review derivation: Euler equation to e^(i pi) + 1 = 0

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
3 simplify
1. 8332931442; locally 1148677:
$$\exp(i \pi) = \cos(\pi)+i \sin(\pi)$$
$$e^{pdg_{3141} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{3141} \right)} + \cos{\left(pdg_{3141} \right)}$$
1. 6885625907; locally 8524301:
$$\exp(i \pi) = -1 + i 0$$
$$e^{pdg_{3141} pdg_{4621}} = -1$$
LHS diff is 0 RHS diff is pdg4621*sin(pdg3141) + cos(pdg3141) + 1 8332931442:
6885625907:
8332931442:
6885625907:
2 change variable X to Y
1. 4938429483; locally 1580045:
$$\exp(i x) = \cos(x)+i \sin(x)$$
$$e^{pdg_{1464} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{1464} \right)} + \cos{\left(pdg_{1464} \right)}$$
1. 3268645065:
$$x$$
$$pdg_{1464}$$
2. 9350663581:
$$\pi$$
$$pdg_{3141}$$
1. 8332931442; locally 1148677:
$$\exp(i \pi) = \cos(\pi)+i \sin(\pi)$$
$$e^{pdg_{3141} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{3141} \right)} + \cos{\left(pdg_{3141} \right)}$$
valid 4938429483:
8332931442:
4938429483:
8332931442:
1 declare initial expr
1. 4938429483; locally 1580045:
$$\exp(i x) = \cos(x)+i \sin(x)$$
$$e^{pdg_{1464} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{1464} \right)} + \cos{\left(pdg_{1464} \right)}$$
no validation is available for declarations 4938429483:
4938429483:
5 add X to both sides
1. 3331824625; locally 9610540:
$$\exp(i \pi) = -1$$
$$e^{pdg_{3141} pdg_{4621}} = -1$$
1. 4901237716:
$$1$$
$$1$$
1. 2501591100; locally 9472905:
$$\exp(i \pi) + 1 = 0$$
$$e^{pdg_{3141} pdg_{4621}} + 1 = 0$$
valid 3331824625:
2501591100: error for dim with 2501591100
3331824625:
2501591100: N/A
4 simplify
1. 6885625907; locally 8524301:
$$\exp(i \pi) = -1 + i 0$$
$$e^{pdg_{3141} pdg_{4621}} = -1$$
1. 3331824625; locally 9610540:
$$\exp(i \pi) = -1$$
$$e^{pdg_{3141} pdg_{4621}} = -1$$
valid 6885625907:
3331824625:
6885625907:
3331824625:
6 declare final expr
1. 2501591100; locally 9472905:
$$\exp(i \pi) + 1 = 0$$
$$e^{pdg_{3141} pdg_{4621}} + 1 = 0$$
no validation is available for declarations 2501591100: error for dim with 2501591100
2501591100: N/A
Physics Derivation Graph: Steps for Euler equation to e^(i pi) + 1 = 0

Symbols for this derivation

symbol ID category latex scope dimension name value Used in derivations references
4621 variable i
$$i$$
['imaginary'] dimensionless imaginary unit
74
3141 constant \pi
$$\pi$$
['real'] dimensionless pi 3.1415   dimensionless
72
1464 variable x
$$x$$
['real'] dimensionless 140
MESSAGE:
• local variable 'all_df' referenced before assignment