{
"LHS of expr 1 equals LHS of expr 2": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"RHS of expr 1 equals RHS of expr 2": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"X cross both sides by": {
"assumptions": "linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Take cross product of $#1$ and Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"X dot both sides": {
"assumptions": "linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Take inner product of $#1$ with Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"add X to both sides": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Add $#1$ to both sides of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"add expr 1 to expr 2": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Add Eq.~\\ref{eq:#1} to Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"add zero to LHS": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"add zero to RHS": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"apply divergence": {
"assumptions": "multi-variable calculus",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Apply divergence to both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"apply function to both sides of expression": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-23",
"latex": "Apply function $#1$ with argument $#2$ to Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}",
"notes": "Example: apply sin(x) to \"a = b + c\"",
"number of feeds": 2,
"number of inputs": 1,
"number of outputs": 1
},
"apply gradient to scalar function": {
"assumptions": "multi-variable calculus",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Apply gradient to both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"apply operator to bra": {
"assumptions": "quantum: Dirac notation",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-05-31",
"latex": "Apply operator in Eq.~\\ref{eq:#1} to bra; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"apply operator to ket": {
"assumptions": "quantum: Dirac notation",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-05-31",
"latex": "Apply operator in Eq.~\\ref{eq:#1} to ket; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"assume N dimensions": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Assume $#1$ dimensions; decompose vector to be Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 0,
"number of outputs": 1
},
"both sides cross X": {
"assumptions": "linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Take cross product of Eq.~\\ref{eq:#2} and $#1$; yields Eq.~\\ref{eq:#3}",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"both sides dot X": {
"assumptions": "linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Take inner product of Eq.~\\ref{eq:#2} with $#1$; yields Eq.~\\ref{eq:#3}",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"boundary condition": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-05-17",
"latex": "Boundary condition: Eq.~\\ref{eq:#2} when Eq.~\\ref{eq#1}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"boundary condition for expr": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "A boundary condition for Eq.~\\ref{eq:#1} is Eq.~\\ref{eq:#2}",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"change five variables in expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 10,
"number of inputs": 1,
"number of outputs": 1
},
"change four variables in expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 8,
"number of inputs": 1,
"number of outputs": 1
},
"change six variables in expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 12,
"number of inputs": 1,
"number of outputs": 1
},
"change three variables in expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 6,
"number of inputs": 1,
"number of outputs": 1
},
"change two variables in expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 4,
"number of inputs": 1,
"number of outputs": 1
},
"change variable X to Y": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.",
"notes": "",
"number of feeds": 2,
"number of inputs": 1,
"number of outputs": 1
},
"claim LHS equals RHS": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Thus we see that LHS of Eq.~\\ref{eq:#1} is equal to RHS.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 0
},
"claim expr 1 equals expr 2": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Thus we see that Eq.~\\ref{eq:#1} is equivalent to Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 0
},
"combine like terms": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Combine like terms in Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"conjugate both sides": {
"assumptions": "complex values",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Conjugate both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"conjugate function X": {
"assumptions": "complex values",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Conjugate $#1$ in Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"conjugate transpose both sides": {
"assumptions": "complex valued linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Conjugate transpose of both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"declare assumption": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Eq.~\\ref{eq:#1} is an assumption.",
"notes": "",
"number of feeds": 0,
"number of inputs": 0,
"number of outputs": 1
},
"declare final expr": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Eq.~\\ref{eq:#1} is one of the final equations.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 0
},
"declare guess solution": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Judicious choice as a guessed solution to Eq.~\\ref{eq:#1} is",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"declare identity": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Eq.~\\ref{eq:#1} is an identity.",
"notes": "",
"number of feeds": 0,
"number of inputs": 0,
"number of outputs": 1
},
"declare initial expr": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Eq.~\\ref{eq:#1} is an initial equation.",
"notes": "",
"number of feeds": 0,
"number of inputs": 0,
"number of outputs": 1
},
"differentiate with respect to": {
"assumptions": "differential equations",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Differentiate Eq.~\\ref{eq:#2} with respect to $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"distribute conjugate to factors": {
"assumptions": "complex values",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Distribute conjugate to factors in Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"distribute conjugate transpose to factors": {
"assumptions": "complex valued linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Distribute conjugate transpose to factors in Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"divide both sides by": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"divide expr 1 by expr 2": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-05-17",
"latex": "Divide Eq.~\\ref{eq:#1} by Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"drop non-dominant term": {
"assumptions": "",
"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}",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"evaluate definite integral": {
"assumptions": "multi-variable calculus",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Evaluate definite integral Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"expand LHS": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Expand the LHS of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"expand RHS": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Expand the RHS of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"expand integrand": {
"assumptions": "multi-variable calculus",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Expand integrand of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"expand magnitude to conjugate": {
