Review Derivation: Physics Derivation Graph

Return to navigation page or list derivations

Review Euler equation to exp(i pi) + 1 = 0

abstract:
reference:

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4938429483 $\exp(i x) = \cos(x)+i \sin(x)$	no validation is available for declarations
2	0000111886: change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\ref{eq:#3}; yields Eq.~\ref{eq:#4}.	4938429483 $\exp(i x) = \cos(x)+i \sin(x)$	9350663581 $\pi$ 3268645065 $x$	8332931442 $\exp(i \pi) = \cos(\pi)+i \sin(\pi)$	LHS diff is exp(pdg0001464pdg0004621) - exp(pdg0003141pdg0004621) RHS diff is pdg0004621sin(pdg0001464) - pdg0004621sin(pdg0003141) + cos(pdg0001464) - cos(pdg0003141)
3	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	8332931442 $\exp(i \pi) = \cos(\pi)+i \sin(\pi)$		6885625907 $\exp(i \pi) = -1 + i 0$	LHS diff is 0 RHS diff is pdg0004621*sin(pdg0003141) + cos(pdg0003141) + 1
4	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	6885625907 $\exp(i \pi) = -1 + i 0$		3331824625 $\exp(i \pi) = -1$	valid
5	0000111530: add X to both sides number of inputs: 1; feeds: 1; outputs: 1 Add $#1$ to both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	3331824625 $\exp(i \pi) = -1$	4901237716 $1$	2501591100 $\exp(i \pi) + 1 = 0$	valid
6	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	2501591100 $\exp(i \pi) + 1 = 0$			no validation is available for declarations

Symbols used in Euler equation to exp(i pi) + 1 = 0

0000003141: $ \pi $
0000004621: $ i $
0000001464: $ x $

d3js visualization of steps and expressions in Euler equation to exp(i pi) + 1 = 0

Hold the mouse over a node to highlight that node and its neighbors. You can zoom in/out. You can pan the image. You can move nodes by clicking and dragging.

Actions: Edit Derivation

You must be logged in to edit the steps of derivation, edit the abstract, or rename the derivation.

Generate Tex file or PDF file

Delete Derivation and all associated steps

You must be logged in to delete the derivation.

timing of Neo4j queries:

0.007 seconds for pdg_app/to_review_derivation 07ddc033-b003-45ab-9320-2ff23f73fa6a
0.018 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivation20bb9128-61b4-4a8a-b1e2-0e3f105c8729
0.007 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_ID20bb9128-61b4-4a8a-b1e2-0e3f105c8729
0.012 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUT20bb9128-61b4-4a8a-b1e2-0e3f105c8729
0.006 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEED20bb9128-61b4-4a8a-b1e2-0e3f105c8729
0.008 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUT20bb9128-61b4-4a8a-b1e2-0e3f105c8729
0.012 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_step20bb9128-61b4-4a8a-b1e2-0e3f105c8729
0.016 seconds for pdg_app/ 07ddc033-b003-45ab-9320-2ff23f73fa6a

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			4938429483 \(\exp(i x) = \cos(x)+i \sin(x)\)	no validation is available for declarations
2	0000111886: change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\ref{eq:#3}; yields Eq.~\ref{eq:#4}.	4938429483 \(\exp(i x) = \cos(x)+i \sin(x)\)	9350663581 \(\pi\) 3268645065 \(x\)	8332931442 \(\exp(i \pi) = \cos(\pi)+i \sin(\pi)\)	LHS diff is exp(pdg0001464pdg0004621) - exp(pdg0003141pdg0004621) RHS diff is pdg0004621sin(pdg0001464) - pdg0004621sin(pdg0003141) + cos(pdg0001464) - cos(pdg0003141)
3	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	8332931442 \(\exp(i \pi) = \cos(\pi)+i \sin(\pi)\)		6885625907 \(\exp(i \pi) = -1 + i 0\)	LHS diff is 0 RHS diff is pdg0004621*sin(pdg0003141) + cos(pdg0003141) + 1
4	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	6885625907 \(\exp(i \pi) = -1 + i 0\)		3331824625 \(\exp(i \pi) = -1\)	valid
5	0000111530: add X to both sides number of inputs: 1; feeds: 1; outputs: 1 Add $#1$ to both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	3331824625 \(\exp(i \pi) = -1\)	4901237716 \(1\)	2501591100 \(\exp(i \pi) + 1 = 0\)	valid
6	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	2501591100 \(\exp(i \pi) + 1 = 0\)			no validation is available for declarations