (id3078632)<-[:expr { local_id: '4600503'}]-(id5962145508) CREATE (id3078632)-[:expr { local_id: '7845152'}]->(id6925244346) CREATE (id3744460:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3744460)<-[:linear_index {linear_index: '1}']-(id146432) CREATE (id3744460)<-[:infrule]-(declareinitialexpr) CREATE (id3744460)-[:expr { local_id: '5888046'}]->(id3464107376) CREATE (id5311790:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5311790)<-[:linear_index {linear_index: '4}']-(id146432) CREATE (id5311790)<-[:infrule]-(simplify) CREATE (id5311790)<-[:expr { local_id: '7236464'}]-(id1311403394) CREATE (id5311790)-[:expr { local_id: '4600503'}]->(id5962145508) CREATE (id5713113:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5713113)<-[:linear_index {linear_index: '6}']-(id146432) CREATE (id5713113)<-[:infrule]-(dividebothsidesby) CREATE (id5713113)<-[:expr { local_id: '5130250'}]-(id8435841627) CREATE (id5713113)<-[:expr { local_id: '4656601'}]-(id7924842770) CREATE (id5713113)-[:expr { local_id: '8283443'}]->(id2613006036) CREATE (id6216231:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6216231)<-[:linear_index {linear_index: '9}']-(id146432) CREATE (id6216231)<-[:infrule]-(declarefinalexpr) CREATE (id6216231)<-[:expr { local_id: '2491768'}]-(id2472653783) CREATE (id8295331:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8295331)<-[:linear_index {linear_index: '3}']-(id146432) CREATE (id8295331)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id8295331)<-[:expr { local_id: '5927974'}]-(id3497828859) CREATE (id8295331)<-[:expr { local_id: '5888046'}]-(id3464107376) CREATE (id8295331)-[:expr { local_id: '7236464'}]->(id1311403394) CREATE (187793:derivation { name: 'equationsofmotionin2Dcalculus', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1117397:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1117397)<-[:linear_index {linear_index: '28}']-(id187793) CREATE (id1117397)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1117397)<-[:expr { local_id: '8435615'}]-(id6134836751) CREATE (id1117397)<-[:expr { local_id: '4895553'}]-(id8460820419) CREATE (id1117397)-[:expr { local_id: '5123314'}]->(id7455581657) CREATE (id1136226:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1136226)<-[:linear_index {linear_index: '17}']-(id187793) CREATE (id1136226)<-[:infrule]-(declareinitialexpr) CREATE (id1136226)-[:expr { local_id: '3936380'}]->(id7252338326) CREATE (id1138623:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1138623)<-[:linear_index {linear_index: '23}']-(id187793) CREATE (id1138623)<-[:infrule]-(multiplybothsidesby) CREATE (id1138623)<-[:expr { local_id: '8742281'}]-(id8750379055) CREATE (id1138623)<-[:expr { local_id: '6139485'}]-(id8717193282) CREATE (id1138623)-[:expr { local_id: '5239397'}]->(id1166310428) CREATE (id1298567:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1298567)<-[:linear_index {linear_index: '10}']-(id187793) CREATE (id1298567)<-[:infrule]-(assumeNdimensions) CREATE (id1298567)<-[:expr { local_id: '7516260'}]-(id8880467139) CREATE (id1298567)-[:expr { local_id: '5359560'}]->(id5349866551) CREATE (id1662112:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1662112)<-[:linear_index {linear_index: '29}']-(id187793) CREATE (id1662112)<-[:infrule]-(multiplybothsidesby) CREATE (id1662112)<-[:expr { local_id: '5123314'}]-(id7455581657) CREATE (id1662112)<-[:expr { local_id: '5587641'}]-(id8607458157) CREATE (id1662112)-[:expr { local_id: '8062944'}]->(id1963253044) CREATE (id2139033:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2139033)<-[:linear_index {linear_index: '16}']-(id187793) CREATE (id2139033)<-[:infrule]-(addXtobothsides) CREATE (id2139033)<-[:expr { local_id: '1321587'}]-(id9973952056) CREATE (id2139033)<-[:expr { local_id: '8163462'}]-(id4167526462) CREATE (id2139033)-[:expr { local_id: '2682139'}]->(id6572039835) CREATE (id2304792:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2304792)<-[:linear_index {linear_index: '11}']-(id187793) CREATE (id2304792)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id2304792)<-[:expr { local_id: '2060958'}]-(id9707028061) CREATE (id2304792)<-[:expr { local_id: '5765841'}]-(id1819663717) CREATE (id2304792)-[:expr { local_id: '8742281'}]->(id8750379055) CREATE (id2739184:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2739184)<-[:linear_index {linear_index: '30}']-(id187793) CREATE (id2739184)<-[:infrule]-(indefiniteintegration) CREATE (id2739184)<-[:expr { local_id: '8062944'}]-(id1963253044) CREATE (id2739184)-[:expr { local_id: '2732393'}]->(id3676159007) CREATE (id2766390:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2766390)<-[:linear_index {linear_index: '39}']-(id187793) CREATE (id2766390)<-[:infrule]-(multiplybothsidesby) CREATE (id2766390)<-[:expr { local_id: '2378061'}]-(id7376526845) CREATE (id2766390)<-[:expr { local_id: '9035634'}]-(id5620558729) CREATE (id2766390)-[:expr { local_id: '3041148'}]->(id8949329361) CREATE (id2851041:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2851041)<-[:linear_index {linear_index: '33}']-(id187793) CREATE (id2851041)<-[:infrule]-(swapLHSwithRHS) CREATE (id2851041)<-[:expr { local_id: '6277762'}]-(id8486706976) CREATE (id2851041)-[:expr { local_id: '3011802'}]->(id1306360899) CREATE (id2904437:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2904437)<-[:linear_index {linear_index: '12}']-(id187793) CREATE (id2904437)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id2904437)<-[:expr { local_id: '1439312'}]-(id2741489181) CREATE (id2904437)<-[:expr { local_id: '2080932'}]-(id8228733125) CREATE (id2904437)-[:expr { local_id: '3939933'}]->(id1977955751) CREATE (id3356600:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3356600)<-[:linear_index {linear_index: '6}']-(id187793) CREATE (id3356600)<-[:infrule]-(separatetwovectorcomponents) CREATE (id3356600)<-[:expr { local_id: '4904941'}]-(id7729413831) CREATE (id3356600)-[:expr { local_id: '5765841'}]->(id1819663717) CREATE (id3356600)-[:expr { local_id: '2080932'}]->(id8228733125) CREATE (id3500836:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3500836)<-[:linear_index {linear_index: '13}']-(id187793) CREATE (id3500836)<-[:infrule]-(multiplybothsidesby) CREATE (id3500836)<-[:expr { local_id: '3939933'}]-(id1977955751) CREATE (id3500836)<-[:expr { local_id: '8813112'}]-(id6672141531) CREATE (id3500836)-[:expr { local_id: '4777195'}]->(id1702349646) CREATE (id3504214:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3504214)<-[:linear_index {linear_index: '37}']-(id187793) CREATE (id3504214)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3504214)<-[:expr { local_id: '6010171'}]-(id6083821265) CREATE (id3504214)<-[:expr { local_id: '3011802'}]-(id1306360899) CREATE (id3504214)-[:expr { local_id: '6795282'}]->(id5438722682) CREATE (id3673220:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3673220)<-[:linear_index {linear_index: '14}']-(id187793) CREATE (id3673220)<-[:infrule]-(indefiniteintegration) CREATE (id3673220)<-[:expr { local_id: '4777195'}]-(id1702349646) CREATE (id3673220)-[:expr { local_id: '3366698'}]->(id8584698994) CREATE (id4385306:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4385306)<-[:linear_index {linear_index: '40}']-(id187793) CREATE (id4385306)<-[:infrule]-(swapLHSwithRHS) CREATE (id4385306)<-[:expr { local_id: '7541692'}]-(id2461349007) CREATE (id4385306)-[:expr { local_id: '1910429'}]->(id1405465835) CREATE (id4389482:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4389482)<-[:linear_index {linear_index: '22}']-(id187793) CREATE (id4389482)<-[:infrule]-(addXtobothsides) CREATE (id4389482)<-[:expr { local_id: '8638087'}]-(id2858549874) CREATE (id4389482)<-[:expr { local_id: '1650323'}]-(id6098638221) CREATE (id4389482)-[:expr { local_id: '7541692'}]->(id2461349007) CREATE (id4553137:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4553137)<-[:linear_index {linear_index: '15}']-(id187793) CREATE (id4553137)<-[:infrule]-(simplify) CREATE (id4553137)<-[:expr { local_id: '3366698'}]-(id8584698994) CREATE (id4553137)-[:expr { local_id: '1321587'}]->(id9973952056) CREATE (id4576718:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4576718)<-[:linear_index {linear_index: '7}']-(id187793) CREATE (id4576718)<-[:infrule]-(declareassumption) CREATE (id4576718)-[:expr { local_id: '2060958'}]->(id9707028061) CREATE (id4691130:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4691130)<-[:linear_index {linear_index: '8}']-(id187793) CREATE (id4691130)<-[:infrule]-(declareassumption) CREATE (id4691130)-[:expr { local_id: '1439312'}]->(id2741489181) CREATE (id5219345:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5219345)<-[:linear_index {linear_index: '36}']-(id187793) CREATE (id5219345)<-[:infrule]-(multiplybothsidesby) CREATE (id5219345)<-[:expr { local_id: '5523081'}]-(id7391837535) CREATE (id5219345)<-[:expr { local_id: '2788936'}]-(id5868731041) CREATE (id5219345)-[:expr { local_id: '6010171'}]->(id6083821265) CREATE (id5993111:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5993111)<-[:linear_index {linear_index: '32}']-(id187793) CREATE (id5993111)<-[:infrule]-(addXtobothsides) CREATE (id5993111)<-[:expr { local_id: '2740672'}]-(id9882526611) CREATE (id5993111)<-[:expr { local_id: '7526914'}]-(id3182907803) CREATE (id5993111)-[:expr { local_id: '6277762'}]->(id8486706976) CREATE (id6387363:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6387363)<-[:linear_index {linear_index: '5}']-(id187793) CREATE (id6387363)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6387363)<-[:expr { local_id: '5359560'}]-(id5349866551) CREATE (id6387363)<-[:expr { local_id: '4755350'}]-(id4158986868) CREATE (id6387363)-[:expr { local_id: '4904941'}]->(id7729413831) CREATE (id6514260:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6514260)<-[:linear_index {linear_index: '24}']-(id187793) CREATE (id6514260)<-[:infrule]-(indefiniteintegration) CREATE (id6514260)<-[:expr { local_id: '5239397'}]-(id1166310428) CREATE (id6514260)-[:expr { local_id: '3137944'}]->(id2366691988) CREATE (id6571218:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6571218)<-[:linear_index {linear_index: '42}']-(id187793) CREATE (id6571218)<-[:infrule]-(declarefinalexpr) CREATE (id6571218)<-[:expr { local_id: '9780510'}]-(id9862900242) CREATE (id6601736:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6601736)<-[:linear_index {linear_index: '38}']-(id187793) CREATE (id6601736)<-[:infrule]-(declarefinalexpr) CREATE (id6601736)<-[:expr { local_id: '6795282'}]-(id5438722682) CREATE (id6602846:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6602846)<-[:linear_index {linear_index: '9}']-(id187793) CREATE (id6602846)<-[:infrule]-(assumeNdimensions) CREATE (id6602846)<-[:expr { local_id: '8167187'}]-(id3270039798) CREATE (id6602846)-[:expr { local_id: '4862823'}]->(id8602512487) CREATE (id6781797:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6781797)<-[:linear_index {linear_index: '18}']-(id187793) CREATE (id6781797)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6781797)<-[:expr { local_id: '3936380'}]-(id7252338326) CREATE (id6781797)<-[:expr { local_id: '2682139'}]-(id6572039835) CREATE (id6781797)-[:expr { local_id: '5010170'}]->(id6204539227) CREATE (id6801838:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6801838)<-[:linear_index {linear_index: '27}']-(id187793) CREATE (id6801838)<-[:infrule]-(declareinitialexpr) CREATE (id6801838)-[:expr { local_id: '4895553'}]->(id8460820419) CREATE (id7192805:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7192805)<-[:linear_index {linear_index: '25}']-(id187793) CREATE (id7192805)<-[:infrule]-(simplify) CREATE (id7192805)<-[:expr { local_id: '3137944'}]-(id2366691988) CREATE (id7192805)-[:expr { local_id: '9737190'}]->(id1676472948) CREATE (id7320561:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7320561)<-[:linear_index {linear_index: '3}']-(id187793) CREATE (id7320561)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7320561)<-[:expr { local_id: '6758737'}]-(id3169580383) CREATE (id7320561)<-[:expr { local_id: '4862823'}]-(id8602512487) CREATE (id7320561)-[:expr { local_id: '4755350'}]->(id4158986868) CREATE (id7412638:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7412638)<-[:linear_index {linear_index: '20}']-(id187793) CREATE (id7412638)<-[:infrule]-(indefiniteintegration) CREATE (id7412638)<-[:expr { local_id: '5577963'}]-(id8145337879) CREATE (id7412638)-[:expr { local_id: '8020644'}]->(id8808860551) CREATE (id7852750:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7852750)<-[:linear_index {linear_index: '35}']-(id187793) CREATE (id7852750)<-[:infrule]-(separatevectorintotwotrigonometricratios) CREATE (id7852750)<-[:expr { local_id: '1381925'}]-(id9341391925) CREATE (id7852750)<-[:expr { local_id: '4315501'}]-(id6410818363) CREATE (id7852750)-[:expr { local_id: '5523081'}]->(id7391837535) CREATE (id7852750)-[:expr { local_id: '2378061'}]->(id7376526845) CREATE (id8183035:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8183035)<-[:linear_index {linear_index: '41}']-(id187793) CREATE (id8183035)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id8183035)<-[:expr { local_id: '3041148'}]-(id8949329361) CREATE (id8183035)<-[:expr { local_id: '1910429'}]-(id1405465835) CREATE (id8183035)-[:expr { local_id: '9780510'}]->(id9862900242) CREATE (id8200501:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8200501)<-[:linear_index {linear_index: '21}']-(id187793) CREATE (id8200501)<-[:infrule]-(simplify) CREATE (id8200501)<-[:expr { local_id: '8020644'}]-(id8808860551) CREATE (id8200501)-[:expr { local_id: '8638087'}]->(id2858549874) CREATE (id8369238:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8369238)<-[:linear_index {linear_index: '31}']-(id187793) CREATE (id8369238)<-[:infrule]-(simplify) CREATE (id8369238)<-[:expr { local_id: '2732393'}]-(id3676159007) CREATE (id8369238)-[:expr { local_id: '2740672'}]->(id9882526611) CREATE (id8974812:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8974812)<-[:linear_index {linear_index: '34}']-(id187793) CREATE (id8974812)<-[:infrule]-(assumeNdimensions) CREATE (id8974812)<-[:expr { local_id: '8345214'}]-(id7049769409) CREATE (id8974812)-[:expr { local_id: '1381925'}]->(id9341391925) CREATE (id9095941:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9095941)<-[:linear_index {linear_index: '19}']-(id187793) CREATE (id9095941)<-[:infrule]-(multiplybothsidesby) CREATE (id9095941)<-[:expr { local_id: '5010170'}]-(id6204539227) CREATE (id9095941)<-[:expr { local_id: '8727369'}]-(id1614343171) CREATE (id9095941)-[:expr { local_id: '5577963'}]->(id8145337879) CREATE (id9736733:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9736733)<-[:linear_index {linear_index: '1}']-(id187793) CREATE (id9736733)<-[:infrule]-(declareinitialexpr) CREATE (id9736733)-[:expr { local_id: '6758737'}]->(id3169580383) CREATE (id9911907:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9911907)<-[:linear_index {linear_index: '26}']-(id187793) CREATE (id9911907)<-[:infrule]-(addXtobothsides) CREATE (id9911907)<-[:expr { local_id: '9737190'}]-(id1676472948) CREATE (id9911907)<-[:expr { local_id: '7247144'}]-(id1439089569) CREATE (id9911907)-[:expr { local_id: '8435615'}]->(id6134836751) CREATE (201726:derivation { name: 'angleofmaximumdistanceforprojectilemotion', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2825295:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2825295)<-[:linear_index {linear_index: '7}']-(id201726) CREATE (id2825295)<-[:infrule]-(dividebothsidesby) CREATE (id2825295)<-[:expr { local_id: '7465542'}]-(id1087417579) CREATE (id2825295)<-[:expr { local_id: '1548440'}]-(id4829590294) CREATE (id2825295)-[:expr { local_id: '5115586'}]->(id2086924031) CREATE (id2888455:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2888455)<-[:linear_index {linear_index: '4}']-(id201726) CREATE (id2888455)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id2888455)<-[:expr { local_id: '8592617'}]-(id5379546684) CREATE (id2888455)<-[:expr { local_id: '4911015'}]-(id9112191201) CREATE (id2888455)-[:expr { local_id: '7336772'}]->(id8198310977) CREATE (id2933842:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2933842)<-[:linear_index {linear_index: '22}']-(id201726) CREATE (id2933842)<-[:infrule]-(declarefinalexpr) CREATE (id2933842)<-[:expr { local_id: '6972103'}]-(id5353282496) CREATE (id3635128:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3635128)<-[:linear_index {linear_index: '16}']-(id201726) CREATE (id3635128)<-[:infrule]-(declareinitialexpr) CREATE (id3635128)-[:expr { local_id: '6199255'}]->(id2405307372) CREATE (id3645843:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3645843)<-[:linear_index {linear_index: '10}']-(id201726) CREATE (id3645843)<-[:infrule]-(declareinitialexpr) CREATE (id3645843)-[:expr { local_id: '2022953'}]->(id5438722682) CREATE (id3846508:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3846508)<-[:linear_index {linear_index: '21}']-(id201726) CREATE (id3846508)<-[:infrule]-(simplify) CREATE (id3846508)<-[:expr { local_id: '9834994'}]-(id3607070319) CREATE (id3846508)-[:expr { local_id: '6972103'}]->(id5353282496) CREATE (id4274767:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4274767)<-[:linear_index {linear_index: '12}']-(id201726) CREATE (id4274767)<-[:infrule]-(boundarycondition) CREATE (id4274767)<-[:expr { local_id: '1654988'}]-(id4370074654) CREATE (id4274767)-[:expr { local_id: '5891715'}]->(id2378095808) CREATE (id5424962:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5424962)<-[:linear_index {linear_index: '13}']-(id201726) CREATE (id5424962)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5424962)<-[:expr { local_id: '5891715'}]-(id2378095808) CREATE (id5424962)<-[:expr { local_id: '2293278'}]-(id3485125659) CREATE (id5424962)-[:expr { local_id: '6742208'}]->(id4268085801) CREATE (id5447490:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5447490)<-[:linear_index {linear_index: '14}']-(id201726) CREATE (id5447490)<-[:infrule]-(subtractXfrombothsides) CREATE (id5447490)<-[:expr { local_id: '6742208'}]-(id4268085801) CREATE (id5447490)<-[:expr { local_id: '5195494'}]-(id8072682558) CREATE (id5447490)-[:expr { local_id: '6756414'}]->(id7233558441) CREATE (id5860845:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5860845)<-[:linear_index {linear_index: '11}']-(id201726) CREATE (id5860845)<-[:infrule]-(changetwovariablesinexpr) CREATE (id5860845)<-[:expr { local_id: '2022953'}]-(id5438722682) CREATE (id5860845)<-[:expr { local_id: '5327191'}]-(id3273630811) CREATE (id5860845)<-[:expr { local_id: '7949442'}]-(id5194141542) CREATE (id5860845)<-[:expr { local_id: '2411880'}]-(id6732786762) CREATE (id5860845)<-[:expr { local_id: '7379457'}]-(id6463266449) CREATE (id5860845)-[:expr { local_id: '2293278'}]->(id3485125659) CREATE (id5937834:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5937834)<-[:linear_index {linear_index: '2}']-(id201726) CREATE (id5937834)<-[:infrule]-(changetwovariablesinexpr) CREATE (id5937834)<-[:expr { local_id: '1292901'}]-(id9862900242) CREATE (id5937834)<-[:expr { local_id: '2028521'}]-(id8406170337) CREATE (id5937834)<-[:expr { local_id: '8356816'}]-(id8120663858) CREATE (id5937834)<-[:expr { local_id: '9370914'}]-(id2403773761) CREATE (id5937834)<-[:expr { local_id: '1536006'}]-(id4162188238) CREATE (id5937834)-[:expr { local_id: '8592617'}]->(id5379546684) CREATE (id6398792:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6398792)<-[:linear_index {linear_index: '6}']-(id201726) CREATE (id6398792)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6398792)<-[:expr { local_id: '7336772'}]-(id8198310977) CREATE (id6398792)<-[:expr { local_id: '2601896'}]-(id1650441634) CREATE (id6398792)-[:expr { local_id: '7465542'}]->(id1087417579) CREATE (id6672580:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6672580)<-[:linear_index {linear_index: '18}']-(id201726) CREATE (id6672580)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6672580)<-[:expr { local_id: '7596368'}]-(id2519058903) CREATE (id6672580)<-[:expr { local_id: '4362314'}]-(id2297105551) CREATE (id6672580)-[:expr { local_id: '5129639'}]->(id8922441655) CREATE (id7068872:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7068872)<-[:linear_index {linear_index: '3}']-(id201726) CREATE (id7068872)<-[:infrule]-(boundarycondition) CREATE (id7068872)<-[:expr { local_id: '7946350'}]-(id5373931751) CREATE (id7068872)-[:expr { local_id: '4911015'}]->(id9112191201) CREATE (id7996351:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7996351)<-[:linear_index {linear_index: '23}']-(id201726) CREATE (id7996351)<-[:infrule]-(declarefinalexpr) CREATE (id7996351)<-[:expr { local_id: '2728170'}]-(id1541916015) CREATE (id8131060:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8131060)<-[:linear_index {linear_index: '9}']-(id201726) CREATE (id8131060)<-[:infrule]-(multiplybothsidesby) CREATE (id8131060)<-[:expr { local_id: '3904454'}]-(id1191796961) CREATE (id8131060)<-[:expr { local_id: '4824772'}]-(id2510804451) CREATE (id8131060)-[:expr { local_id: '8982886'}]->(id4778077984) CREATE (id8352636:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8352636)<-[:linear_index {linear_index: '15}']-(id201726) CREATE (id8352636)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id8352636)<-[:expr { local_id: '8982886'}]-(id4778077984) CREATE (id8352636)<-[:expr { local_id: '6756414'}]-(id7233558441) CREATE (id8352636)-[:expr { local_id: '4362314'}]->(id2297105551) CREATE (id8794366:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8794366)<-[:linear_index {linear_index: '1}']-(id201726) CREATE (id8794366)<-[:infrule]-(declareinitialexpr) CREATE (id8794366)-[:expr { local_id: '1292901'}]->(id9862900242) CREATE (id9270409:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9270409)<-[:linear_index {linear_index: '8}']-(id201726) CREATE (id9270409)<-[:infrule]-(addXtobothsides) CREATE (id9270409)<-[:expr { local_id: '5115586'}]-(id2086924031) CREATE (id9270409)<-[:expr { local_id: '7072262'}]-(id6974054946) CREATE (id9270409)-[:expr { local_id: '3904454'}]->(id1191796961) CREATE (id9551659:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9551659)<-[:linear_index {linear_index: '20}']-(id201726) CREATE (id9551659)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id9551659)<-[:expr { local_id: '2728170'}]-(id1541916015) CREATE (id9551659)<-[:expr { local_id: '5129639'}]-(id8922441655) CREATE (id9551659)-[:expr { local_id: '9834994'}]->(id3607070319) CREATE (id9561765:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9561765)<-[:linear_index {linear_index: '5}']-(id201726) CREATE (id9561765)<-[:infrule]-(declareassumption) CREATE (id9561765)-[:expr { local_id: '2601896'}]->(id1650441634) CREATE (id9760197:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9760197)<-[:linear_index {linear_index: '17}']-(id201726) CREATE (id9760197)<-[:infrule]-(changevariableXtoY) CREATE (id9760197)<-[:expr { local_id: '6199255'}]-(id2405307372) CREATE (id9760197)<-[:expr { local_id: '7109663'}]-(id7587034465) CREATE (id9760197)<-[:expr { local_id: '8655530'}]-(id7214442790) CREATE (id9760197)-[:expr { local_id: '7596368'}]->(id2519058903) CREATE (id9804800:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9804800)<-[:linear_index {linear_index: '19}']-(id201726) CREATE (id9804800)<-[:infrule]-(maximumofexpr) CREATE (id9804800)<-[:expr { local_id: '5129639'}]-(id8922441655) CREATE (id9804800)<-[:expr { local_id: '4113753'}]-(id5667870149) CREATE (id9804800)-[:expr { local_id: '2728170'}]->(id1541916015) CREATE (207210:derivation { name: 'NewtonsLawofGravitation', notes: 'from https://www.youtube.com/watch?v=fJYdFIZlD8k', creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1345199:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1345199)<-[:linear_index {linear_index: '17}']-(id207210) CREATE (id1345199)<-[:infrule]-(substituteLHSoftwoexpressionsintoexpr) CREATE (id1345199)<-[:expr { local_id: '8320848'}]-(id4264859781) CREATE (id1345199)<-[:expr { local_id: '5440061'}]-(id4490788873) CREATE (id1345199)<-[:expr { local_id: '6174613'}]-(id1571582377) CREATE (id1345199)-[:expr { local_id: '1206000'}]->(id3650814381) CREATE (id1388833:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1388833)<-[:linear_index {linear_index: '8}']-(id207210) CREATE (id1388833)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1388833)<-[:expr { local_id: '3755872'}]-(id6026694087) CREATE (id1388833)<-[:expr { local_id: '5891249'}]-(id4820320578) CREATE (id1388833)-[:expr { local_id: '2239910'}]->(id4267808354) CREATE (id1894519:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1894519)<-[:linear_index {linear_index: '10}']-(id207210) CREATE (id1894519)<-[:infrule]-(declareinitialexpr) CREATE (id1894519)-[:expr { local_id: '5154120'}]->(id6785303857) CREATE (id2320827:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2320827)<-[:linear_index {linear_index: '9}']-(id207210) CREATE (id2320827)<-[:infrule]-(declareinitialexpr) CREATE (id2320827)-[:expr { local_id: '9055493'}]->(id3411994811) CREATE (id2431777:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2431777)<-[:linear_index {linear_index: '5}']-(id207210) CREATE (id2431777)<-[:infrule]-(declareassumption) CREATE (id2431777)-[:expr { local_id: '5891249'}]->(id4820320578) CREATE (id2676398:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2676398)<-[:linear_index {linear_index: '19}']-(id207210) CREATE (id2676398)<-[:infrule]-(declarefinalexpr) CREATE (id2676398)<-[:expr { local_id: '8373934'}]-(id1292735067) CREATE (id2901381:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2901381)<-[:linear_index {linear_index: '7}']-(id207210) CREATE (id2901381)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id2901381)<-[:expr { local_id: '6969192'}]-(id8361238989) CREATE (id2901381)<-[:expr { local_id: '2020292'}]-(id5345738321) CREATE (id2901381)-[:expr { local_id: '3755872'}]->(id6026694087) CREATE (id3408108:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3408108)<-[:linear_index {linear_index: '15}']-(id207210) CREATE (id3408108)<-[:infrule]-(simplify) CREATE (id3408108)<-[:expr { local_id: '4470678'}]-(id3004158505) CREATE (id3408108)-[:expr { local_id: '7324555'}]->(id3650370389) CREATE (id3492706:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3492706)<-[:linear_index {linear_index: '11}']-(id207210) CREATE (id3492706)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3492706)<-[:expr { local_id: '5154120'}]-(id6785303857) CREATE (id3492706)<-[:expr { local_id: '9055493'}]-(id3411994811) CREATE (id3492706)-[:expr { local_id: '7653722'}]->(id5177311762) CREATE (id4575140:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4575140)<-[:linear_index {linear_index: '3}']-(id207210) CREATE (id4575140)<-[:infrule]-(changevariableXtoY) CREATE (id4575140)<-[:expr { local_id: '5546471'}]-(id1848400430) CREATE (id4575140)<-[:expr { local_id: '4627450'}]-(id3876446703) CREATE (id4575140)<-[:expr { local_id: '6309279'}]-(id7905984866) CREATE (id4575140)-[:expr { local_id: '8320848'}]->(id4264859781) CREATE (id4705210:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4705210)<-[:linear_index {linear_index: '18}']-(id207210) CREATE (id4705210)<-[:infrule]-(simplify) CREATE (id4705210)<-[:expr { local_id: '1206000'}]-(id3650814381) CREATE (id4705210)-[:expr { local_id: '8373934'}]->(id1292735067) CREATE (id5400789:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5400789)<-[:linear_index {linear_index: '13}']-(id207210) CREATE (id5400789)<-[:infrule]-(simplify) CREATE (id5400789)<-[:expr { local_id: '9170078'}]-(id6268336290) CREATE (id5400789)-[:expr { local_id: '5175707'}]->(id7672365885) CREATE (id5550676:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5550676)<-[:linear_index {linear_index: '14}']-(id207210) CREATE (id5550676)<-[:infrule]-(multiplybothsidesby) CREATE (id5550676)<-[:expr { local_id: '5175707'}]-(id7672365885) CREATE (id5550676)<-[:expr { local_id: '7991420'}]-(id3448601530) CREATE (id5550676)-[:expr { local_id: '4470678'}]->(id3004158505) CREATE (id5863314:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5863314)<-[:linear_index {linear_index: '1}']-(id207210) CREATE (id5863314)<-[:infrule]-(declareinitialexpr) CREATE (id5863314)-[:expr { local_id: '2020292'}]->(id5345738321) CREATE (id6715674:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6715674)<-[:linear_index {linear_index: '6}']-(id207210) CREATE (id6715674)<-[:infrule]-(declareinitialexpr) CREATE (id6715674)-[:expr { local_id: '6969192'}]->(id8361238989) CREATE (id7387809:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7387809)<-[:linear_index {linear_index: '4}']-(id207210) CREATE (id7387809)<-[:infrule]-(changevariableXtoY) CREATE (id7387809)<-[:expr { local_id: '5546471'}]-(id1848400430) CREATE (id7387809)<-[:expr { local_id: '4770215'}]-(id2346952973) CREATE (id7387809)<-[:expr { local_id: '3625079'}]-(id9594072504) CREATE (id7387809)-[:expr { local_id: '5440061'}]->(id4490788873) CREATE (id7878437:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7878437)<-[:linear_index {linear_index: '12}']-(id207210) CREATE (id7878437)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7878437)<-[:expr { local_id: '7653722'}]-(id5177311762) CREATE (id7878437)<-[:expr { local_id: '2239910'}]-(id4267808354) CREATE (id7878437)-[:expr { local_id: '9170078'}]->(id6268336290) CREATE (id8162484:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8162484)<-[:linear_index {linear_index: '16}']-(id207210) CREATE (id8162484)<-[:infrule]-(declareguesssolution) CREATE (id8162484)<-[:expr { local_id: '7324555'}]-(id3650370389) CREATE (id8162484)-[:expr { local_id: '6174613'}]->(id1571582377) CREATE (id9492883:step { creation_date: '2023-06-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9492883)<-[:linear_index {linear_index: '2}']-(id207210) CREATE (id9492883)<-[:infrule]-(simplify) CREATE (id9492883)<-[:expr { local_id: '2020292'}]-(id5345738321) CREATE (id9492883)-[:expr { local_id: '5546471'}]->(id1848400430) CREATE (282755:derivation { name: 'radiusforsatelliteingeostationaryorbit', notes: 'https://en.wikipedia.org/wiki/Geostationary_orbit#Derivation_of_geostationary_altitude', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1306821:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1306821)<-[:linear_index {linear_index: '3}']-(id282755) CREATE (id1306821)<-[:infrule]-(changefourvariablesinexpr) CREATE (id1306821)<-[:expr { local_id: '8242154'}]-(id9226945488) CREATE (id1306821)<-[:expr { local_id: '2995236'}]-(id5089196493) CREATE (id1306821)<-[:expr { local_id: '6777096'}]-(id1333474099) CREATE (id1306821)<-[:expr { local_id: '2460941'}]-(id3342155559) CREATE (id1306821)<-[:expr { local_id: '4257540'}]-(id2114570475) CREATE (id1306821)<-[:expr { local_id: '7008990'}]-(id7912578203) CREATE (id1306821)<-[:expr { local_id: '9633268'}]-(id9789485295) CREATE (id1306821)-[:expr { local_id: '6845877'}]->(id4627284246) CREATE (id1608311:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1608311)<-[:linear_index {linear_index: '12}']-(id282755) CREATE (id1608311)<-[:infrule]-(multiplybothsidesby) CREATE (id1608311)<-[:expr { local_id: '2871066'}]-(id3906710072) CREATE (id1608311)<-[:expr { local_id: '9152268'}]-(id6238632840) CREATE (id1608311)-[:expr { local_id: '7188516'}]->(id7010294143) CREATE (id1834675:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1834675)<-[:linear_index {linear_index: '14}']-(id282755) CREATE (id1834675)<-[:infrule]-(raisebothsidestopower) CREATE (id1834675)<-[:expr { local_id: '6238570'}]-(id4858693811) CREATE (id1834675)<-[:expr { local_id: '1393618'}]-(id4319544433) CREATE (id1834675)-[:expr { local_id: '7139326'}]->(id2617541067) CREATE (id2499406:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2499406)<-[:linear_index {linear_index: '10}']-(id282755) CREATE (id2499406)<-[:infrule]-(dividebothsidesby) CREATE (id2499406)<-[:expr { local_id: '4948724'}]-(id4072200527) CREATE (id2499406)<-[:expr { local_id: '2502147'}]-(id5359471792) CREATE (id2499406)-[:expr { local_id: '2009493'}]->(id1994296484) CREATE (id3688405:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3688405)<-[:linear_index {linear_index: '16}']-(id282755) CREATE (id3688405)<-[:infrule]-(changetwovariablesinexpr) CREATE (id3688405)<-[:expr { local_id: '7139326'}]-(id2617541067) CREATE (id3688405)<-[:expr { local_id: '4499742'}]-(id3846345263) CREATE (id3688405)<-[:expr { local_id: '4868465'}]-(id5208737840) CREATE (id3688405)<-[:expr { local_id: '6714950'}]-(id5770088141) CREATE (id3688405)<-[:expr { local_id: '6613807'}]-(id7053449926) CREATE (id3688405)-[:expr { local_id: '4507350'}]->(id1559688463) CREATE (id4469272:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4469272)<-[:linear_index {linear_index: '7}']-(id282755) CREATE (id4469272)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id4469272)<-[:expr { local_id: '5369477'}]-(id9262596735) CREATE (id4469272)<-[:expr { local_id: '5114041'}]-(id5426308937) CREATE (id4469272)-[:expr { local_id: '8090893'}]->(id4245712581) CREATE (id4586003:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4586003)<-[:linear_index {linear_index: '1}']-(id282755) CREATE (id4586003)<-[:infrule]-(changefourvariablesinexpr) CREATE (id4586003)<-[:expr { local_id: '2820438'}]-(id6935745841) CREATE (id4586003)<-[:expr { local_id: '2150270'}]-(id3398368564) CREATE (id4586003)<-[:expr { local_id: '2040029'}]-(id3594626260) CREATE (id4586003)<-[:expr { local_id: '1853847'}]-(id9794128647) CREATE (id4586003)<-[:expr { local_id: '6646457'}]-(id4153613253) CREATE (id4586003)<-[:expr { local_id: '1832423'}]-(id3088463019) CREATE (id4586003)<-[:expr { local_id: '3130389'}]-(id3486213448) CREATE (id4586003)<-[:expr { local_id: '1832424'}]-(id4830480629) CREATE (id4586003)<-[:expr { local_id: '1380211'}]-(id7819443873) CREATE (id4586003)-[:expr { local_id: '1917654'}]->(id5563580265) CREATE (id6127864:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6127864)<-[:linear_index {linear_index: '8}']-(id282755) CREATE (id6127864)<-[:infrule]-(changevariableXtoY) CREATE (id6127864)<-[:expr { local_id: '8090893'}]-(id4245712581) CREATE (id6127864)<-[:expr { local_id: '4544527'}]-(id3722461713) CREATE (id6127864)<-[:expr { local_id: '5607083'}]-(id9346215480) CREATE (id6127864)-[:expr { local_id: '2392562'}]->(id3614055652) CREATE (id7853333:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7853333)<-[:linear_index {linear_index: '9}']-(id282755) CREATE (id7853333)<-[:infrule]-(raisebothsidestopower) CREATE (id7853333)<-[:expr { local_id: '2392562'}]-(id3614055652) CREATE (id7853333)<-[:expr { local_id: '7248942'}]-(id2754264786) CREATE (id7853333)-[:expr { local_id: '6390693'}]->(id8059639673) CREATE (id8603083:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8603083)<-[:linear_index {linear_index: '11}']-(id282755) CREATE (id8603083)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id8603083)<-[:expr { local_id: '2009493'}]-(id1994296484) CREATE (id8603083)<-[:expr { local_id: '6390693'}]-(id8059639673) CREATE (id8603083)-[:expr { local_id: '2871066'}]->(id3906710072) CREATE (id8643391:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8643391)<-[:linear_index {linear_index: '15}']-(id282755) CREATE (id8643391)<-[:infrule]-(declareassumption) CREATE (id8643391)-[:expr { local_id: '9978909'}]->(id3920616792) CREATE (id8659528:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8659528)<-[:linear_index {linear_index: '5}']-(id282755) CREATE (id8659528)<-[:infrule]-(substituteLHSoftwoexpressionsintoexpr) CREATE (id8659528)<-[:expr { local_id: '1917654'}]-(id5563580265) CREATE (id8659528)<-[:expr { local_id: '6845877'}]-(id4627284246) CREATE (id8659528)<-[:expr { local_id: '2154616'}]-(id3176662571) CREATE (id8659528)-[:expr { local_id: '4948724'}]->(id4072200527) CREATE (id8796814:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8796814)<-[:linear_index {linear_index: '13}']-(id282755) CREATE (id8796814)<-[:infrule]-(dividebothsidesby) CREATE (id8796814)<-[:expr { local_id: '7188516'}]-(id7010294143) CREATE (id8796814)<-[:expr { local_id: '3314982'}]-(id7556442438) CREATE (id8796814)-[:expr { local_id: '6238570'}]->(id4858693811) CREATE (id9698967:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9698967)<-[:linear_index {linear_index: '2}']-(id282755) CREATE (id9698967)<-[:infrule]-(declareinitialexpr) CREATE (id9698967)-[:expr { local_id: '8242154'}]->(id9226945488) CREATE (id9835541:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9835541)<-[:linear_index {linear_index: '6}']-(id282755) CREATE (id9835541)<-[:infrule]-(changevariableXtoY) CREATE (id9835541)<-[:expr { local_id: '1115424'}]-(id6785303857) CREATE (id9835541)<-[:expr { local_id: '1893411'}]-(id1823570358) CREATE (id9835541)<-[:expr { local_id: '8115404'}]-(id3236313290) CREATE (id9835541)-[:expr { local_id: '5369477'}]->(id9262596735) CREATE (id9847336:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9847336)<-[:linear_index {linear_index: '4}']-(id282755) CREATE (id9847336)<-[:infrule]-(declareassumption) CREATE (id9847336)-[:expr { local_id: '2154616'}]->(id3176662571) CREATE (332170:derivation { name: 'equationsofmotionin1DwithconstantaccelerationSUVATalgebra', notes: 'https://en.wikipedia.org/wiki/Equations_of_motion', creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1044455:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1044455)<-[:linear_index {linear_index: '19}']-(id332170) CREATE (id1044455)<-[:infrule]-(swapLHSwithRHS) CREATE (id1044455)<-[:expr { local_id: '4127918'}]-(id9759901995) CREATE (id1044455)-[:expr { local_id: '5666935'}]->(id4748157455) CREATE (id1643757:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1643757)<-[:linear_index {linear_index: '30}']-(id332170) CREATE (id1643757)<-[:infrule]-(simplify) CREATE (id1643757)<-[:expr { local_id: '8442394'}]-(id4580545876) CREATE (id1643757)-[:expr { local_id: '3917794'}]->(id6421241247) CREATE (id2416859:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2416859)<-[:linear_index {linear_index: '1}']-(id332170) CREATE (id2416859)<-[:infrule]-(declareinitialexpr) CREATE (id2416859)-[:expr { local_id: '7864125'}]->(id3366703541) CREATE (id2562830:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2562830)<-[:linear_index {linear_index: '3}']-(id332170) CREATE (id2562830)<-[:infrule]-(addXtobothsides) CREATE (id2562830)<-[:expr { local_id: '5666935'}]-(id4748157455) CREATE (id2562830)<-[:expr { local_id: '1515971'}]-(id6417359412) CREATE (id2562830)-[:expr { local_id: '3386860'}]->(id4798787814) CREATE (id2591191:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2591191)<-[:linear_index {linear_index: '5}']-(id332170) CREATE (id2591191)<-[:infrule]-(declarefinalexpr) CREATE (id2591191)<-[:expr { local_id: '8873965'}]-(id3462972452) CREATE (id2743537:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2743537)<-[:linear_index {linear_index: '14}']-(id332170) CREATE (id2743537)<-[:infrule]-(raisebothsidestopower) CREATE (id2743537)<-[:expr { local_id: '8873965'}]-(id3462972452) CREATE (id2743537)<-[:expr { local_id: '3267212'}]-(id5799753649) CREATE (id2743537)-[:expr { local_id: '4385757'}]->(id7215099603) CREATE (id2812689:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2812689)<-[:linear_index {linear_index: '20}']-(id332170) CREATE (id2812689)<-[:infrule]-(dividebothsidesby) CREATE (id2812689)<-[:expr { local_id: '5666935'}]-(id4748157455) CREATE (id2812689)<-[:expr { local_id: '5979850'}]-(id2242144313) CREATE (id2812689)-[:expr { local_id: '8222540'}]->(id1967582749) CREATE (id2848379:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2848379)<-[:linear_index {linear_index: '12}']-(id332170) CREATE (id2848379)<-[:infrule]-(simplify) CREATE (id2848379)<-[:expr { local_id: '6881977'}]-(id1265150401) CREATE (id2848379)-[:expr { local_id: '5385244'}]->(id9658195023) CREATE (id3304384:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3304384)<-[:linear_index {linear_index: '31}']-(id332170) CREATE (id3304384)<-[:infrule]-(declarefinalexpr) CREATE (id3304384)<-[:expr { local_id: '3917794'}]-(id6421241247) CREATE (id3636217:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3636217)<-[:linear_index {linear_index: '21}']-(id332170) CREATE (id3636217)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id3636217)<-[:expr { local_id: '8222540'}]-(id1967582749) CREATE (id3636217)<-[:expr { local_id: '1476448'}]-(id8706092970) CREATE (id3636217)-[:expr { local_id: '9270356'}]->(id5733721198) CREATE (id5355580:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5355580)<-[:linear_index {linear_index: '13}']-(id332170) CREATE (id5355580)<-[:infrule]-(declarefinalexpr) CREATE (id5355580)<-[:expr { local_id: '5385244'}]-(id9658195023) CREATE (id5369106:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5369106)<-[:linear_index {linear_index: '24}']-(id332170) CREATE (id5369106)<-[:infrule]-(addXtobothsides) CREATE (id5369106)<-[:expr { local_id: '6814979'}]-(id8269198922) CREATE (id5369106)<-[:expr { local_id: '2590216'}]-(id9070454719) CREATE (id5369106)-[:expr { local_id: '7086842'}]->(id4948763856) CREATE (id5379322:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5379322)<-[:linear_index {linear_index: '16}']-(id332170) CREATE (id5379322)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id5379322)<-[:expr { local_id: '9796063'}]-(id5144263777) CREATE (id5379322)<-[:expr { local_id: '5385244'}]-(id9658195023) CREATE (id5379322)-[:expr { local_id: '7702534'}]->(id7939765107) CREATE (id5815479:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5815479)<-[:linear_index {linear_index: '9}']-(id332170) CREATE (id5815479)<-[:infrule]-(multiplybothsidesby) CREATE (id5815479)<-[:expr { local_id: '4622149'}]-(id9897284307) CREATE (id5815479)<-[:expr { local_id: '7874342'}]-(id8865085668) CREATE (id5815479)-[:expr { local_id: '1476448'}]->(id8706092970) CREATE (id6053987:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6053987)<-[:linear_index {linear_index: '17}']-(id332170) CREATE (id6053987)<-[:infrule]-(declarefinalexpr) CREATE (id6053987)<-[:expr { local_id: '7702534'}]-(id7939765107) CREATE (id6224974:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6224974)<-[:linear_index {linear_index: '28}']-(id332170) CREATE (id6224974)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id6224974)<-[:expr { local_id: '8007427'}]-(id6457044853) CREATE (id6224974)<-[:expr { local_id: '5385244'}]-(id9658195023) CREATE (id6224974)-[:expr { local_id: '5577530'}]->(id1259826355) CREATE (id6814904:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6814904)<-[:linear_index {linear_index: '29}']-(id332170) CREATE (id6814904)<-[:infrule]-(simplify) CREATE (id6814904)<-[:expr { local_id: '5577530'}]-(id1259826355) CREATE (id6814904)-[:expr { local_id: '8442394'}]->(id4580545876) CREATE (id6829719:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6829719)<-[:linear_index {linear_index: '8}']-(id332170) CREATE (id6829719)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id6829719)<-[:expr { local_id: '8658331'}]-(id3411994811) CREATE (id6829719)<-[:expr { local_id: '5013638'}]-(id6175547907) CREATE (id6829719)-[:expr { local_id: '4622149'}]->(id9897284307) CREATE (id6932861:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6932861)<-[:linear_index {linear_index: '10}']-(id332170) CREATE (id6932861)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id6932861)<-[:expr { local_id: '8873965'}]-(id3462972452) CREATE (id6932861)<-[:expr { local_id: '1476448'}]-(id8706092970) CREATE (id6932861)-[:expr { local_id: '3069767'}]->(id7011114072) CREATE (id7095007:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7095007)<-[:linear_index {linear_index: '23}']-(id332170) CREATE (id7095007)<-[:infrule]-(multiplybothsidesby) CREATE (id7095007)<-[:expr { local_id: '7103968'}]-(id5611024898) CREATE (id7095007)<-[:expr { local_id: '1522729'}]-(id5542390646) CREATE (id7095007)-[:expr { local_id: '6814979'}]->(id8269198922) CREATE (id7173255:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7173255)<-[:linear_index {linear_index: '2}']-(id332170) CREATE (id7173255)<-[:infrule]-(multiplybothsidesby) CREATE (id7173255)<-[:expr { local_id: '7864125'}]-(id3366703541) CREATE (id7173255)<-[:expr { local_id: '1647066'}]-(id7083390553) CREATE (id7173255)-[:expr { local_id: '5666935'}]->(id4748157455) CREATE (id7275831:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7275831)<-[:linear_index {linear_index: '27}']-(id332170) CREATE (id7275831)<-[:infrule]-(subtractXfrombothsides) CREATE (id7275831)<-[:expr { local_id: '8873965'}]-(id3462972452) CREATE (id7275831)<-[:expr { local_id: '9050104'}]-(id9645178657) CREATE (id7275831)-[:expr { local_id: '8007427'}]->(id6457044853) CREATE (id7602827:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7602827)<-[:linear_index {linear_index: '22}']-(id332170) CREATE (id7602827)<-[:infrule]-(simplify) CREATE (id7602827)<-[:expr { local_id: '9270356'}]-(id5733721198) CREATE (id7602827)-[:expr { local_id: '7103968'}]->(id5611024898) CREATE (id7962856:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7962856)<-[:linear_index {linear_index: '18}']-(id332170) CREATE (id7962856)<-[:infrule]-(subtractXfrombothsides) CREATE (id7962856)<-[:expr { local_id: '8873965'}]-(id3462972452) CREATE (id7962856)<-[:expr { local_id: '4852828'}]-(id6729698807) CREATE (id7962856)-[:expr { local_id: '4127918'}]->(id9759901995) CREATE (id7991401:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7991401)<-[:linear_index {linear_index: '4}']-(id332170) CREATE (id7991401)<-[:infrule]-(swapLHSwithRHS) CREATE (id7991401)<-[:expr { local_id: '3386860'}]-(id4798787814) CREATE (id7991401)-[:expr { local_id: '8873965'}]->(id3462972452) CREATE (id8096380:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8096380)<-[:linear_index {linear_index: '25}']-(id332170) CREATE (id8096380)<-[:infrule]-(swapLHSwithRHS) CREATE (id8096380)<-[:expr { local_id: '7086842'}]-(id4948763856) CREATE (id8096380)-[:expr { local_id: '7702534'}]->(id7939765107) CREATE (id8205479:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8205479)<-[:linear_index {linear_index: '15}']-(id332170) CREATE (id8205479)<-[:infrule]-(simplify) CREATE (id8205479)<-[:expr { local_id: '4385757'}]-(id7215099603) CREATE (id8205479)-[:expr { local_id: '9796063'}]->(id5144263777) CREATE (id8839945:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8839945)<-[:linear_index {linear_index: '26}']-(id332170) CREATE (id8839945)<-[:infrule]-(declarefinalexpr) CREATE (id8839945)<-[:expr { local_id: '1476448'}]-(id8706092970) CREATE (id9357941:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9357941)<-[:linear_index {linear_index: '11}']-(id332170) CREATE (id9357941)<-[:infrule]-(simplify) CREATE (id9357941)<-[:expr { local_id: '3069767'}]-(id7011114072) CREATE (id9357941)-[:expr { local_id: '6881977'}]->(id1265150401) CREATE (id9381314:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9381314)<-[:linear_index {linear_index: '7}']-(id332170) CREATE (id9381314)<-[:infrule]-(declareinitialexpr) CREATE (id9381314)-[:expr { local_id: '5013638'}]->(id6175547907) CREATE (id9823399:step { creation_date: '2020-05-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9823399)<-[:linear_index {linear_index: '6}']-(id332170) CREATE (id9823399)<-[:infrule]-(declareinitialexpr) CREATE (id9823399)-[:expr { local_id: '8658331'}]->(id3411994811) CREATE (374317:derivation { name: 'velocityatdistancerofobjectdroppedfrominfinity', notes: 'https://www.youtube.com/watch?v=5F1XcTjpJs4 - Derivation of Gravitational Potential Energy by Rhett Allain', creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1153771:step { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1153771)<-[:linear_index {linear_index: '5}']-(id374317) CREATE (id1153771)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1153771)<-[:expr { local_id: '3470082'}]-(id5902985919) CREATE (id1153771)<-[:expr { local_id: '6798426'}]-(id7882872592) CREATE (id1153771)-[:expr { local_id: '7300369'}]->(id3566149658) CREATE (id1302085:step { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1302085)<-[:linear_index {linear_index: '2}']-(id374317) CREATE (id1302085)<-[:infrule]-(declareinitialexpr) CREATE (id1302085)-[:expr { local_id: '3470082'}]->(id5902985919) CREATE (id1322174:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1322174)<-[:linear_index {linear_index: '12}']-(id374317) CREATE (id1322174)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1322174)<-[:expr { local_id: '9781919'}]-(id8049905441) CREATE (id1322174)<-[:expr { local_id: '9835406'}]-(id1114820451) CREATE (id1322174)-[:expr { local_id: '8118190'}]->(id5779256336) CREATE (id1875894:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1875894)<-[:linear_index {linear_index: '15}']-(id374317) CREATE (id1875894)<-[:infrule]-(declareinitialexpr) CREATE (id1875894)-[:expr { local_id: '1712972'}]->(id2924222857) CREATE (id1962578:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1962578)<-[:linear_index {linear_index: '8}']-(id374317) CREATE (id1962578)<-[:infrule]-(simplify) CREATE (id1962578)<-[:expr { local_id: '5818573'}]-(id5596822289) CREATE (id1962578)-[:expr { local_id: '2429271'}]->(id2061086175) CREATE (id2603561:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2603561)<-[:linear_index {linear_index: '11}']-(id374317) CREATE (id2603561)<-[:infrule]-(declareinitialexpr) CREATE (id2603561)-[:expr { local_id: '5104592'}]->(id8357234146) CREATE (id2893958:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2893958)<-[:linear_index {linear_index: '26}']-(id374317) CREATE (id2893958)<-[:infrule]-(declarefinalexpr) CREATE (id2893958)<-[:expr { local_id: '3435796'}]-(id2005061870) CREATE (id3433370:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3433370)<-[:linear_index {linear_index: '7}']-(id374317) CREATE (id3433370)<-[:infrule]-(evaluatedefiniteintegral) CREATE (id3433370)<-[:expr { local_id: '9707318'}]-(id8405272745) CREATE (id3433370)-[:expr { local_id: '5818573'}]->(id5596822289) CREATE (id3576436:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3576436)<-[:linear_index {linear_index: '9}']-(id374317) CREATE (id3576436)<-[:infrule]-(simplify) CREATE (id3576436)<-[:expr { local_id: '2429271'}]-(id2061086175) CREATE (id3576436)-[:expr { local_id: '4947999'}]->(id4393670960) CREATE (id3577090:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3577090)<-[:linear_index {linear_index: '25}']-(id374317) CREATE (id3577090)<-[:infrule]-(changevariableXtoY) CREATE (id3577090)<-[:expr { local_id: '7112224'}]-(id5846639423) CREATE (id3577090)<-[:expr { local_id: '1383337'}]-(id6599829782) CREATE (id3577090)<-[:expr { local_id: '6547572'}]-(id3531380618) CREATE (id3577090)-[:expr { local_id: '3435796'}]->(id2005061870) CREATE (id3633525:step { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3633525)<-[:linear_index {linear_index: '6}']-(id374317) CREATE (id3633525)<-[:infrule]-(simplify) CREATE (id3633525)<-[:expr { local_id: '7300369'}]-(id3566149658) CREATE (id3633525)-[:expr { local_id: '9707318'}]->(id8405272745) CREATE (id3641174:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3641174)<-[:linear_index {linear_index: '16}']-(id374317) CREATE (id3641174)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3641174)<-[:expr { local_id: '8462685'}]-(id3214170322) CREATE (id3641174)<-[:expr { local_id: '1712972'}]-(id2924222857) CREATE (id3641174)-[:expr { local_id: '6923850'}]->(id2998709778) CREATE (id3660209:step { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3660209)<-[:linear_index {linear_index: '3}']-(id374317) CREATE (id3660209)<-[:infrule]-(declareinitialexpr) CREATE (id3660209)-[:expr { local_id: '9835406'}]->(id1114820451) CREATE (id3724598:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3724598)<-[:linear_index {linear_index: '18}']-(id374317) CREATE (id3724598)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3724598)<-[:expr { local_id: '7110498'}]-(id9510328252) CREATE (id3724598)<-[:expr { local_id: '8118190'}]-(id5779256336) CREATE (id3724598)-[:expr { local_id: '2751634'}]->(id5850144586) CREATE (id4513518:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4513518)<-[:linear_index {linear_index: '10}']-(id374317) CREATE (id4513518)<-[:infrule]-(declareinitialexpr) CREATE (id4513518)-[:expr { local_id: '9781919'}]->(id8049905441) CREATE (id5188363:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5188363)<-[:linear_index {linear_index: '13}']-(id374317) CREATE (id5188363)<-[:infrule]-(changethreevariablesinexpr) CREATE (id5188363)<-[:expr { local_id: '5104592'}]-(id8357234146) CREATE (id5188363)<-[:expr { local_id: '8771215'}]-(id3731774096) CREATE (id5188363)<-[:expr { local_id: '2089366'}]-(id3350802342) CREATE (id5188363)<-[:expr { local_id: '1530135'}]-(id5904227750) CREATE (id5188363)<-[:expr { local_id: '4230607'}]-(id6281834543) CREATE (id5188363)<-[:expr { local_id: '5239069'}]-(id8066819515) CREATE (id5188363)<-[:expr { local_id: '2668466'}]-(id3274176452) CREATE (id5188363)-[:expr { local_id: '9031887'}]->(id6091977310) CREATE (id5454987:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5454987)<-[:linear_index {linear_index: '21}']-(id374317) CREATE (id5454987)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5454987)<-[:expr { local_id: '6536576'}]-(id9081138616) CREATE (id5454987)<-[:expr { local_id: '2619766'}]-(id2907404069) CREATE (id5454987)-[:expr { local_id: '8655239'}]->(id4947831649) CREATE (id5679035:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5679035)<-[:linear_index {linear_index: '20}']-(id374317) CREATE (id5679035)<-[:infrule]-(declareinitialexpr) CREATE (id5679035)-[:expr { local_id: '2619766'}]->(id2907404069) CREATE (id6228957:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6228957)<-[:linear_index {linear_index: '22}']-(id374317) CREATE (id6228957)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6228957)<-[:expr { local_id: '4947999'}]-(id4393670960) CREATE (id6228957)<-[:expr { local_id: '8655239'}]-(id4947831649) CREATE (id6228957)-[:expr { local_id: '2942416'}]->(id6892595652) CREATE (id7795985:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7795985)<-[:linear_index {linear_index: '17}']-(id374317) CREATE (id7795985)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7795985)<-[:expr { local_id: '6923850'}]-(id2998709778) CREATE (id7795985)<-[:expr { local_id: '9031887'}]-(id6091977310) CREATE (id7795985)-[:expr { local_id: '7110498'}]->(id9510328252) CREATE (id7925705:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7925705)<-[:linear_index {linear_index: '14}']-(id374317) CREATE (id7925705)<-[:infrule]-(changethreevariablesinexpr) CREATE (id7925705)<-[:expr { local_id: '5104592'}]-(id8357234146) CREATE (id7925705)<-[:expr { local_id: '5647474'}]-(id4587046017) CREATE (id7925705)<-[:expr { local_id: '1175033'}]-(id3939572542) CREATE (id7925705)<-[:expr { local_id: '4353144'}]-(id9350720370) CREATE (id7925705)<-[:expr { local_id: '1515675'}]-(id3166466250) CREATE (id7925705)<-[:expr { local_id: '3538025'}]-(id6038673136) CREATE (id7925705)<-[:expr { local_id: '1983598'}]-(id1616666229) CREATE (id7925705)-[:expr { local_id: '1397156'}]->(id8552710882) CREATE (id7936249:step { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7936249)<-[:linear_index {linear_index: '4}']-(id374317) CREATE (id7936249)<-[:infrule]-(declareinitialexpr) CREATE (id7936249)-[:expr { local_id: '6798426'}]->(id7882872592) CREATE (id8435512:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8435512)<-[:linear_index {linear_index: '24}']-(id374317) CREATE (id8435512)<-[:infrule]-(squarerootbothsides) CREATE (id8435512)<-[:expr { local_id: '4594601'}]-(id7112646057) CREATE (id8435512)-[:expr { local_id: '7112224'}]->(id5846639423) CREATE (id8435512)-[:expr { local_id: '1366396'}]->(id5693047217) CREATE (id9878340:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9878340)<-[:linear_index {linear_index: '19}']-(id374317) CREATE (id9878340)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id9878340)<-[:expr { local_id: '1397156'}]-(id8552710882) CREATE (id9878340)<-[:expr { local_id: '2751634'}]-(id5850144586) CREATE (id9878340)-[:expr { local_id: '6536576'}]->(id9081138616) CREATE (id9887933:step { creation_date: '2020-08-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9887933)<-[:linear_index {linear_index: '23}']-(id374317) CREATE (id9887933)<-[:infrule]-(multiplybothsidesby) CREATE (id9887933)<-[:expr { local_id: '2942416'}]-(id6892595652) CREATE (id9887933)<-[:expr { local_id: '3542696'}]-(id7410526982) CREATE (id9887933)-[:expr { local_id: '4594601'}]->(id7112646057) CREATE (id9935422:step { creation_date: '2020-08-10', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9935422)<-[:linear_index {linear_index: '1}']-(id374317) CREATE (id9935422)<-[:infrule]-(declareinitialexpr) CREATE (id9935422)-[:expr { local_id: '8462685'}]->(id3214170322) CREATE (375160:derivation { name: 