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

Generate Tex file or PDF file

Delete Derivation and all associated steps

This does not remove expressions, symbols, and operations.

timing of Neo4j queries:

0.008 seconds for pdg_app/to_review_derivation c505651c-4c94-4cf7-9e2e-980357128410
0.013 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivation134cc3eb-971d-40c8-99e9-c76a22b9cb2c
0.017 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_ID134cc3eb-971d-40c8-99e9-c76a22b9cb2c
0.014 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUT134cc3eb-971d-40c8-99e9-c76a22b9cb2c
0.015 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEED134cc3eb-971d-40c8-99e9-c76a22b9cb2c
0.016 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUT134cc3eb-971d-40c8-99e9-c76a22b9cb2c
0.017 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_step134cc3eb-971d-40c8-99e9-c76a22b9cb2c
0.004 seconds for pdg_app/ c505651c-4c94-4cf7-9e2e-980357128410

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