"assumptions": "complex values",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Expand $#1$ in Eq.~\\ref{eq:#2} with conjugate; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"expr 1 is equivalent to expr 2 under the condition": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"expr 1 is true under condition expr 2": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"factor out X": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Factor $#1$ from Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"factor out X from LHS": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Factor $#1$ from the LHS of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"factor out X from RHS": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Factor $#1$ from the RHS of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"function is even": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 3,
"number of inputs": 1,
"number of outputs": 1
},
"function is odd": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 3,
"number of inputs": 1,
"number of outputs": 1
},
"indefinite integral over": {
"assumptions": "multi-variable calculus",
"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}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"indefinite integrate LHS over": {
"assumptions": "multi-variable calculus",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Indefinite integral of LHS of Eq.~\\ref{eq:#2} over $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"indefinite integrate RHS over": {
"assumptions": "multi-variable calculus",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Indefinite integral of RHS of Eq.~\\ref{eq:#2} over $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"indefinite integration": {
"assumptions": "multi-variable calculus",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Indefinite integral of both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"integrate": {
"assumptions": "multi-variable calculus",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-05-24",
"latex": "Integrate Eq.~ref{eq:#1}; yields Eq.~ref{eq:#2}.",
"notes": "not clear how to specify limits for an arbitrary number of integrals",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"integrate over from to": {
"assumptions": "multi-variable calculus",
"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}.",
"notes": "",
"number of feeds": 3,
"number of inputs": 1,
"number of outputs": 1
},
"make expr power": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Make Eq.~\\ref{eq:#2} the power of $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"maximum of expr": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-05-17",
"latex": "The maximum of Eq.~\\ref{eq:#2} with respect to $#1$ is Eq.~\\ref{eq:#3}",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"multiply LHS by unity": {
"assumptions": "",
"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}",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"multiply RHS by unity": {
"assumptions": "",
"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}",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"multiply both sides by": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"multiply expr 1 by expr 2": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Multiply Eq.~\\ref{eq:#1} by Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"normalization condition": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Normalization condition is Eq.~\\ref{eq:#1}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 0,
"number of outputs": 1
},
"partially differentiate with respect to": {
"assumptions": "differential equations",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Partially differentiate Eq.~\\ref{eq:#2} with respect to $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"raise both sides to power": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Raise both sides of Eq.~\\ref{eq:#2} to $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"replace constant with value": {
"assumptions": "",
"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}",
"notes": "",
"number of feeds": 3,
"number of inputs": 1,
"number of outputs": 1
},
"replace curl with LeviCevita summation contravariant": {
"assumptions": "linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Replace curl in Eq.~\\ref{eq:#1} with Levi-Cevita contravariant; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"replace scalar with vector": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"replace summation notation with vector notation": {
"assumptions": "linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Replace summation notation in Eq.~\\ref{eq:#1} with vector notation; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"select imaginary parts": {
"assumptions": "complex values",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Select imaginary parts of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"select real parts": {
"assumptions": "complex values",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Select real parts of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"separate three vector components": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 3
},
"separate two vector components": {
"assumptions": "",
"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}",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 2
},
"separate vector into two trigonometric ratios": {
"assumptions": "",
"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}.",
"notes": "geometry argument in 2D",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 2
},
"simplify": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"solve for X": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Solve Eq.~\\ref{eq:#2} for $#1$; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"square root both sides": {
"assumptions": "",
"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}.",
"notes": "related to raise both sides to power",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 2
},
"substitute LHS of expr 1 into expr 2": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"substitute LHS of five expressions into expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 6,
"number of outputs": 1
},
"substitute LHS of four expressions into expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 5,
"number of outputs": 1
},
"substitute LHS of six expressions into expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 7,
"number of outputs": 1
},
"substitute LHS of three expressions into expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 4,
"number of outputs": 1
},
"substitute LHS of two expressions into expr": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 3,
"number of outputs": 1
},
"substitute RHS of expr 1 into expr 2": {
"assumptions": "",
"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}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"subtract X from both sides": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Subtract $#1$ from both sides of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.",
"notes": "",
"number of feeds": 1,
"number of inputs": 1,
"number of outputs": 1
},
"subtract expr 1 from expr 2": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-20",
"latex": "Subtract Eq.~\\ref{eq:#1} from Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#2}.",
"notes": "complement of \"add expr X to expr Y\"",
"number of feeds": 0,
"number of inputs": 2,
"number of outputs": 1
},
"sum exponents": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Sum exponents on LHS and RHS of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"sum exponents LHS": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Sum exponents on LHS of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"sum exponents RHS": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Sum exponents on RHS of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"swap LHS with RHS": {
"assumptions": "",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Swap LHS of Eq.~\\ref{eq:#1} with RHS; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
},
"take curl of both sides": {
"assumptions": "linear algebra",
"author": "4a0987466473c589d2c328d12856760e",
"creation date": "2020-04-14",
"latex": "Apply curl to both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.",
"notes": "",
"number of feeds": 0,
"number of inputs": 1,
"number of outputs": 1
}
}