'coefficientofisothermalcompressibilityusingtheequationofstateforanidealgas', notes: 'https://notendur.hi.is/hj/EE2/HD1lausn.pdf', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1059017:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1059017)<-[:linear_index {linear_index: '9}']-(id375160) CREATE (id1059017)<-[:infrule]-(declarefinalexpr) CREATE (id1059017)<-[:expr { local_id: '2206759'}]-(id9718685793) CREATE (id1873674:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1873674)<-[:linear_index {linear_index: '6}']-(id375160) CREATE (id1873674)<-[:infrule]-(simplify) CREATE (id1873674)<-[:expr { local_id: '3915956'}]-(id1190768176) CREATE (id1873674)-[:expr { local_id: '6275836'}]->(id3605073197) CREATE (id3831533:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3831533)<-[:linear_index {linear_index: '1}']-(id375160) CREATE (id3831533)<-[:infrule]-(declareinitialexpr) CREATE (id3831533)-[:expr { local_id: '4239912'}]->(id9781951738) CREATE (id3862516:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3862516)<-[:linear_index {linear_index: '3}']-(id375160) CREATE (id3862516)<-[:infrule]-(dividebothsidesby) CREATE (id3862516)<-[:expr { local_id: '4454896'}]-(id8435841627) CREATE (id3862516)<-[:expr { local_id: '6719179'}]-(id6296166842) CREATE (id3862516)-[:expr { local_id: '5840241'}]->(id3497828859) CREATE (id5391858:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5391858)<-[:linear_index {linear_index: '7}']-(id375160) CREATE (id5391858)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5391858)<-[:expr { local_id: '4454896'}]-(id8435841627) CREATE (id5391858)<-[:expr { local_id: '6275836'}]-(id3605073197) CREATE (id5391858)-[:expr { local_id: '1003658'}]->(id9847143017) CREATE (id6914144:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6914144)<-[:linear_index {linear_index: '5}']-(id375160) CREATE (id6914144)<-[:infrule]-(simplify) CREATE (id6914144)<-[:expr { local_id: '5196207'}]-(id8368984890) CREATE (id6914144)-[:expr { local_id: '3915956'}]->(id1190768176) CREATE (id8648371:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8648371)<-[:linear_index {linear_index: '8}']-(id375160) CREATE (id8648371)<-[:infrule]-(simplify) CREATE (id8648371)<-[:expr { local_id: '1003658'}]-(id9847143017) CREATE (id8648371)-[:expr { local_id: '2206759'}]->(id9718685793) CREATE (id9225696:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9225696)<-[:linear_index {linear_index: '4}']-(id375160) CREATE (id9225696)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id9225696)<-[:expr { local_id: '5840241'}]-(id3497828859) CREATE (id9225696)<-[:expr { local_id: '4239912'}]-(id9781951738) CREATE (id9225696)-[:expr { local_id: '5196207'}]->(id8368984890) CREATE (id9872032:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9872032)<-[:linear_index {linear_index: '2}']-(id375160) CREATE (id9872032)<-[:infrule]-(declareinitialexpr) CREATE (id9872032)-[:expr { local_id: '4454896'}]->(id8435841627) CREATE (387954:derivation { name: 'speedofEartharoundSun', notes: 'from \cite{1999_Tipler_Llewellyn}, page 9', creation_date: '2020-05-06', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1143551:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1143551)<-[:linear_index {linear_index: '13}']-(id387954) CREATE (id1143551)<-[:infrule]-(declarefinalexpr) CREATE (id1143551)<-[:expr { local_id: '1001745'}]-(id4180845508) CREATE (id1317920:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1317920)<-[:linear_index {linear_index: '6}']-(id387954) CREATE (id1317920)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1317920)<-[:expr { local_id: '5753220'}]-(id6348260313) CREATE (id1317920)<-[:expr { local_id: '5320197'}]-(id3046191961) CREATE (id1317920)-[:expr { local_id: '9129246'}]->(id3080027960) CREATE (id1909003:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1909003)<-[:linear_index {linear_index: '12}']-(id387954) CREATE (id1909003)<-[:infrule]-(simplify) CREATE (id1909003)<-[:expr { local_id: '8698819'}]-(id6998364753) CREATE (id1909003)-[:expr { local_id: '1001745'}]->(id4180845508) CREATE (id3035476:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3035476)<-[:linear_index {linear_index: '9}']-(id387954) CREATE (id3035476)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3035476)<-[:expr { local_id: '9417128'}]-(id8721295221) CREATE (id3035476)<-[:expr { local_id: '9129246'}]-(id3080027960) CREATE (id3035476)-[:expr { local_id: '1441436'}]->(id4593428198) CREATE (id3198144:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3198144)<-[:linear_index {linear_index: '3}']-(id387954) CREATE (id3198144)<-[:infrule]-(declareinitialexpr) CREATE (id3198144)-[:expr { local_id: '7959026'}]->(id6785303857) CREATE (id5559943:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5559943)<-[:linear_index {linear_index: '10}']-(id387954) CREATE (id5559943)<-[:infrule]-(declareassumption) CREATE (id5559943)-[:expr { local_id: '4133484'}]->(id3472836147) CREATE (id5700345:step { creation_date: '2020-05-06', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5700345)<-[:linear_index {linear_index: '2}']-(id387954) CREATE (id5700345)<-[:infrule]-(changevariableXtoY) CREATE (id5700345)<-[:expr { local_id: '1131405'}]-(id5426308937) CREATE (id5700345)<-[:expr { local_id: '8635770'}]-(id1277713901) CREATE (id5700345)<-[:expr { local_id: '1022830'}]-(id7476820482) CREATE (id5700345)-[:expr { local_id: '7360652'}]->(id6946088325) CREATE (id6292792:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6292792)<-[:linear_index {linear_index: '7}']-(id387954) CREATE (id6292792)<-[:infrule]-(declareassumption) CREATE (id6292792)-[:expr { local_id: '9494155'}]->(id7175416299) CREATE (id6456434:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6456434)<-[:linear_index {linear_index: '5}']-(id387954) CREATE (id6456434)<-[:infrule]-(changethreevariablesinexpr) CREATE (id6456434)<-[:expr { local_id: '7360652'}]-(id6946088325) CREATE (id6456434)<-[:expr { local_id: '3915320'}]-(id4057686137) CREATE (id6456434)<-[:expr { local_id: '8725566'}]-(id7708501762) CREATE (id6456434)<-[:expr { local_id: '6364366'}]-(id9753878784) CREATE (id6456434)<-[:expr { local_id: '4451366'}]-(id9601500174) CREATE (id6456434)<-[:expr { local_id: '4443760'}]-(id8135396036) CREATE (id6456434)<-[:expr { local_id: '1489039'}]-(id4470433702) CREATE (id6456434)-[:expr { local_id: '5320197'}]->(id3046191961) CREATE (id9488257:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9488257)<-[:linear_index {linear_index: '4}']-(id387954) CREATE (id9488257)<-[:infrule]-(changetwovariablesinexpr) CREATE (id9488257)<-[:expr { local_id: '7959026'}]-(id6785303857) CREATE (id9488257)<-[:expr { local_id: '3915321'}]-(id4057686137) CREATE (id9488257)<-[:expr { local_id: '5440162'}]-(id6239815585) CREATE (id9488257)<-[:expr { local_id: '3383852'}]-(id2346150725) CREATE (id9488257)<-[:expr { local_id: '9586925'}]-(id4202292449) CREATE (id9488257)-[:expr { local_id: '5753220'}]->(id6348260313) CREATE (id9626463:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9626463)<-[:linear_index {linear_index: '8}']-(id387954) CREATE (id9626463)<-[:infrule]-(multiplyRHSbyunity) CREATE (id9626463)<-[:expr { local_id: '9494155'}]-(id7175416299) CREATE (id9626463)<-[:expr { local_id: '4603243'}]-(id3219318145) CREATE (id9626463)-[:expr { local_id: '9417128'}]->(id8721295221) CREATE (id9784411:step { creation_date: '2020-05-06', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9784411)<-[:linear_index {linear_index: '1}']-(id387954) CREATE (id9784411)<-[:infrule]-(declareinitialexpr) CREATE (id9784411)-[:expr { local_id: '1131405'}]->(id5426308937) CREATE (id9955987:step { creation_date: '2020-05-07', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9955987)<-[:linear_index {linear_index: '11}']-(id387954) CREATE (id9955987)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id9955987)<-[:expr { local_id: '4133484'}]-(id3472836147) CREATE (id9955987)<-[:expr { local_id: '1441436'}]-(id4593428198) CREATE (id9955987)-[:expr { local_id: '8698819'}]->(id6998364753) CREATE (513999:derivation { name: 'firstlawofthermodynamics', notes: 'https://www.youtube.com/watch?v=QTiqF-HtkS0 and https://www.youtube.com/watch?v=3Yls-t3B49U', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1993589:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1993589)<-[:linear_index {linear_index: '9}']-(id513999) CREATE (id1993589)<-[:infrule]-(multiplybothsidesby) CREATE (id1993589)<-[:expr { local_id: '2714175'}]-(id3464107376) CREATE (id1993589)<-[:expr { local_id: '5246571'}]-(id5074423401) CREATE (id1993589)-[:expr { local_id: '7939101'}]->(id6397683463) CREATE (id2711162:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2711162)<-[:linear_index {linear_index: '6}']-(id513999) CREATE (id2711162)<-[:infrule]-(substituteLHSoftwoexpressionsintoexpr) CREATE (id2711162)<-[:expr { local_id: '4576755'}]-(id1085150613) CREATE (id2711162)<-[:expr { local_id: '7384950'}]-(id5634116660) CREATE (id2711162)<-[:expr { local_id: '2445123'}]-(id9941599459) CREATE (id2711162)-[:expr { local_id: '5358683'}]->(id5002539602) CREATE (id4779130:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4779130)<-[:linear_index {linear_index: '8}']-(id513999) CREATE (id4779130)<-[:infrule]-(declareinitialexpr) CREATE (id4779130)-[:expr { local_id: '2714175'}]->(id3464107376) CREATE (id4965571:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4965571)<-[:linear_index {linear_index: '1}']-(id513999) CREATE (id4965571)<-[:infrule]-(declareinitialexpr) CREATE (id4965571)-[:expr { local_id: '7368252'}]->(id1815398659) CREATE (id5592617:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5592617)<-[:linear_index {linear_index: '7}']-(id513999) CREATE (id5592617)<-[:infrule]-(dividebothsidesby) CREATE (id5592617)<-[:expr { local_id: '5358683'}]-(id5002539602) CREATE (id5592617)<-[:expr { local_id: '9803021'}]-(id8854422847) CREATE (id5592617)-[:expr { local_id: '3830663'}]->(id6055078815) CREATE (id6605632:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6605632)<-[:linear_index {linear_index: '11}']-(id513999) CREATE (id6605632)<-[:infrule]-(simplify) CREATE (id6605632)<-[:expr { local_id: '1136968'}]-(id2257410739) CREATE (id6605632)-[:expr { local_id: '1189259'}]->(id7826132469) CREATE (id6666476:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6666476)<-[:linear_index {linear_index: '5}']-(id513999) CREATE (id6666476)<-[:infrule]-(declareinitialexpr) CREATE (id6666476)-[:expr { local_id: '7384950'}]->(id5634116660) CREATE (id7017521:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7017521)<-[:linear_index {linear_index: '10}']-(id513999) CREATE (id7017521)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7017521)<-[:expr { local_id: '7939101'}]-(id6397683463) CREATE (id7017521)<-[:expr { local_id: '3830663'}]-(id6055078815) CREATE (id7017521)-[:expr { local_id: '1136968'}]->(id2257410739) CREATE (id7164757:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7164757)<-[:linear_index {linear_index: '2}']-(id513999) CREATE (id7164757)<-[:infrule]-(declareinitialexpr) CREATE (id7164757)-[:expr { local_id: '2445123'}]->(id9941599459) CREATE (id8168352:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8168352)<-[:linear_index {linear_index: '3}']-(id513999) CREATE (id8168352)<-[:infrule]-(declareinitialexpr) CREATE (id8168352)-[:expr { local_id: '8155541'}]->(id3547519267) CREATE (id9131071:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9131071)<-[:linear_index {linear_index: '4}']-(id513999) CREATE (id9131071)<-[:infrule]-(declareinitialexpr) CREATE (id9131071)-[:expr { local_id: '4576755'}]->(id1085150613) CREATE (id9782579:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9782579)<-[:linear_index {linear_index: '12}']-(id513999) CREATE (id9782579)<-[:infrule]-(declareinitialexpr) CREATE (id9782579)-[:expr { local_id: '9670239'}]->(id9781951738) CREATE (522862:derivation { name: 'opticsLawofrefractiontoBrewstersangle', notes: '\cite{2001_HRW}; see figure 34-27 on page 824', creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1148993:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1148993)<-[:linear_index {linear_index: '6}']-(id522862) CREATE (id1148993)<-[:infrule]-(declareidentity) CREATE (id1148993)-[:expr { local_id: '3940135'}]->(id8588429722) CREATE (id1206301:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1206301)<-[:linear_index {linear_index: '8}']-(id522862) CREATE (id1206301)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1206301)<-[:expr { local_id: '7426234'}]-(id6831637424) CREATE (id1206301)<-[:expr { local_id: '4962698'}]-(id7696214507) CREATE (id1206301)-[:expr { local_id: '9701820'}]->(id3061811650) CREATE (id2068603:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2068603)<-[:linear_index {linear_index: '15}']-(id522862) CREATE (id2068603)<-[:infrule]-(declarefinalexpr) CREATE (id2068603)<-[:expr { local_id: '8186016'}]-(id8495187962) CREATE (id2215432:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2215432)<-[:linear_index {linear_index: '3}']-(id522862) CREATE (id2215432)<-[:infrule]-(declareinitialexpr) CREATE (id2215432)-[:expr { local_id: '9932375'}]->(id6450985774) CREATE (id2967028:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2967028)<-[:linear_index {linear_index: '11}']-(id522862) CREATE (id2967028)<-[:infrule]-(declareidentity) CREATE (id2967028)-[:expr { local_id: '2621708'}]->(id4968680693) CREATE (id3169869:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3169869)<-[:linear_index {linear_index: '9}']-(id522862) CREATE (id3169869)<-[:infrule]-(dividebothsidesby) CREATE (id3169869)<-[:expr { local_id: '9701820'}]-(id3061811650) CREATE (id3169869)<-[:expr { local_id: '2502645'}]-(id7857757625) CREATE (id3169869)-[:expr { local_id: '9314305'}]->(id9756089533) CREATE (id5001869:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5001869)<-[:linear_index {linear_index: '5}']-(id522862) CREATE (id5001869)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5001869)<-[:expr { local_id: '3893026'}]-(id1310571337) CREATE (id5001869)<-[:expr { local_id: '4176694'}]-(id2575937347) CREATE (id5001869)-[:expr { local_id: '4962698'}]->(id7696214507) CREATE (id5372769:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5372769)<-[:linear_index {linear_index: '4}']-(id522862) CREATE (id5372769)<-[:infrule]-(changetwovariablesinexpr) CREATE (id5372769)<-[:expr { local_id: '9932375'}]-(id6450985774) CREATE (id5372769)<-[:expr { local_id: '1539856'}]-(id7154592211) CREATE (id5372769)<-[:expr { local_id: '3700347'}]-(id6353701615) CREATE (id5372769)<-[:expr { local_id: '9873426'}]-(id2773628333) CREATE (id5372769)<-[:expr { local_id: '8587761'}]-(id9029795851) CREATE (id5372769)-[:expr { local_id: '4176694'}]->(id2575937347) CREATE (id6119314:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6119314)<-[:linear_index {linear_index: '12}']-(id522862) CREATE (id6119314)<-[:infrule]-(changevariableXtoY) CREATE (id6119314)<-[:expr { local_id: '2621708'}]-(id4968680693) CREATE (id6119314)<-[:expr { local_id: '4429055'}]-(id7321695558) CREATE (id6119314)<-[:expr { local_id: '1588002'}]-(id9906920183) CREATE (id6119314)-[:expr { local_id: '1898054'}]->(id4501377629) CREATE (id6146931:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6146931)<-[:linear_index {linear_index: '13}']-(id522862) CREATE (id6146931)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6146931)<-[:expr { local_id: '1898054'}]-(id4501377629) CREATE (id6146931)<-[:expr { local_id: '8585856'}]-(id2768857871) CREATE (id6146931)-[:expr { local_id: '5179630'}]->(id3417126140) CREATE (id7919446:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7919446)<-[:linear_index {linear_index: '1}']-(id522862) CREATE (id7919446)<-[:infrule]-(declareinitialexpr) CREATE (id7919446)-[:expr { local_id: '5563180'}]->(id8945218208) CREATE (id8072315:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8072315)<-[:linear_index {linear_index: '14}']-(id522862) CREATE (id8072315)<-[:infrule]-(applyfunctiontobothsidesofexpression) CREATE (id8072315)<-[:expr { local_id: '5179630'}]-(id3417126140) CREATE (id8072315)<-[:expr { local_id: '2844676'}]-(id5453995431) CREATE (id8072315)<-[:expr { local_id: '9430397'}]-(id6023986360) CREATE (id8072315)-[:expr { local_id: '8186016'}]->(id8495187962) CREATE (id8509796:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8509796)<-[:linear_index {linear_index: '10}']-(id522862) CREATE (id8509796)<-[:infrule]-(dividebothsidesby) CREATE (id8509796)<-[:expr { local_id: '9314305'}]-(id9756089533) CREATE (id8509796)<-[:expr { local_id: '6763636'}]-(id5632428182) CREATE (id8509796)-[:expr { local_id: '8585856'}]->(id2768857871) CREATE (id9056504:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9056504)<-[:linear_index {linear_index: '7}']-(id522862) CREATE (id9056504)<-[:infrule]-(changevariableXtoY) CREATE (id9056504)<-[:expr { local_id: '3940135'}]-(id8588429722) CREATE (id9056504)<-[:expr { local_id: '8421271'}]-(id7375348852) CREATE (id9056504)<-[:expr { local_id: '9516318'}]-(id1512581563) CREATE (id9056504)-[:expr { local_id: '7426234'}]->(id6831637424) CREATE (id9582699:step { creation_date: '2020-04-23', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9582699)<-[:linear_index {linear_index: '2}']-(id522862) CREATE (id9582699)<-[:infrule]-(subtractXfrombothsides) CREATE (id9582699)<-[:expr { local_id: '5563180'}]-(id8945218208) CREATE (id9582699)<-[:expr { local_id: '7475090'}]-(id9025853427) CREATE (id9582699)-[:expr { local_id: '3893026'}]->(id1310571337) CREATE (527822:derivation { name: 'massoftheEarth', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1220683:step { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1220683)<-[:linear_index {linear_index: '6}']-(id527822) CREATE (id1220683)<-[:infrule]-(replaceconstantwithvalue) CREATE (id1220683)<-[:expr { local_id: '9133599'}]-(id9440616166) CREATE (id1220683)<-[:expr { local_id: '1042264'}]-(id2091584724) CREATE (id1220683)<-[:expr { local_id: '3982459'}]-(id9590696981) CREATE (id1220683)<-[:expr { local_id: '7373814'}]-(id7816982139) CREATE (id1220683)-[:expr { local_id: '2593741'}]->(id7846240076) CREATE (id1400184:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1400184)<-[:linear_index {linear_index: '4}']-(id527822) CREATE (id1400184)<-[:infrule]-(dividebothsidesby) CREATE (id1400184)<-[:expr { local_id: '7388891'}]-(id9407192813) CREATE (id1400184)<-[:expr { local_id: '2061733'}]-(id3246378279) CREATE (id1400184)-[:expr { local_id: '9159337'}]->(id2308660627) CREATE (id1874718:step { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1874718)<-[:linear_index {linear_index: '8}']-(id527822) CREATE (id1874718)<-[:infrule]-(replaceconstantwithvalue) CREATE (id1874718)<-[:expr { local_id: '1218257'}]-(id7112613117) CREATE (id1874718)<-[:expr { local_id: '4110249'}]-(id7935917166) CREATE (id1874718)<-[:expr { local_id: '3566114'}]-(id3723096423) CREATE (id1874718)<-[:expr { local_id: '8415948'}]-(id7560908617) CREATE (id1874718)-[:expr { local_id: '9815516'}]->(id1132941271) CREATE (id2667299:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2667299)<-[:linear_index {linear_index: '1}']-(id527822) CREATE (id2667299)<-[:infrule]-(changevariableXtoY) CREATE (id2667299)<-[:expr { local_id: '3843242'}]-(id5345738321) CREATE (id2667299)<-[:expr { local_id: '9132281'}]-(id9881106100) CREATE (id2667299)<-[:expr { local_id: '4041665'}]-(id5781435087) CREATE (id2667299)-[:expr { local_id: '6779814'}]->(id2484824786) CREATE (id3237021:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3237021)<-[:linear_index {linear_index: '2}']-(id527822) CREATE (id3237021)<-[:infrule]-(changethreevariablesinexpr) CREATE (id3237021)<-[:expr { local_id: '2737346'}]-(id6935745841) CREATE (id3237021)<-[:expr { local_id: '9478532'}]-(id3921072591) CREATE (id3237021)<-[:expr { local_id: '4879958'}]-(id1193980495) CREATE (id3237021)<-[:expr { local_id: '8914722'}]-(id4651061153) CREATE (id3237021)<-[:expr { local_id: '2716715'}]-(id9903988330) CREATE (id3237021)<-[:expr { local_id: '1333038'}]-(id3353418803) CREATE (id3237021)<-[:expr { local_id: '7054973'}]-(id6535639720) CREATE (id3237021)-[:expr { local_id: '6771172'}]->(id8661803554) CREATE (id3858247:step { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3858247)<-[:linear_index {linear_index: '9}']-(id527822) CREATE (id3858247)<-[:infrule]-(simplify) CREATE (id3858247)<-[:expr { local_id: '9815516'}]-(id1132941271) CREATE (id3858247)-[:expr { local_id: '1635641'}]->(id3364286646) CREATE (id5760226:step { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5760226)<-[:linear_index {linear_index: '7}']-(id527822) CREATE (id5760226)<-[:infrule]-(replaceconstantwithvalue) CREATE (id5760226)<-[:expr { local_id: '2593741'}]-(id7846240076) CREATE (id5760226)<-[:expr { local_id: '2156099'}]-(id7326066466) CREATE (id5760226)<-[:expr { local_id: '5000579'}]-(id9956609318) CREATE (id5760226)<-[:expr { local_id: '1522932'}]-(id2957211007) CREATE (id5760226)-[:expr { local_id: '1218257'}]->(id7112613117) CREATE (id6200455:step { creation_date: '2020-05-28', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6200455)<-[:linear_index {linear_index: '0.5}']-(id527822) CREATE (id6200455)<-[:infrule]-(declareinitialexpr) CREATE (id6200455)-[:expr { local_id: '3843242'}]->(id5345738321) CREATE (id6715984:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6715984)<-[:linear_index {linear_index: '3}']-(id527822) CREATE (id6715984)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id6715984)<-[:expr { local_id: '6771172'}]-(id8661803554) CREATE (id6715984)<-[:expr { local_id: '6086107'}]-(id4800170179) CREATE (id6715984)-[:expr { local_id: '7388891'}]->(id9407192813) CREATE (id8079031:step { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8079031)<-[:linear_index {linear_index: '1.5}']-(id527822) CREATE (id8079031)<-[:infrule]-(declareinitialexpr) CREATE (id8079031)-[:expr { local_id: '2737346'}]->(id6935745841) CREATE (id9601593:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9601593)<-[:linear_index {linear_index: '5}']-(id527822) CREATE (id9601593)<-[:infrule]-(multiplybothsidesby) CREATE (id9601593)<-[:expr { local_id: '9159337'}]-(id2308660627) CREATE (id9601593)<-[:expr { local_id: '8784765'}]-(id2685587762) CREATE (id9601593)-[:expr { local_id: '9133599'}]->(id9440616166) CREATE (id9676005:step { creation_date: '2020-05-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9676005)<-[:linear_index {linear_index: '1.25}']-(id527822) CREATE (id9676005)<-[:infrule]-(changevariableXtoY) CREATE (id9676005)<-[:expr { local_id: '6779814'}]-(id2484824786) CREATE (id9676005)<-[:expr { local_id: '4510044'}]-(id9355039511) CREATE (id9676005)<-[:expr { local_id: '8916427'}]-(id2232825726) CREATE (id9676005)-[:expr { local_id: '6086107'}]->(id4800170179) CREATE (539398:derivation { name: 'doubleintensitywhenphaseiscoherentoptics', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1304801:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1304801)<-[:linear_index {linear_index: '24}']-(id539398) CREATE (id1304801)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1304801)<-[:expr { local_id: '7781977'}]-(id6774684564) CREATE (id1304801)<-[:expr { local_id: '5493675'}]-(id8497631728) CREATE (id1304801)-[:expr { local_id: '2413866'}]->(id8283354808) CREATE (id1330727:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1330727)<-[:linear_index {linear_index: '13}']-(id539398) CREATE (id1330727)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1330727)<-[:expr { local_id: '2303305'}]-(id7107090465) CREATE (id1330727)<-[:expr { local_id: '4729665'}]-(id5125940051) CREATE (id1330727)-[:expr { local_id: '8296872'}]->(id1525861537) CREATE (id1410856:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1410856)<-[:linear_index {linear_index: '29}']-(id539398) CREATE (id1410856)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1410856)<-[:expr { local_id: '4842351'}]-(id8602221482) CREATE (id1410856)<-[:expr { local_id: '5493675'}]-(id8497631728) CREATE (id1410856)-[:expr { local_id: '8093224'}]->(id6240206408) CREATE (id1791333:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1791333)<-[:linear_index {linear_index: '18}']-(id539398) CREATE (id1791333)<-[:infrule]-(substituteLHSoffourexpressionsintoexpr) CREATE (id1791333)<-[:expr { local_id: '7875296'}]-(id4192519596) CREATE (id1791333)<-[:expr { local_id: '1174231'}]-(id4504256452) CREATE (id1791333)<-[:expr { local_id: '2018605'}]-(id1357848476) CREATE (id1791333)-[:expr { local_id: '1405078'}]->(id7621705408) CREATE (id2270901:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2270901)<-[:linear_index {linear_index: '15}']-(id539398) CREATE (id2270901)<-[:infrule]-(changevariableXtoY) CREATE (id2270901)<-[:expr { local_id: '4809503'}]-(id4182362050) CREATE (id2270901)<-[:expr { local_id: '4787865'}]-(id2064205392) CREATE (id2270901)<-[:expr { local_id: '9108208'}]-(id1894894315) CREATE (id2270901)-[:expr { local_id: '2018605'}]->(id1357848476) CREATE (id3099726:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3099726)<-[:linear_index {linear_index: '25}']-(id539398) CREATE (id3099726)<-[:infrule]-(declareinitialexpr) CREATE (id3099726)-[:expr { local_id: '9739736'}]->(id2719691582) CREATE (id3105609:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3105609)<-[:linear_index {linear_index: '31}']-(id539398) CREATE (id3105609)<-[:infrule]-(simplify) CREATE (id3105609)<-[:expr { local_id: '5409843'}]-(id6529793063) CREATE (id3105609)-[:expr { local_id: '3246829'}]->(id3060393541) CREATE (id3232460:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3232460)<-[:linear_index {linear_index: '22}']-(id539398) CREATE (id3232460)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3232460)<-[:expr { local_id: '8635275'}]-(id2700934933) CREATE (id3232460)<-[:expr { local_id: '5595798'}]-(id3085575328) CREATE (id3232460)-[:expr { local_id: '5493675'}]->(id8497631728) CREATE (id3264098:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3264098)<-[:linear_index {linear_index: '17}']-(id539398) CREATE (id3264098)<-[:infrule]-(conjugatebothsides) CREATE (id3264098)<-[:expr { local_id: '7875296'}]-(id4192519596) CREATE (id3264098)-[:expr { local_id: '1174231'}]->(id4504256452) CREATE (id3346106:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3346106)<-[:linear_index {linear_index: '33}']-(id539398) CREATE (id3346106)<-[:infrule]-(declarefinalexpr) CREATE (id3346106)<-[:expr { local_id: '6088608'}]-(id6556875579) CREATE (id3822400:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3822400)<-[:linear_index {linear_index: '10}']-(id539398) CREATE (id3822400)<-[:infrule]-(changevariableXtoY) CREATE (id3822400)<-[:expr { local_id: '4362190'}]-(id3350830826) CREATE (id3822400)<-[:expr { local_id: '5235989'}]-(id9761485403) CREATE (id3822400)<-[:expr { local_id: '4014685'}]-(id8710504862) CREATE (id3822400)-[:expr { local_id: '3404497'}]->(id4075539836) CREATE (id3859105:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3859105)<-[:linear_index {linear_index: '5}']-(id539398) CREATE (id3859105)<-[:infrule]-(declareinitialexpr) CREATE (id3859105)-[:expr { local_id: '6461198'}]->(id8396997949) CREATE (id4037583:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4037583)<-[:linear_index {linear_index: '19}']-(id539398) CREATE (id4037583)<-[:infrule]-(simplify) CREATE (id4037583)<-[:expr { local_id: '1405078'}]-(id7621705408) CREATE (id4037583)-[:expr { local_id: '5595798'}]->(id3085575328) CREATE (id4285950:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4285950)<-[:linear_index {linear_index: '20}']-(id539398) CREATE (id4285950)<-[:infrule]-(changevariableXtoY) CREATE (id4285950)<-[:expr { local_id: '7002927'}]-(id4585932229) CREATE (id4285950)<-[:expr { local_id: '4506735'}]-(id4935235303) CREATE (id4285950)<-[:expr { local_id: '3003461'}]-(id2293352649) CREATE (id4285950)-[:expr { local_id: '9190817'}]->(id3660957533) CREATE (id4450503:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4450503)<-[:linear_index {linear_index: '6}']-(id539398) CREATE (id4450503)<-[:infrule]-(changevariableXtoY) CREATE (id4450503)<-[:expr { local_id: '4362190'}]-(id3350830826) CREATE (id4450503)<-[:expr { local_id: '1490071'}]-(id4437214608) CREATE (id4450503)<-[:expr { local_id: '7219466'}]-(id5623794884) CREATE (id4450503)-[:expr { local_id: '4137499'}]->(id2236639474) CREATE (id4581255:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4581255)<-[:linear_index {linear_index: '32}']-(id539398) CREATE (id4581255)<-[:infrule]-(divideexpr1byexpr2) CREATE (id4581255)<-[:expr { local_id: '7442815'}]-(id1172039918) CREATE (id4581255)<-[:expr { local_id: '3246829'}]-(id3060393541) CREATE (id4581255)-[:expr { local_id: '6088608'}]->(id6556875579) CREATE (id5037316:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5037316)<-[:linear_index {linear_index: '11}']-(id539398) CREATE (id5037316)<-[:infrule]-(changevariableXtoY) CREATE (id5037316)<-[:expr { local_id: '4362190'}]-(id3350830826) CREATE (id5037316)<-[:expr { local_id: '1916131'}]-(id6529120965) CREATE (id5037316)<-[:expr { local_id: '5191462'}]-(id1511199318) CREATE (id5037316)-[:expr { local_id: '2303305'}]->(id7107090465) CREATE (id5061134:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5061134)<-[:linear_index {linear_index: '27}']-(id539398) CREATE (id5061134)<-[:infrule]-(simplify) CREATE (id5061134)<-[:expr { local_id: '2139818'}]-(id8046208134) CREATE (id5061134)-[:expr { local_id: '7442815'}]->(id1172039918) CREATE (id5273445:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5273445)<-[:linear_index {linear_index: '3}']-(id539398) CREATE (id5273445)<-[:infrule]-(multiplyexpr1byexpr2) CREATE (id5273445)<-[:expr { local_id: '4809503'}]-(id4182362050) CREATE (id5273445)<-[:expr { local_id: '5663009'}]-(id1928085940) CREATE (id5273445)-[:expr { local_id: '4577339'}]->(id9191880568) CREATE (id5464106:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5464106)<-[:linear_index {linear_index: '8}']-(id539398) CREATE (id5464106)<-[:infrule]-(distributeconjugatetofactors) CREATE (id5464106)<-[:expr { local_id: '9192406'}]-(id1020854560) CREATE (id5464106)-[:expr { local_id: '2300056'}]->(id6306552185) CREATE (id5816138:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5816138)<-[:linear_index {linear_index: '23}']-(id539398) CREATE (id5816138)<-[:infrule]-(declareinitialexpr) CREATE (id5816138)-[:expr { local_id: '7781977'}]->(id6774684564) CREATE (id6945646:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6945646)<-[:linear_index {linear_index: '1}']-(id539398) CREATE (id6945646)<-[:infrule]-(declareinitialexpr) CREATE (id6945646)-[:expr { local_id: '4809503'}]->(id4182362050) CREATE (id6988426:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6988426)<-[:linear_index {linear_index: '14}']-(id539398) CREATE (id6988426)<-[:infrule]-(changetwovariablesinexpr) CREATE (id6988426)<-[:expr { local_id: '5513927'}]-(id7607271250) CREATE (id6988426)<-[:expr { local_id: '4809503'}]-(id4182362050) CREATE (id6988426)<-[:expr { local_id: '8712395'}]-(id1742775076) CREATE (id6988426)<-[:expr { local_id: '8685004'}]-(id4583868070) CREATE (id6988426)-[:expr { local_id: '7875296'}]->(id4192519596) CREATE (id7201861:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7201861)<-[:linear_index {linear_index: '12}']-(id539398) CREATE (id7201861)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7201861)<-[:expr { local_id: '3404497'}]-(id4075539836) CREATE (id7201861)<-[:expr { local_id: '9934418'}]-(id8065128065) CREATE (id7201861)-[:expr { local_id: '4729665'}]->(id5125940051) CREATE (id8130270:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8130270)<-[:linear_index {linear_index: '28}']-(id539398) CREATE (id8130270)<-[:infrule]-(declareinitialexpr) CREATE (id8130270)-[:expr { local_id: '4842351'}]->(id8602221482) CREATE (id8135505:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8135505)<-[:linear_index {linear_index: '4}']-(id539398) CREATE (id8135505)<-[:infrule]-(simplify) CREATE (id8135505)<-[:expr { local_id: '4577339'}]-(id9191880568) CREATE (id8135505)-[:expr { local_id: '4362190'}]->(id3350830826) CREATE (id8475410:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8475410)<-[:linear_index {linear_index: '7}']-(id539398) CREATE (id8475410)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id8475410)<-[:expr { local_id: '4137499'}]-(id2236639474) CREATE (id8475410)<-[:expr { local_id: '6461198'}]-(id8396997949) CREATE (id8475410)-[:expr { local_id: '9192406'}]->(id1020854560) CREATE (id8612576:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8612576)<-[:linear_index {linear_index: '30}']-(id539398) CREATE (id8612576)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id8612576)<-[:expr { local_id: '9739736'}]-(id2719691582) CREATE (id8612576)<-[:expr { local_id: '8093224'}]-(id6240206408) CREATE (id8612576)-[:expr { local_id: '5409843'}]->(id6529793063) CREATE (id8712986:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8712986)<-[:linear_index {linear_index: '26}']-(id539398) CREATE (id8712986)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id8712986)<-[:expr { local_id: '9739736'}]-(id2719691582) CREATE (id8712986)<-[:expr { local_id: '2413866'}]-(id8283354808) CREATE (id8712986)-[:expr { local_id: '2139818'}]->(id8046208134) CREATE (id8915037:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8915037)<-[:linear_index {linear_index: '9}']-(id539398) CREATE (id8915037)<-[:infrule]-(simplify) CREATE (id8915037)<-[:expr { local_id: '2300056'}]-(id6306552185) CREATE (id8915037)-[:expr { local_id: '9934418'}]->(id8065128065) CREATE (id9260286:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9260286)<-[:linear_index {linear_index: '2}']-(id539398) CREATE (id9260286)<-[:infrule]-(conjugatebothsides) CREATE (id9260286)<-[:expr { local_id: '4809503'}]-(id4182362050) CREATE (id9260286)-[:expr { local_id: '5663009'}]->(id1928085940) CREATE (id9512128:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9512128)<-[:linear_index {linear_index: '16}']-(id539398) CREATE (id9512128)<-[:infrule]-(conjugatebothsides) CREATE (id9512128)<-[:expr { local_id: '2018605'}]-(id1357848476) CREATE (id9512128)-[:expr { local_id: '1584527'}]->(id6555185548) CREATE (id9585552:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9585552)<-[:linear_index {linear_index: '21}']-(id539398) CREATE (id9585552)<-[:infrule]-(multiplybothsidesby) CREATE (id9585552)<-[:expr { local_id: '9190817'}]-(id3660957533) CREATE (id9585552)<-[:expr { local_id: '4399863'}]-(id3967985562) CREATE (id9585552)-[:expr { local_id: '8635275'}]->(id2700934933) CREATE (551770:derivation { name: 'Lorentztransformation', notes: 'source: \cite{1999_Tipler_Llewellyn}, page 21; see also https://en.wikipedia.org/wiki/Lorentz_transformation and https://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations', creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1336657:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1336657)<-[:linear_index {linear_index: '20}']-(id551770) CREATE (id1336657)<-[:infrule]-(expr1isequivalenttoexpr2underthecondition) CREATE (id1336657)<-[:expr { local_id: '6319661'}]-(id4287102261) CREATE (id1336657)<-[:expr { local_id: '4202425'}]-(id1586866563) CREATE (id1336657)-[:expr { local_id: '3640931'}]->(id1916173354) CREATE (id1337934:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1337934)<-[:linear_index {linear_index: '1}']-(id551770) CREATE (id1337934)<-[:infrule]-(declareinitialexpr) CREATE (id1337934)-[:expr { local_id: '5427510'}]->(id4662369843) CREATE (id2712078:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2712078)<-[:linear_index {linear_index: '15}']-(id551770) CREATE (id2712078)<-[:infrule]-(declareassumption) CREATE (id2712078)-[:expr { local_id: '7666907'}]->(id8515803375) CREATE (id3002960:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3002960)<-[:linear_index {linear_index: '11}']-(id551770) CREATE (id3002960)<-[:infrule]-(swapLHSwithRHS) CREATE (id3002960)<-[:expr { local_id: '7546640'}]-(id8730201316) CREATE (id3002960)-[:expr { local_id: '1693888'}]->(id5148266645) CREATE (id3151962:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3151962)<-[:linear_index {linear_index: '12}']-(id551770) CREATE (id3151962)<-[:infrule]-(declareinitialexpr) CREATE (id3151962)-[:expr { local_id: '6319661'}]->(id4287102261) CREATE (id3201871:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3201871)<-[:linear_index {linear_index: '25}']-(id551770) CREATE (id3201871)<-[:infrule]-(addXtobothsides) CREATE (id3201871)<-[:expr { local_id: '8195408'}]-(id5763749235) CREATE (id3201871)<-[:expr { local_id: '5277900'}]-(id6408214498) CREATE (id3201871)-[:expr { local_id: '6913493'}]->(id2999795755) CREATE (id3244831:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3244831)<-[:linear_index {linear_index: '6}']-(id551770) CREATE (id3244831)<-[:infrule]-(subtractXfrombothsides) CREATE (id3244831)<-[:expr { local_id: '6463955'}]-(id7741202861) CREATE (id3244831)<-[:expr { local_id: '8548879'}]-(id7337056406) CREATE (id3244831)-[:expr { local_id: '8494407'}]->(id4139999399) CREATE (id3464414:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3464414)<-[:linear_index {linear_index: '23}']-(id551770) CREATE (id3464414)<-[:infrule]-(dividebothsidesby) CREATE (id3464414)<-[:expr { local_id: '7403799'}]-(id2417941373) CREATE (id3464414)<-[:expr { local_id: '3550368'}]-(id5787469164) CREATE (id3464414)-[:expr { local_id: '4052253'}]->(id1639827492) CREATE (id4044426:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4044426)<-[:linear_index {linear_index: '24}']-(id551770) CREATE (id4044426)<-[:infrule]-(multiplybothsidesby) CREATE (id4044426)<-[:expr { local_id: '4052253'}]-(id1639827492) CREATE (id4044426)<-[:expr { local_id: '7396508'}]-(id5669500954) CREATE (id4044426)-[:expr { local_id: '8195408'}]->(id5763749235) CREATE (id4052521:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4052521)<-[:linear_index {linear_index: '10}']-(id551770) CREATE (id4052521)<-[:infrule]-(simplify) CREATE (id4052521)<-[:expr { local_id: '5995189'}]-(id1974334644) CREATE (id4052521)-[:expr { local_id: '7546640'}]->(id8730201316) CREATE (id4777578:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4777578)<-[:linear_index {linear_index: '4}']-(id551770) CREATE (id4777578)<-[:infrule]-(simplify) CREATE (id4777578)<-[:expr { local_id: '4471422'}]-(id3426941928) CREATE (id4777578)-[:expr { local_id: '7169020'}]->(id2096918413) CREATE (id4875843:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4875843)<-[:linear_index {linear_index: '19}']-(id551770) CREATE (id4875843)<-[:infrule]-(expr1isequivalenttoexpr2underthecondition) CREATE (id4875843)<-[:expr { local_id: '6319661'}]-(id4287102261) CREATE (id4875843)<-[:expr { local_id: '4202425'}]-(id1586866563) CREATE (id4875843)-[:expr { local_id: '2562123'}]->(id3182633789) CREATE (id5029881:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5029881)<-[:linear_index {linear_index: '22}']-(id551770) CREATE (id5029881)<-[:infrule]-(subtractXfrombothsides) CREATE (id5029881)<-[:expr { local_id: '2562123'}]-(id3182633789) CREATE (id5029881)<-[:expr { local_id: '9371489'}]-(id5284610349) CREATE (id5029881)-[:expr { local_id: '7403799'}]->(id2417941373) CREATE (id5211114:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5211114)<-[:linear_index {linear_index: '29}']-(id551770) CREATE (id5211114)<-[:infrule]-(squarerootbothsides) CREATE (id5211114)<-[:expr { local_id: '7595841'}]-(id7906112355) CREATE (id5211114)-[:expr { local_id: '3040283'}]->(id1528310784) CREATE (id5211114)-[:expr { local_id: '6010461'}]->(id8360117126) CREATE (id5537889:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5537889)<-[:linear_index {linear_index: '17}']-(id551770) CREATE (id5537889)<-[:infrule]-(simplify) CREATE (id5537889)<-[:expr { local_id: '4326342'}]-(id9805063945) CREATE (id5537889)-[:expr { local_id: '6066191'}]->(id1935543849) CREATE (id5619063:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5619063)<-[:linear_index {linear_index: '30}']-(id551770) CREATE (id5619063)<-[:infrule]-(declarefinalexpr) CREATE (id5619063)<-[:expr { local_id: '3040283'}]-(id1528310784) CREATE (id5637413:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5637413)<-[:linear_index {linear_index: '13}']-(id551770) CREATE (id5637413)<-[:infrule]-(declareinitialexpr) CREATE (id5637413)-[:expr { local_id: '5649086'}]->(id1201689765) CREATE (id5708661:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5708661)<-[:linear_index {linear_index: '5}']-(id551770) CREATE (id5708661)<-[:infrule]-(simplify) CREATE (id5708661)<-[:expr { local_id: '7169020'}]-(id2096918413) CREATE (id5708661)-[:expr { local_id: '6463955'}]->(id7741202861) CREATE (id5796383:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5796383)<-[:linear_index {linear_index: '14}']-(id551770) CREATE (id5796383)<-[:infrule]-(declareassumption) CREATE (id5796383)-[:expr { local_id: '6316097'}]->(id7057864873) CREATE (id6150706:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6150706)<-[:linear_index {linear_index: '3}']-(id551770) CREATE (id6150706)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6150706)<-[:expr { local_id: '5427510'}]-(id4662369843) CREATE (id6150706)<-[:expr { local_id: '2283140'}]-(id2983053062) CREATE (id6150706)-[:expr { local_id: '4471422'}]->(id3426941928) CREATE (id6431475:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6431475)<-[:linear_index {linear_index: '9}']-(id551770) CREATE (id6431475)<-[:infrule]-(dividebothsidesby) CREATE (id6431475)<-[:expr { local_id: '6047713'}]-(id9409776983) CREATE (id6431475)<-[:expr { local_id: '9446753'}]-(id2226340358) CREATE (id6431475)-[:expr { local_id: '5995189'}]->(id1974334644) CREATE (id7160101:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7160101)<-[:linear_index {linear_index: '18}']-(id551770) CREATE (id7160101)<-[:infrule]-(simplify) CREATE (id7160101)<-[:expr { local_id: '6066191'}]-(id1935543849) CREATE (id7160101)-[:expr { local_id: '4202425'}]->(id1586866563) CREATE (id7599260:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7599260)<-[:linear_index {linear_index: '27}']-(id551770) CREATE (id7599260)<-[:infrule]-(factoroutXfromLHS) CREATE (id7599260)<-[:expr { local_id: '5207615'}]-(id2542420160) CREATE (id7599260)<-[:expr { local_id: '1650804'}]-(id7743841045) CREATE (id7599260)-[:expr { local_id: '8842089'}]->(id7513513483) CREATE (id7832193:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7832193)<-[:linear_index {linear_index: '21}']-(id551770) CREATE (id7832193)<-[:infrule]-(expr1isequivalenttoexpr2underthecondition) CREATE (id7832193)<-[:expr { local_id: '6319661'}]-(id4287102261) CREATE (id7832193)<-[:expr { local_id: '4202425'}]-(id1586866563) CREATE (id7832193)-[:expr { local_id: '6685577'}]->(id2076171250) CREATE (id8057586:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8057586)<-[:linear_index {linear_index: '16}']-(id551770) CREATE (id8057586)<-[:infrule]-(substituteLHSoffourexpressionsintoexpr) CREATE (id8057586)<-[:expr { local_id: '7666907'}]-(id8515803375) CREATE (id8057586)<-[:expr { local_id: '6316097'}]-(id7057864873) CREATE (id8057586)<-[:expr { local_id: '1693888'}]-(id5148266645) CREATE (id8057586)<-[:expr { local_id: '5427510'}]-(id4662369843) CREATE (id8057586)<-[:expr { local_id: '5649086'}]-(id1201689765) CREATE (id8057586)-[:expr { local_id: '4326342'}]->(id9805063945) CREATE (id8199201:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8199201)<-[:linear_index {linear_index: '8}']-(id551770) CREATE (id8199201)<-[:infrule]-(addXtobothsides) CREATE (id8199201)<-[:expr { local_id: '3992172'}]-(id9031609275) CREATE (id8199201)<-[:expr { local_id: '4820907'}]-(id8014566709) CREATE (id8199201)-[:expr { local_id: '6047713'}]->(id9409776983) CREATE (id8488825:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8488825)<-[:linear_index {linear_index: '26}']-(id551770) CREATE (id8488825)<-[:infrule]-(subtractXfrombothsides) CREATE (id8488825)<-[:expr { local_id: '6913493'}]-(id2999795755) CREATE (id8488825)<-[:expr { local_id: '8026131'}]-(id3412946408) CREATE (id8488825)-[:expr { local_id: '5207615'}]->(id2542420160) CREATE (id9486255:step { creation_date: '2020-05-09', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9486255)<-[:linear_index {linear_index: '28}']-(id551770) CREATE (id9486255)<-[:infrule]-(dividebothsidesby) CREATE (id9486255)<-[:expr { local_id: '8842089'}]-(id7513513483) CREATE (id9486255)<-[:expr { local_id: '5253559'}]-(id8571466509) CREATE (id9486255)-[:expr { local_id: '7595841'}]->(id7906112355) CREATE (id9520931:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9520931)<-[:linear_index {linear_index: '7}']-(id551770) CREATE (id9520931)<-[:infrule]-(factoroutXfromLHS) CREATE (id9520931)<-[:expr { local_id: '8494407'}]-(id4139999399) CREATE (id9520931)<-[:expr { local_id: '6980367'}]-(id3495403335) CREATE (id9520931)-[:expr { local_id: '3992172'}]->(id9031609275) CREATE (id9869359:step { creation_date: '2020-05-08', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9869359)<-[:linear_index {linear_index: '2}']-(id551770) CREATE (id9869359)<-[:infrule]-(declareinitialexpr) CREATE (id9869359)-[:expr { local_id: '2283140'}]->(id2983053062) CREATE (608598:derivation { name: 'upperlimitonvelocityincondensedmatter', notes: 'https://arxiv.org/pdf/2004.04818.pdf', creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1346919:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1346919)<-[:linear_index {linear_index: '11}']-(id608598) CREATE (id1346919)<-[:infrule]-(declareinitialexpr) CREATE (id1346919)-[:expr { local_id: '9431422'}]->(id8106885760) CREATE (id1452028:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1452028)<-[:linear_index {linear_index: '12}']-(id608598) CREATE (id1452028)<-[:infrule]-(multiplybothsidesby) CREATE (id1452028)<-[:expr { local_id: '9431422'}]-(id8106885760) CREATE (id1452028)<-[:expr { local_id: '8320432'}]-(id8857931498) CREATE (id1452028)-[:expr { local_id: '6181437'}]->(id5838268428) CREATE (id2951905:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2951905)<-[:linear_index {linear_index: '9}']-(id608598) CREATE (id2951905)<-[:infrule]-(declareinitialexpr) CREATE (id2951905)-[:expr { local_id: '5961293'}]->(id1556389363) CREATE (id3423374:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3423374)<-[:linear_index {linear_index: '7}']-(id608598) CREATE (id3423374)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id3423374)<-[:expr { local_id: '7834577'}]-(id8688588981) CREATE (id3423374)<-[:expr { local_id: '5077893'}]-(id8090924099) CREATE (id3423374)-[:expr { local_id: '5020923'}]->(id7837519722) CREATE (id3709291:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3709291)<-[:linear_index {linear_index: '19}']-(id608598) CREATE (id3709291)<-[:infrule]-(maximumofexpr) CREATE (id3709291)<-[:expr { local_id: '8323044'}]-(id2897612567) CREATE (id3709291)<-[:expr { local_id: '1809997'}]-(id6259833695) CREATE (id3709291)-[:expr { local_id: '9568206'}]->(id7701249282) CREATE (id4186156:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4186156)<-[:linear_index {linear_index: '18}']-(id608598) CREATE (id4186156)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id4186156)<-[:expr { local_id: '6979804'}]-(id5646314683) CREATE (id4186156)<-[:expr { local_id: '5883117'}]-(id5789289057) CREATE (id4186156)-[:expr { local_id: '8323044'}]->(id2897612567) CREATE (id4663270:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4663270)<-[:linear_index {linear_index: '20}']-(id608598) CREATE (id4663270)<-[:infrule]-(declarefinalexpr) CREATE (id4663270)<-[:expr { local_id: '9568206'}]-(id7701249282) CREATE (id5023393:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5023393)<-[:linear_index {linear_index: '13}']-(id608598) CREATE (id5023393)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5023393)<-[:expr { local_id: '6901924'}]-(id4107032818) CREATE (id5023393)<-[:expr { local_id: '5961293'}]-(id1556389363) CREATE (id5023393)-[:expr { local_id: '3642765'}]->(id3291685884) CREATE (id5093643:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5093643)<-[:linear_index {linear_index: '10}']-(id608598) CREATE (id5093643)<-[:infrule]-(declareassumption) CREATE (id5093643)-[:expr { local_id: '6901924'}]->(id4107032818) CREATE (id5522705:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5522705)<-[:linear_index {linear_index: '15}']-(id608598) CREATE (id5522705)<-[:infrule]-(simplify) CREATE (id5522705)<-[:expr { local_id: '2063484'}]-(id3935058307) CREATE (id5522705)-[:expr { local_id: '4586348'}]->(id9640720571) CREATE (id6240791:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6240791)<-[:linear_index {linear_index: '6}']-(id608598) CREATE (id6240791)<-[:infrule]-(multiplybothsidesby) CREATE (id6240791)<-[:expr { local_id: '2438445'}]-(id8908736791) CREATE (id6240791)<-[:expr { local_id: '7822040'}]-(id2397692197) CREATE (id6240791)-[:expr { local_id: '7834577'}]->(id8688588981) CREATE (id6342896:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6342896)<-[:linear_index {linear_index: '2}']-(id608598) CREATE (id6342896)<-[:infrule]-(declareinitialexpr) CREATE (id6342896)-[:expr { local_id: '2178289'}]->(id9376481176) CREATE (id6394441:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6394441)<-[:linear_index {linear_index: '5}']-(id608598) CREATE (id6394441)<-[:infrule]-(declareinitialexpr) CREATE (id6394441)-[:expr { local_id: '2438445'}]->(id8908736791) CREATE (id7117931:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7117931)<-[:linear_index {linear_index: '4}']-(id608598) CREATE (id7117931)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7117931)<-[:expr { local_id: '2178289'}]-(id9376481176) CREATE (id7117931)<-[:expr { local_id: '9155336'}]-(id6504442697) CREATE (id7117931)-[:expr { local_id: '5077893'}]->(id8090924099) CREATE (id7232268:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7232268)<-[:linear_index {linear_index: '1}']-(id608598) CREATE (id7232268)<-[:infrule]-(declareinitialexpr) CREATE (id7232268)-[:expr { local_id: '1719451'}]->(id4560648264) CREATE (id7588540:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7588540)<-[:linear_index {linear_index: '14}']-(id608598) CREATE (id7588540)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7588540)<-[:expr { local_id: '3642765'}]-(id3291685884) CREATE (id7588540)<-[:expr { local_id: '4534919'}]-(id9854442418) CREATE (id7588540)-[:expr { local_id: '2063484'}]->(id3935058307) CREATE (id8867459:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8867459)<-[:linear_index {linear_index: '17}']-(id608598) CREATE (id8867459)<-[:infrule]-(declareinitialexpr) CREATE (id8867459)-[:expr { local_id: '6979804'}]->(id5646314683) CREATE (id9057006:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9057006)<-[:linear_index {linear_index: '8}']-(id608598) CREATE (id9057006)<-[:infrule]-(dropnondominantterm) CREATE (id9057006)<-[:expr { local_id: '5020923'}]-(id7837519722) CREATE (id9057006)<-[:expr { local_id: '7076437'}]-(id3685779219) CREATE (id9057006)-[:expr { local_id: '4534919'}]->(id9854442418) CREATE (id9182821:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9182821)<-[:linear_index {linear_index: '3}']-(id608598) CREATE (id9182821)<-[:infrule]-(dropnondominantterm) CREATE (id9182821)<-[:expr { local_id: '1719451'}]-(id4560648264) CREATE (id9182821)<-[:expr { local_id: '9255270'}]-(id9674924517) CREATE (id9182821)-[:expr { local_id: '9155336'}]->(id6504442697) CREATE (id9573616:step { creation_date: '2020-06-14', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9573616)<-[:linear_index {linear_index: '16}']-(id608598) CREATE (id9573616)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id9573616)<-[:expr { local_id: '6181437'}]-(id5838268428) CREATE (id9573616)<-[:expr { local_id: '4586348'}]-(id9640720571) CREATE (id9573616)-[:expr { local_id: '5883117'}]->(id5789289057) CREATE (670255:derivation { name: 'equationofmotionforaspring', creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1216158:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1216158)<-[:linear_index {linear_index: '3}']-(id670255) CREATE (id1216158)<-[:infrule]-(declareinitialexpr) CREATE (id1216158)-[:expr { local_id: '9761157'}]->(id6831694380) CREATE (id2315272:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2315272)<-[:linear_index {linear_index: '7}']-(id670255) CREATE (id2315272)<-[:infrule]-(declareguesssolution) CREATE (id2315272)<-[:expr { local_id: '4154219'}]-(id8991236357) CREATE (id2315272)-[:expr { local_id: '2877569'}]->(id5415824175) CREATE (id3234596:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3234596)<-[:linear_index {linear_index: '10}']-(id670255) CREATE (id3234596)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id3234596)<-[:expr { local_id: '4836115'}]-(id5945893986) CREATE (id3234596)<-[:expr { local_id: '4154219'}]-(id8991236357) CREATE (id3234596)-[:expr { local_id: '7792692'}]->(id1772973171) CREATE (id4208810:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4208810)<-[:linear_index {linear_index: '11}']-(id670255) CREATE (id4208810)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id4208810)<-[:expr { local_id: '2877569'}]-(id5415824175) CREATE (id4208810)<-[:expr { local_id: '7792692'}]-(id1772973171) CREATE (id4208810)-[:expr { local_id: '7745098'}]->(id2148049269) CREATE (id4482244:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4482244)<-[:linear_index {linear_index: '13}']-(id670255) CREATE (id4482244)<-[:infrule]-(squarerootbothsides) CREATE (id4482244)<-[:expr { local_id: '8360924'}]-(id1931103031) CREATE (id4482244)-[:expr { local_id: '7243628'}]->(id1784114349) CREATE (id4482244)-[:expr { local_id: '2051755'}]->(id1888494137) CREATE (id4514656:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4514656)<-[:linear_index {linear_index: '1}']-(id670255) CREATE (id4514656)<-[:infrule]-(declareinitialexpr) CREATE (id4514656)-[:expr { local_id: '3065061'}]->(id5345738321) CREATE (id4790069:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4790069)<-[:linear_index {linear_index: '2}']-(id670255) CREATE (id4790069)<-[:infrule]-(declareinitialexpr) CREATE (id4790069)-[:expr { local_id: '2664105'}]->(id4428528271) CREATE (id5272817:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5272817)<-[:linear_index {linear_index: '6}']-(id670255) CREATE (id5272817)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id5272817)<-[:expr { local_id: '5403312'}]-(id8655294002) CREATE (id5272817)<-[:expr { local_id: '9761157'}]-(id6831694380) CREATE (id5272817)-[:expr { local_id: '4154219'}]->(id8991236357) CREATE (id5376872:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5376872)<-[:linear_index {linear_index: '4}']-(id670255) CREATE (id5376872)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id5376872)<-[:expr { local_id: '3065061'}]-(id5345738321) CREATE (id5376872)<-[:expr { local_id: '2664105'}]-(id4428528271) CREATE (id5376872)-[:expr { local_id: '7273319'}]->(id2334518266) CREATE (id5391046:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5391046)<-[:linear_index {linear_index: '12}']-(id670255) CREATE (id5391046)<-[:infrule]-(multiplybothsidesby) CREATE (id5391046)<-[:expr { local_id: '7745098'}]-(id2148049269) CREATE (id5391046)<-[:expr { local_id: '9713990'}]-(id7473576008) CREATE (id5391046)-[:expr { local_id: '8360924'}]->(id1931103031) CREATE (id5435505:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5435505)<-[:linear_index {linear_index: '9}']-(id670255) CREATE (id5435505)<-[:infrule]-(differentiatewithrespectto) CREATE (id5435505)<-[:expr { local_id: '4463004'}]-(id7652131521) CREATE (id5435505)<-[:expr { local_id: '9332704'}]-(id1451839362) CREATE (id5435505)-[:expr { local_id: '4836115'}]->(id5945893986) CREATE (id6129880:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6129880)<-[:linear_index {linear_index: '5}']-(id670255) CREATE (id6129880)<-[:infrule]-(dividebothsidesby) CREATE (id6129880)<-[:expr { local_id: '7273319'}]-(id2334518266) CREATE (id6129880)<-[:expr { local_id: '1294073'}]-(id3634715785) CREATE (id6129880)-[:expr { local_id: '5403312'}]->(id8655294002) CREATE (id8476862:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8476862)<-[:linear_index {linear_index: '8}']-(id670255) CREATE (id8476862)<-[:infrule]-(differentiatewithrespectto) CREATE (id8476862)<-[:expr { local_id: '2877569'}]-(id5415824175) CREATE (id8476862)<-[:expr { local_id: '5689050'}]-(id5846177002) CREATE (id8476862)-[:expr { local_id: '4463004'}]->(id7652131521) CREATE (id8522636:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8522636)<-[:linear_index {linear_index: '14}']-(id670255) CREATE (id8522636)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id8522636)<-[:expr { local_id: '7243628'}]-(id1784114349) CREATE (id8522636)<-[:expr { local_id: '2877569'}]-(id5415824175) CREATE (id8522636)-[:expr { local_id: '5872898'}]->(id6908055431) CREATE (id8719992:step { creation_date: '2021-08-22', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8719992)<-[:linear_index {linear_index: '15}']-(id670255) CREATE (id8719992)<-[:infrule]-(declarefinalexpr) CREATE (id8719992)<-[:expr { local_id: '5872898'}]-(id6908055431) CREATE (681943:derivation { name: 'totalelectricalresistanceforcircuitwithtworesistorsinparallel', notes: 'http://www.dfcd.net/articles/derivations/resistors.html', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1391174:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1391174)<-[:linear_index {linear_index: '1}']-(id681943) CREATE (id1391174)<-[:infrule]-(changetwovariablesinexpr) CREATE (id1391174)<-[:expr { local_id: '8922008'}]-(id4087145886) CREATE (id1391174)<-[:expr { local_id: '4152602'}]-(id2867848403) CREATE (id1391174)<-[:expr { local_id: '5140250'}]-(id1323602089) CREATE (id1391174)<-[:expr { local_id: '3693601'}]-(id7191277455) CREATE (id1391174)<-[:expr { local_id: '1100444'}]-(id5258419993) CREATE (id1391174)-[:expr { local_id: '8148802'}]->(id4128500715) CREATE (id1468462:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1468462)<-[:linear_index {linear_index: '10}']-(id681943) CREATE (id1468462)<-[:infrule]-(declarefinalexpr) CREATE (id1468462)<-[:expr { local_id: '8713399'}]-(id1457415749) CREATE (id3724854:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3724854)<-[:linear_index {linear_index: '5}']-(id681943) CREATE (id3724854)<-[:infrule]-(declareinitialexpr) CREATE (id3724854)-[:expr { local_id: '3843569'}]->(id6753224061) CREATE (id4777295:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4777295)<-[:linear_index {linear_index: '7}']-(id681943) CREATE (id4777295)<-[:infrule]-(dividebothsidesby) CREATE (id4777295)<-[:expr { local_id: '8002723'}]-(id2271186630) CREATE (id4777295)<-[:expr { local_id: '4577073'}]-(id6546594355) CREATE (id4777295)-[:expr { local_id: '1708642'}]->(id2809345867) CREATE (id5478696:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5478696)<-[:linear_index {linear_index: '9}']-(id681943) CREATE (id5478696)<-[:infrule]-(dividebothsidesby) CREATE (id5478696)<-[:expr { local_id: '6759349'}]-(id4866160902) CREATE (id5478696)<-[:expr { local_id: '3308740'}]-(id3433441359) CREATE (id5478696)-[:expr { local_id: '8713399'}]->(id1457415749) CREATE (id5878391:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5878391)<-[:linear_index {linear_index: '8}']-(id681943) CREATE (id5878391)<-[:infrule]-(substituteLHSofthreeexpressionsintoexpr) CREATE (id5878391)<-[:expr { local_id: '1708642'}]-(id2809345867) CREATE (id5878391)<-[:expr { local_id: '5168370'}]-(id2051901211) CREATE (id5878391)<-[:expr { local_id: '4037937'}]-(id7002609475) CREATE (id5878391)<-[:expr { local_id: '3843569'}]-(id6753224061) CREATE (id5878391)-[:expr { local_id: '6759349'}]->(id4866160902) CREATE (id6114977:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6114977)<-[:linear_index {linear_index: '4}']-(id681943) CREATE (id6114977)<-[:infrule]-(dividebothsidesby) CREATE (id6114977)<-[:expr { local_id: '8148802'}]-(id4128500715) CREATE (id6114977)<-[:expr { local_id: '7969677'}]-(id5181421075) CREATE (id6114977)-[:expr { local_id: '5168370'}]->(id2051901211) CREATE (id7576732:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7576732)<-[:linear_index {linear_index: '6}']-(id681943) CREATE (id7576732)<-[:infrule]-(changetwovariablesinexpr) CREATE (id7576732)<-[:expr { local_id: '8922008'}]-(id4087145886) CREATE (id7576732)<-[:expr { local_id: '1987304'}]-(id9053099840) CREATE (id7576732)<-[:expr { local_id: '2060382'}]-(id7798615279) CREATE (id7576732)<-[:expr { local_id: '5679513'}]-(id1100332145) CREATE (id7576732)<-[:expr { local_id: '7037795'}]-(id7410124465) CREATE (id7576732)-[:expr { local_id: '8002723'}]->(id2271186630) CREATE (id8121398:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8121398)<-[:linear_index {linear_index: '2}']-(id681943) CREATE (id8121398)<-[:infrule]-(changetwovariablesinexpr) CREATE (id8121398)<-[:expr { local_id: '8922008'}]-(id4087145886) CREATE (id8121398)<-[:expr { local_id: '7586662'}]-(id5585739998) CREATE (id8121398)<-[:expr { local_id: '8551025'}]-(id5463275819) CREATE (id8121398)<-[:expr { local_id: '9962307'}]-(id1377431959) CREATE (id8121398)<-[:expr { local_id: '9354200'}]-(id9746066299) CREATE (id8121398)-[:expr { local_id: '6313158'}]->(id9243879541) CREATE (id8616052:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8616052)<-[:linear_index {linear_index: '3}']-(id681943) CREATE (id8616052)<-[:infrule]-(dividebothsidesby) CREATE (id8616052)<-[:expr { local_id: '6313158'}]-(id9243879541) CREATE (id8616052)<-[:expr { local_id: '6815205'}]-(id3031116098) CREATE (id8616052)-[:expr { local_id: '4037937'}]->(id7002609475) CREATE (713234:derivation { name: 'hyperbolictrigonometricidentities', notes: 'http://www.physics.miami.edu/~nearing/mathmethods/mathematical_methods-one.pdf', creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1207155:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1207155)<-[:linear_index {linear_index: '11}']-(id713234) CREATE (id1207155)<-[:infrule]-(declareinitialexpr) CREATE (id1207155)-[:expr { local_id: '3077940'}]->(id2103023049) CREATE (id1756608:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1756608)<-[:linear_index {linear_index: '26}']-(id713234) CREATE (id1756608)<-[:infrule]-(simplify) CREATE (id1756608)<-[:expr { local_id: '6426652'}]-(id1128605625) CREATE (id1756608)-[:expr { local_id: '6070484'}]->(id4830221561) CREATE (id1879109:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1879109)<-[:linear_index {linear_index: '25}']-(id713234) CREATE (id1879109)<-[:infrule]-(addexpr1toexpr2) CREATE (id1879109)<-[:expr { local_id: '5395954'}]-(id3868998312) CREATE (id1879109)<-[:expr { local_id: '9317216'}]-(id2121790783) CREATE (id1879109)-[:expr { local_id: '6426652'}]->(id1128605625) CREATE (id2347440:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2347440)<-[:linear_index {linear_index: '15}']-(id713234) CREATE (id2347440)<-[:infrule]-(declareinitialexpr) CREATE (id2347440)-[:expr { local_id: '4731536'}]->(id4585932229) CREATE (id2584092:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2584092)<-[:linear_index {linear_index: '19}']-(id713234) CREATE (id2584092)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id2584092)<-[:expr { local_id: '4319733'}]-(id6404535647) CREATE (id2584092)<-[:expr { local_id: '3909583'}]-(id7731226616) CREATE (id2584092)-[:expr { local_id: '7222556'}]->(id4166155526) CREATE (id2595607:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2595607)<-[:linear_index {linear_index: '21}']-(id713234) CREATE (id2595607)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id2595607)<-[:expr { local_id: '3145608'}]-(id1038566242) CREATE (id2595607)<-[:expr { local_id: '3867418'}]-(id4872163189) CREATE (id2595607)-[:expr { local_id: '6831354'}]->(id2902772962) CREATE (id2606241:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2606241)<-[:linear_index {linear_index: '27}']-(id713234) CREATE (id2606241)<-[:infrule]-(simplify) CREATE (id2606241)<-[:expr { local_id: '6070484'}]-(id4830221561) CREATE (id2606241)-[:expr { local_id: '8702257'}]->(id5866629429) CREATE (id2831850:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2831850)<-[:linear_index {linear_index: '2}']-(id713234) CREATE (id2831850)<-[:infrule]-(declareinitialexpr) CREATE (id2831850)-[:expr { local_id: '3145608'}]->(id1038566242) CREATE (id2845819:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2845819)<-[:linear_index {linear_index: '12}']-(id713234) CREATE (id2845819)<-[:infrule]-(changevariableXtoY) CREATE (id2845819)<-[:expr { local_id: '3077940'}]-(id2103023049) CREATE (id2845819)<-[:expr { local_id: '5183800'}]-(id6976493023) CREATE (id2845819)<-[:expr { local_id: '5404156'}]-(id7159989263) CREATE (id2845819)-[:expr { local_id: '5823930'}]->(id4878728014) CREATE (id3159546:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3159546)<-[:linear_index {linear_index: '24}']-(id713234) CREATE (id3159546)<-[:infrule]-(multiplyexpr1byexpr2) CREATE (id3159546)<-[:expr { local_id: '7222556'}]-(id4166155526) CREATE (id3159546)<-[:expr { local_id: '7222556'}]-(id4166155526) CREATE (id3159546)-[:expr { local_id: '5395954'}]->(id3868998312) CREATE (id3428690:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3428690)<-[:linear_index {linear_index: '28}']-(id713234) CREATE (id3428690)<-[:infrule]-(declarefinalexpr) CREATE (id3428690)<-[:expr { local_id: '8702257'}]-(id5866629429) CREATE (id3636266:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3636266)<-[:linear_index {linear_index: '14}']-(id713234) CREATE (id3636266)<-[:infrule]-(multiplybothsidesby) CREATE (id3636266)<-[:expr { local_id: '2016533'}]-(id5323719091) CREATE (id3636266)<-[:expr { local_id: '9699965'}]-(id9885190237) CREATE (id3636266)-[:expr { local_id: '3145608'}]->(id1038566242) CREATE (id3877159:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3877159)<-[:linear_index {linear_index: '7}']-(id713234) CREATE (id3877159)<-[:infrule]-(simplify) CREATE (id3877159)<-[:expr { local_id: '4009221'}]-(id2762326680) CREATE (id3877159)-[:expr { local_id: '6300507'}]->(id9413609246) CREATE (id3919490:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3919490)<-[:linear_index {linear_index: '3}']-(id713234) CREATE (id3919490)<-[:infrule]-(multiplyexpr1byexpr2) CREATE (id3919490)<-[:expr { local_id: '3145608'}]-(id1038566242) CREATE (id3919490)<-[:expr { local_id: '3145608'}]-(id1038566242) CREATE (id3919490)-[:expr { local_id: '7844176'}]->(id6031385191) CREATE (id4596442:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4596442)<-[:linear_index {linear_index: '16}']-(id713234) CREATE (id4596442)<-[:infrule]-(changevariableXtoY) CREATE (id4596442)<-[:expr { local_id: '4731536'}]-(id4585932229) CREATE (id4596442)<-[:expr { local_id: '1091475'}]-(id7453225570) CREATE (id4596442)<-[:expr { local_id: '8392798'}]-(id1716984328) CREATE (id4596442)-[:expr { local_id: '6479977'}]->(id8651044341) CREATE (id4598639:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4598639)<-[:linear_index {linear_index: '8}']-(id713234) CREATE (id4598639)<-[:infrule]-(declarefinalexpr) CREATE (id4598639)<-[:expr { local_id: '6300507'}]-(id9413609246) CREATE (id5415197:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5415197)<-[:linear_index {linear_index: '10}']-(id713234) CREATE (id5415197)<-[:infrule]-(declareinitialexpr) CREATE (id5415197)-[:expr { local_id: '5377003'}]->(id8418527415) CREATE (id5521272:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5521272)<-[:linear_index {linear_index: '22}']-(id713234) CREATE (id5521272)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5521272)<-[:expr { local_id: '4319733'}]-(id6404535647) CREATE (id5521272)<-[:expr { local_id: '6831354'}]-(id2902772962) CREATE (id5521272)-[:expr { local_id: '5313211'}]->(id5349669879) CREATE (id5783204:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5783204)<-[:linear_index {linear_index: '13}']-(id713234) CREATE (id5783204)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id5783204)<-[:expr { local_id: '5823930'}]-(id4878728014) CREATE (id5783204)<-[:expr { local_id: '5377003'}]-(id8418527415) CREATE (id5783204)-[:expr { local_id: '2016533'}]->(id5323719091) CREATE (id6213336:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6213336)<-[:linear_index {linear_index: '20}']-(id713234) CREATE (id6213336)<-[:infrule]-(declareinitialexpr) CREATE (id6213336)-[:expr { local_id: '3867418'}]->(id4872163189) CREATE (id6389859:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6389859)<-[:linear_index {linear_index: '17}']-(id713234) CREATE (id6389859)<-[:infrule]-(LHSofexpr1equalsLHSofexpr2) CREATE (id6389859)<-[:expr { local_id: '7404421'}]-(id8747785338) CREATE (id6389859)<-[:expr { local_id: '6479977'}]-(id8651044341) CREATE (id6389859)-[:expr { local_id: '4319733'}]->(id6404535647) CREATE (id6625389:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6625389)<-[:linear_index {linear_index: '18}']-(id713234) CREATE (id6625389)<-[:infrule]-(declareinitialexpr) CREATE (id6625389)-[:expr { local_id: '3909583'}]->(id7731226616) CREATE (id8230503:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8230503)<-[:linear_index {linear_index: '23}']-(id713234) CREATE (id8230503)<-[:infrule]-(multiplyexpr1byexpr2) CREATE (id8230503)<-[:expr { local_id: '5313211'}]-(id5349669879) CREATE (id8230503)<-[:expr { local_id: '5313211'}]-(id5349669879) CREATE (id8230503)-[:expr { local_id: '9317216'}]->(id2121790783) CREATE (id8480572:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8480572)<-[:linear_index {linear_index: '6}']-(id713234) CREATE (id8480572)<-[:infrule]-(simplify) CREATE (id8480572)<-[:expr { local_id: '4001109'}]-(id8563535636) CREATE (id8480572)-[:expr { local_id: '4009221'}]->(id2762326680) CREATE (id9173195:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9173195)<-[:linear_index {linear_index: '9}']-(id713234) CREATE (id9173195)<-[:infrule]-(declareinitialexpr) CREATE (id9173195)-[:expr { local_id: '7404421'}]->(id8747785338) CREATE (id9643987:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9643987)<-[:linear_index {linear_index: '5}']-(id713234) CREATE (id9643987)<-[:infrule]-(subtractexpr1fromexpr2) CREATE (id9643987)<-[:expr { local_id: '7844176'}]-(id6031385191) CREATE (id9643987)<-[:expr { local_id: '9245668'}]-(id8532702080) CREATE (id9643987)-[:expr { local_id: '4001109'}]->(id8563535636) CREATE (id9722132:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9722132)<-[:linear_index {linear_index: '4}']-(id713234) CREATE (id9722132)<-[:infrule]-(multiplyexpr1byexpr2) CREATE (id9722132)<-[:expr { local_id: '4319733'}]-(id6404535647) CREATE (id9722132)<-[:expr { local_id: '4319733'}]-(id6404535647) CREATE (id9722132)-[:expr { local_id: '9245668'}]->(id8532702080) CREATE (id9934180:step { creation_date: '2020-08-29', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9934180)<-[:linear_index {linear_index: '1}']-(id713234) CREATE (id9934180)<-[:infrule]-(declareinitialexpr) CREATE (id9934180)-[:expr { local_id: '4319733'}]->(id6404535647) CREATE (764666:derivation { name: 'LangmuirAdsorption', notes: 'from https://arxiv.org/pdf/2210.12150.pdf', creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1573241:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1573241)<-[:linear_index {linear_index: '10}']-(id764666) CREATE (id1573241)<-[:infrule]-(dividebothsidesby) CREATE (id1573241)<-[:expr { local_id: '2575148'}]-(id3488423948) CREATE (id1573241)<-[:expr { local_id: '5179934'}]-(id1945487024) CREATE (id1573241)-[:expr { local_id: '2552367'}]->(id5085809757) CREATE (id2080556:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2080556)<-[:linear_index {linear_index: '11}']-(id764666) CREATE (id2080556)<-[:infrule]-(declareinitialexpr) CREATE (id2080556)-[:expr { local_id: '5044727'}]->(id7924063906) CREATE (id2371653:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2371653)<-[:linear_index {linear_index: '6}']-(id764666) CREATE (id2371653)<-[:infrule]-(dividebothsidesby) CREATE (id2371653)<-[:expr { local_id: '2575148'}]-(id3488423948) CREATE (id2371653)<-[:expr { local_id: '1990849'}]-(id8162179726) CREATE (id2371653)-[:expr { local_id: '5003983'}]->(id9562264720) CREATE (id2420735:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2420735)<-[:linear_index {linear_index: '16}']-(id764666) CREATE (id2420735)<-[:infrule]-(raisebothsidestopower) CREATE (id2420735)<-[:expr { local_id: '7042641'}]-(id2114909846) CREATE (id2420735)<-[:expr { local_id: '1707483'}]-(id7564010952) CREATE (id2420735)-[:expr { local_id: '4039036'}]->(id8131665171) CREATE (id2537687:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2537687)<-[:linear_index {linear_index: '12}']-(id764666) CREATE (id2537687)<-[:infrule]-(raisebothsidestopower) CREATE (id2537687)<-[:expr { local_id: '5044727'}]-(id7924063906) CREATE (id2537687)<-[:expr { local_id: '6943575'}]-(id5516739892) CREATE (id2537687)-[:expr { local_id: '8620451'}]->(id6240546932) CREATE (id3651783:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3651783)<-[:linear_index {linear_index: '18}']-(id764666) CREATE (id3651783)<-[:infrule]-(changevariableXtoY) CREATE (id3651783)<-[:expr { local_id: '8754546'}]-(id7928111771) CREATE (id3651783)<-[:expr { local_id: '8164525'}]-(id6346902704) CREATE (id3651783)<-[:expr { local_id: '4008926'}]-(id7630953440) CREATE (id3651783)-[:expr { local_id: '4829867'}]->(id7267424860) CREATE (id4202402:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4202402)<-[:linear_index {linear_index: '14}']-(id764666) CREATE (id4202402)<-[:infrule]-(dividebothsidesby) CREATE (id4202402)<-[:expr { local_id: '4487508'}]-(id7517073655) CREATE (id4202402)<-[:expr { local_id: '3240507'}]-(id5426418187) CREATE (id4202402)-[:expr { local_id: '5382248'}]->(id6457999644) CREATE (id4242980:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4242980)<-[:linear_index {linear_index: '17}']-(id764666) CREATE (id4242980)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id4242980)<-[:expr { local_id: '4039036'}]-(id8131665171) CREATE (id4242980)<-[:expr { local_id: '5382248'}]-(id6457999644) CREATE (id4242980)-[:expr { local_id: '8754546'}]->(id7928111771) CREATE (id4463019:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4463019)<-[:linear_index {linear_index: '19}']-(id764666) CREATE (id4463019)<-[:infrule]-(raisebothsidestopower) CREATE (id4463019)<-[:expr { local_id: '4829867'}]-(id7267424860) CREATE (id4463019)<-[:expr { local_id: '1437372'}]-(id3911081515) CREATE (id4463019)-[:expr { local_id: '8722827'}]->(id4689334676) CREATE (id4708398:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4708398)<-[:linear_index {linear_index: '3}']-(id764666) CREATE (id4708398)<-[:infrule]-(declareassumption) CREATE (id4708398)-[:expr { local_id: '9492936'}]->(id6783009163) CREATE (id5303332:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5303332)<-[:linear_index {linear_index: '5}']-(id764666) CREATE (id5303332)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id5303332)<-[:expr { local_id: '8859060'}]-(id6955192897) CREATE (id5303332)<-[:expr { local_id: '1615903'}]-(id3507029294) CREATE (id5303332)-[:expr { local_id: '2575148'}]->(id3488423948) CREATE (id5941581:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5941581)<-[:linear_index {linear_index: '15}']-(id764666) CREATE (id5941581)<-[:infrule]-(declareinitialexpr) CREATE (id5941581)-[:expr { local_id: '7042641'}]->(id2114909846) CREATE (id6500091:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6500091)<-[:linear_index {linear_index: '4}']-(id764666) CREATE (id6500091)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6500091)<-[:expr { local_id: '7133735'}]-(id3736177473) CREATE (id6500091)<-[:expr { local_id: '9492936'}]-(id6783009163) CREATE (id6500091)-[:expr { local_id: '1615903'}]->(id3507029294) CREATE (id6549607:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6549607)<-[:linear_index {linear_index: '2}']-(id764666) CREATE (id6549607)<-[:infrule]-(declareinitialexpr) CREATE (id6549607)-[:expr { local_id: '8859060'}]->(id6955192897) CREATE (id7080403:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7080403)<-[:linear_index {linear_index: '20}']-(id764666) CREATE (id7080403)<-[:infrule]-(declarefinalexpr) CREATE (id7080403)<-[:expr { local_id: '8722827'}]-(id4689334676) CREATE (id7766035:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7766035)<-[:linear_index {linear_index: '7}']-(id764666) CREATE (id7766035)<-[:infrule]-(declareinitialexpr) CREATE (id7766035)-[:expr { local_id: '7265984'}]->(id3599953931) CREATE (id7979473:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7979473)<-[:linear_index {linear_index: '8}']-(id764666) CREATE (id7979473)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id7979473)<-[:expr { local_id: '5003983'}]-(id9562264720) CREATE (id7979473)<-[:expr { local_id: '7265984'}]-(id3599953931) CREATE (id7979473)-[:expr { local_id: '1337055'}]->(id4301729661) CREATE (id8400219:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8400219)<-[:linear_index {linear_index: '9}']-(id764666) CREATE (id8400219)<-[:infrule]-(factoroutX) CREATE (id8400219)<-[:expr { local_id: '1337055'}]-(id4301729661) CREATE (id8400219)<-[:expr { local_id: '5460074'}]-(id1268845856) CREATE (id8400219)-[:expr { local_id: '9195751'}]->(id2168306601) CREATE (id8982754:step { creation_date: '2023-06-12', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8982754)<-[:linear_index {linear_index: '13}']-(id764666) CREATE (id8982754)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id8982754)<-[:expr { local_id: '8620451'}]-(id6240546932) CREATE (id8982754)<-[:expr { local_id: '9195751'}]-(id2168306601) CREATE (id8982754)-[:expr { local_id: '4487508'}]->(id7517073655) CREATE (id9643014:step { creation_date: '2023-06-11', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9643014)<-[:linear_index {linear_index: '1}']-(id764666) CREATE (id9643014)<-[:infrule]-(declareinitialexpr) CREATE (id9643014)-[:expr { local_id: '7133735'}]->(id3736177473) CREATE (820976:derivation { name: 'KeplersThirdLawperiodsquaredproptodistancecubed', notes: 'https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law', creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1401711:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1401711)<-[:linear_index {linear_index: '8}']-(id820976) CREATE (id1401711)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1401711)<-[:expr { local_id: '2340248'}]-(id3132131132) CREATE (id1401711)<-[:expr { local_id: '9388996'}]-(id3896798826) CREATE (id1401711)-[:expr { local_id: '4575586'}]->(id9070394000) CREATE (id1630245:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1630245)<-[:linear_index {linear_index: '19}']-(id820976) CREATE (id1630245)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1630245)<-[:expr { local_id: '9110206'}]-(id2217103163) CREATE (id1630245)<-[:expr { local_id: '1709969'}]-(id4188580242) CREATE (id1630245)-[:expr { local_id: '8711868'}]->(id5658865948) CREATE (id1709854:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1709854)<-[:linear_index {linear_index: '7}']-(id820976) CREATE (id1709854)<-[:infrule]-(declareinitialexpr) CREATE (id1709854)-[:expr { local_id: '2340248'}]->(id3132131132) CREATE (id1785558:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1785558)<-[:linear_index {linear_index: '12}']-(id820976) CREATE (id1785558)<-[:infrule]-(multiplyRHSbyunity) CREATE (id1785558)<-[:expr { local_id: '7795202'}]-(id9170048197) CREATE (id1785558)<-[:expr { local_id: '3601544'}]-(id8122039815) CREATE (id1785558)-[:expr { local_id: '6577160'}]->(id1811867899) CREATE (id1810306:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1810306)<-[:linear_index {linear_index: '3}']-(id820976) CREATE (id1810306)<-[:infrule]-(changetwovariablesinexpr) CREATE (id1810306)<-[:expr { local_id: '8072137'}]-(id4393258808) CREATE (id1810306)<-[:expr { local_id: '2217101'}]-(id8916428651) CREATE (id1810306)<-[:expr { local_id: '1379855'}]-(id1635147226) CREATE (id1810306)<-[:expr { local_id: '4166166'}]-(id9884115626) CREATE (id1810306)<-[:expr { local_id: '4537297'}]-(id1036530438) CREATE (id1810306)-[:expr { local_id: '6652843'}]->(id3649797559) CREATE (id3184002:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3184002)<-[:linear_index {linear_index: '11}']-(id820976) CREATE (id3184002)<-[:infrule]-(raisebothsidestopower) CREATE (id3184002)<-[:expr { local_id: '7556753'}]-(id9152823411) CREATE (id3184002)<-[:expr { local_id: '6803169'}]-(id7445388869) CREATE (id3184002)-[:expr { local_id: '7795202'}]->(id9170048197) CREATE (id3800497:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3800497)<-[:linear_index {linear_index: '6}']-(id820976) CREATE (id3800497)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id3800497)<-[:expr { local_id: '6652843'}]-(id3649797559) CREATE (id3800497)<-[:expr { local_id: '4382594'}]-(id6829281943) CREATE (id3800497)-[:expr { local_id: '9388996'}]->(id3896798826) CREATE (id6033269:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6033269)<-[:linear_index {linear_index: '17}']-(id820976) CREATE (id6033269)<-[:infrule]-(declareinitialexpr) CREATE (id6033269)-[:expr { local_id: '4476518'}]->(id5128670694) CREATE (id6781365:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6781365)<-[:linear_index {linear_index: '16}']-(id820976) CREATE (id6781365)<-[:infrule]-(simplify) CREATE (id6781365)<-[:expr { local_id: '6644719'}]-(id3781109867) CREATE (id6781365)-[:expr { local_id: '1709969'}]->(id4188580242) CREATE (id6873690:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6873690)<-[:linear_index {linear_index: '1}']-(id820976) CREATE (id6873690)<-[:infrule]-(declareinitialexpr) CREATE (id6873690)-[:expr { local_id: '5331094'}]->(id1292735067) CREATE (id7496236:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7496236)<-[:linear_index {linear_index: '10}']-(id820976) CREATE (id7496236)<-[:infrule]-(multiplybothsidesby) CREATE (id7496236)<-[:expr { local_id: '6210646'}]-(id9838128064) CREATE (id7496236)<-[:expr { local_id: '5360317'}]-(id5684907106) CREATE (id7496236)-[:expr { local_id: '7556753'}]->(id9152823411) CREATE (id7602695:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7602695)<-[:linear_index {linear_index: '20}']-(id820976) CREATE (id7602695)<-[:infrule]-(declarefinalexpr) CREATE (id7602695)<-[:expr { local_id: '8711868'}]-(id5658865948) CREATE (id7749118:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7749118)<-[:linear_index {linear_index: '15}']-(id820976) CREATE (id7749118)<-[:infrule]-(multiplyRHSbyunity) CREATE (id7749118)<-[:expr { local_id: '8324356'}]-(id2906548078) CREATE (id7749118)<-[:expr { local_id: '1729739'}]-(id9524810853) CREATE (id7749118)-[:expr { local_id: '6644719'}]->(id3781109867) CREATE (id7784926:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7784926)<-[:linear_index {linear_index: '13}']-(id820976) CREATE (id7784926)<-[:infrule]-(declareassumption) CREATE (id7784926)-[:expr { local_id: '8233899'}]->(id5586102077) CREATE (id7947474:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7947474)<-[:linear_index {linear_index: '5}']-(id820976) CREATE (id7947474)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id7947474)<-[:expr { local_id: '2600680'}]-(id3176662571) CREATE (id7947474)<-[:expr { local_id: '5331094'}]-(id1292735067) CREATE (id7947474)-[:expr { local_id: '4382594'}]->(id6829281943) CREATE (id8457537:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8457537)<-[:linear_index {linear_index: '18}']-(id820976) CREATE (id8457537)<-[:infrule]-(dividebothsidesby) CREATE (id8457537)<-[:expr { local_id: '4476518'}]-(id5128670694) CREATE (id8457537)<-[:expr { local_id: '7400943'}]-(id8044416349) CREATE (id8457537)-[:expr { local_id: '9110206'}]->(id2217103163) CREATE (id9076010:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9076010)<-[:linear_index {linear_index: '4}']-(id820976) CREATE (id9076010)<-[:infrule]-(declareassumption) CREATE (id9076010)-[:expr { local_id: '2600680'}]->(id3176662571) CREATE (id9471787:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9471787)<-[:linear_index {linear_index: '9}']-(id820976) CREATE (id9471787)<-[:infrule]-(simplify) CREATE (id9471787)<-[:expr { local_id: '4575586'}]-(id9070394000) CREATE (id9471787)-[:expr { local_id: '6210646'}]->(id9838128064) CREATE (id9781109:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9781109)<-[:linear_index {linear_index: '14}']-(id820976) CREATE (id9781109)<-[:infrule]-(substituteRHSofexpr1intoexpr2) CREATE (id9781109)<-[:expr { local_id: '8233899'}]-(id5586102077) CREATE (id9781109)<-[:expr { local_id: '6577160'}]-(id1811867899) CREATE (id9781109)-[:expr { local_id: '8324356'}]->(id2906548078) CREATE (id9893296:step { creation_date: '2023-08-27', author: '4a0987466473c589d2c328d12856760e'} CREATE (id9893296)<-[:linear_index {linear_index: '2}']-(id820976) CREATE (id9893296)<-[:infrule]-(declareinitialexpr) CREATE (id9893296)-[:expr { local_id: '8072137'}]->(id4393258808) CREATE (884319:derivation { name: 'frequencyandperiod', notes: 'subset of the frequency relation derivation. Intended for display on the homepage', creation_date: '2020-04-23', author: 'bp'} CREATE (id2169431:step { creation_date: '2020-04-23', author: 'bp'} CREATE (id2169431)<-[:linear_index {linear_index: '3}']-(id884319) CREATE (id2169431)<-[:infrule]-(dividebothsidesby) CREATE (id2169431)<-[:expr { local_id: '2414344'}]-(id2131616531) CREATE (id2169431)<-[:expr { local_id: '8147899'}]-(id9565166889) CREATE (id2169431)-[:expr { local_id: '5564581'}]->(id2113211456) CREATE (id4718871:step { creation_date: '2020-04-23', author: 'bp'} CREATE (id4718871)<-[:linear_index {linear_index: '2}']-(id884319) CREATE (id4718871)<-[:infrule]-(multiplybothsidesby) CREATE (id4718871)<-[:expr { local_id: '6650345'}]-(id3131111133) CREATE (id4718871)<-[:expr { local_id: '4277577'}]-(id9040079362) CREATE (id4718871)-[:expr { local_id: '2414344'}]->(id2131616531) CREATE (id6286448:step { creation_date: '2020-04-23', author: 'bp'} CREATE (id6286448)<-[:linear_index {linear_index: '4}']-(id884319) CREATE (id6286448)<-[:infrule]-(declarefinalexpr) CREATE (id6286448)<-[:expr { local_id: '5564581'}]-(id2113211456) CREATE (id9278347:step { creation_date: '2020-04-23', author: 'bp'} CREATE (id9278347)<-[:linear_index {linear_index: '1}']-(id884319) CREATE (id9278347)<-[:infrule]-(declareinitialexpr) CREATE (id9278347)-[:expr { local_id: '6650345'}]->(id3131111133) CREATE (909006:derivation { name: 'totalelectricalresistanceforcircuitwithtworesistorsinseries', notes: 'http://www.dfcd.net/articles/derivations/resistors.html', creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1300532:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1300532)<-[:linear_index {linear_index: '7}']-(id909006) CREATE (id1300532)<-[:infrule]-(dividebothsidesby) CREATE (id1300532)<-[:expr { local_id: '4870091'}]-(id2715678478) CREATE (id1300532)<-[:expr { local_id: '7266552'}]-(id7844317489) CREATE (id1300532)-[:expr { local_id: '5454988'}]->(id7217021879) CREATE (id1423642:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1423642)<-[:linear_index {linear_index: '2}']-(id909006) CREATE (id1423642)<-[:infrule]-(changetwovariablesinexpr) CREATE (id1423642)<-[:expr { local_id: '3843961'}]-(id4087145886) CREATE (id1423642)<-[:expr { local_id: '4224430'}]-(id2698469612) CREATE (id1423642)<-[:expr { local_id: '9805089'}]-(id9830343096) CREATE (id1423642)<-[:expr { local_id: '3841737'}]-(id7774819339) CREATE (id1423642)<-[:expr { local_id: '9544818'}]-(id9174439158) CREATE (id1423642)-[:expr { local_id: '8012785'}]->(id7675171493) CREATE (id2221674:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2221674)<-[:linear_index {linear_index: '3}']-(id909006) CREATE (id2221674)<-[:infrule]-(changetwovariablesinexpr) CREATE (id2221674)<-[:expr { local_id: '3843961'}]-(id4087145886) CREATE (id2221674)<-[:expr { local_id: '6580231'}]-(id7497687256) CREATE (id2221674)<-[:expr { local_id: '9164799'}]-(id1608399874) CREATE (id2221674)<-[:expr { local_id: '4845850'}]-(id5890617067) CREATE (id2221674)<-[:expr { local_id: '6553310'}]-(id1484794622) CREATE (id2221674)-[:expr { local_id: '6379878'}]->(id6061695358) CREATE (id2247327:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2247327)<-[:linear_index {linear_index: '6}']-(id909006) CREATE (id2247327)<-[:infrule]-(substituteLHSofthreeexpressionsintoexpr) CREATE (id2247327)<-[:expr { local_id: '4107950'}]-(id4939880586) CREATE (id2247327)<-[:expr { local_id: '8012785'}]-(id7675171493) CREATE (id2247327)<-[:expr { local_id: '6379878'}]-(id6061695358) CREATE (id2247327)<-[:expr { local_id: '1124189'}]-(id9063568209) CREATE (id2247327)-[:expr { local_id: '4870091'}]->(id2715678478) CREATE (id3650891:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3650891)<-[:linear_index {linear_index: '1}']-(id909006) CREATE (id3650891)<-[:infrule]-(declareinitialexpr) CREATE (id3650891)-[:expr { local_id: '3843961'}]->(id4087145886) CREATE (id6550809:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6550809)<-[:linear_index {linear_index: '5}']-(id909006) CREATE (id6550809)<-[:infrule]-(declareinitialexpr) CREATE (id6550809)-[:expr { local_id: '4107950'}]->(id4939880586) CREATE (id6614719:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6614719)<-[:linear_index {linear_index: '8}']-(id909006) CREATE (id6614719)<-[:infrule]-(declarefinalexpr) CREATE (id6614719)<-[:expr { local_id: '5454988'}]-(id7217021879) CREATE (id7233885:step { creation_date: '2020-05-26', author: '4a0987466473c589d2c328d12856760e'} CREATE (id7233885)<-[:linear_index {linear_index: '4}']-(id909006) CREATE (id7233885)<-[:infrule]-(declareinitialexpr) CREATE (id7233885)-[:expr { local_id: '1124189'}]->(id9063568209) CREATE (918264:derivation { name: 'projectilepathin2Disparabolic', notes: 'Using the 2D equations of motion, show that projectile path is second order polynomial of the form y = a x^2 + b x + c', creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1975942:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1975942)<-[:linear_index {linear_index: '4}']-(id918264) CREATE (id1975942)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id1975942)<-[:expr { local_id: '8858248'}]-(id3274926090) CREATE (id1975942)<-[:expr { local_id: '5756391'}]-(id1405465835) CREATE (id1975942)-[:expr { local_id: '9683207'}]->(id7354529102) CREATE (id2879756:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2879756)<-[:linear_index {linear_index: '2}']-(id918264) CREATE (id2879756)<-[:infrule]-(dividebothsidesby) CREATE (id2879756)<-[:expr { local_id: '4718749'}]-(id9882526611) CREATE (id2879756)<-[:expr { local_id: '4648848'}]-(id6050070428) CREATE (id2879756)-[:expr { local_id: '8858248'}]->(id3274926090) CREATE (id3092929:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3092929)<-[:linear_index {linear_index: '5}']-(id918264) CREATE (id3092929)<-[:infrule]-(declarefinalexpr) CREATE (id3092929)<-[:expr { local_id: '9683207'}]-(id7354529102) CREATE (id4439032:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4439032)<-[:linear_index {linear_index: '1}']-(id918264) CREATE (id4439032)<-[:infrule]-(declareinitialexpr) CREATE (id4439032)-[:expr { local_id: '4718749'}]->(id9882526611) CREATE (id6487343:step { creation_date: '2020-05-17', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6487343)<-[:linear_index {linear_index: '3}']-(id918264) CREATE (id6487343)<-[:infrule]-(declareinitialexpr) CREATE (id6487343)-[:expr { local_id: '5756391'}]->(id1405465835) CREATE (920011:derivation { name: 'workandforceandenergy', creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1136729:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id1136729)<-[:linear_index {linear_index: '8}']-(id920011) CREATE (id1136729)<-[:infrule]-(substituteLHSoftwoexpressionsintoexpr) CREATE (id1136729)<-[:expr { local_id: '8207477'}]-(id7676652285) CREATE (id1136729)<-[:expr { local_id: '8883350'}]-(id4928007622) CREATE (id1136729)<-[:expr { local_id: '4236963'}]-(id4811121942) CREATE (id1136729)-[:expr { local_id: '4943050'}]->(id3360172339) CREATE (id2756830:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id2756830)<-[:linear_index {linear_index: '2}']-(id920011) CREATE (id2756830)<-[:infrule]-(integrate) CREATE (id2756830)<-[:expr { local_id: '2237799'}]-(id1590774089) CREATE (id2756830)-[:expr { local_id: '2565189'}]->(id5542528160) CREATE (id3538142:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id3538142)<-[:linear_index {linear_index: '7}']-(id920011) CREATE (id3538142)<-[:infrule]-(simplify) CREATE (id3538142)<-[:expr { local_id: '6760874'}]-(id9413699705) CREATE (id3538142)-[:expr { local_id: '4236963'}]->(id4811121942) CREATE (id4403236:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id4403236)<-[:linear_index {linear_index: '9}']-(id920011) CREATE (id4403236)<-[:infrule]-(declarefinalexpr) CREATE (id4403236)<-[:expr { local_id: '4943050'}]-(id3360172339) CREATE (id5622476:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id5622476)<-[:linear_index {linear_index: '3}']-(id920011) CREATE (id5622476)<-[:infrule]-(evaluatedefiniteintegral) CREATE (id5622476)<-[:expr { local_id: '2565189'}]-(id5542528160) CREATE (id5622476)-[:expr { local_id: '7362045'}]->(id3512166162) CREATE (id6093238:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6093238)<-[:linear_index {linear_index: '1}']-(id920011) CREATE (id6093238)<-[:infrule]-(declareinitialexpr) CREATE (id6093238)-[:expr { local_id: '2237799'}]->(id1590774089) CREATE (id6287856:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6287856)<-[:linear_index {linear_index: '4}']-(id920011) CREATE (id6287856)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id6287856)<-[:expr { local_id: '7362045'}]-(id3512166162) CREATE (id6287856)<-[:expr { local_id: '3086821'}]-(id5345738321) CREATE (id6287856)-[:expr { local_id: '6167182'}]->(id8953094349) CREATE (id6311864:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id6311864)<-[:linear_index {linear_index: '5}']-(id920011) CREATE (id6311864)<-[:infrule]-(changethreevariablesinexpr) CREATE (id6311864)<-[:expr { local_id: '4741344'}]-(id5611024898) CREATE (id6311864)<-[:expr { local_id: '5597968'}]-(id9623791270) CREATE (id6311864)<-[:expr { local_id: '3063741'}]-(id8111389082) CREATE (id6311864)<-[:expr { local_id: '2007644'}]-(id3652511721) CREATE (id6311864)<-[:expr { local_id: '2483388'}]-(id6701855578) CREATE (id6311864)<-[:expr { local_id: '5398681'}]-(id5398681502) CREATE (id6311864)<-[:expr { local_id: '2724984'}]-(id3183197515) CREATE (id6311864)-[:expr { local_id: '5997798'}]->(id3253234559) CREATE (id8305798:step { creation_date: '2020-05-24', author: '4a0987466473c589d2c328d12856760e'} CREATE (id8305798)<-[:linear_index {linear_index: '6}']-(id920011) CREATE (id8305798)<-[:infrule]-(substituteLHSofexpr1intoexpr2) CREATE (id8305798)<-[:expr { local_id: '5997798'}]-(id3253234559) CREATE (id8305798)<-[:expr { local_id: '6167182'}]-(id8953094349) CREATE (id8305798)-[:expr { local_id: '6760874'}]->(id9413699705)