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Review frequency relations

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.			5900595848 $k = \frac{\omega}{v}$	no validation is available for declarations
2	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			0404050504 $\lambda = \frac{v}{f}$	no validation is available for declarations
3	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			3131211131 $\omega = 2 \pi f$	no validation is available for declarations
4	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			3131111133 $T = 1 / f$	no validation is available for declarations
5	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	5900595848 $k = \frac{\omega}{v}$ 3132131132 $\omega = \frac{2\pi}{T}$		0934990943 $k = \frac{2 \pi}{v T}$	LHS diff is pdg0002321 - pdg0005321 RHS diff is 2pdg0003141(pdg0001357 - 1)/(pdg0001357*pdg0009491)
6	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	0404050504 $\lambda = \frac{v}{f}$ 3131111133 $T = 1 / f$		1293923844 $\lambda = v T$	LHS diff is -pdg0001115 + pdg0009491 RHS diff is -pdg0001357*pdg0009491 + 1/pdg0004201
7	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	0934990943 $k = \frac{2 \pi}{v T}$ 1293923844 $\lambda = v T$		3121513111 $k = \frac{2 \pi}{\lambda}$	LHS diff is pdg0001115 - pdg0005321 RHS diff is pdg0001357pdg0009491 - 2pdg0003141/pdg0001115
8	0000111182: multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	3131111133 $T = 1 / f$	0005749291 $f$	2131616531 $T f = 1$	LHS arithmetic error. Diff: pdg0009491*(-pdg0004201 + pdg0006235)
9	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	2131616531 $T f = 1$	0008837284 $T$	2113211456 $f = 1/T$	valid
10	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	3131211131 $\omega = 2 \pi f$ 2113211456 $f = 1/T$		3132131132 $\omega = \frac{2\pi}{T}$	LHS diff is -pdg0002321 + pdg0004201 RHS diff is (1 - 2*pdg0003141)/pdg0009491
11	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	3121513111 $k = \frac{2 \pi}{\lambda}$			no validation is available for declarations

Symbols used in frequency relations

0000001115: $ \lambda $
0000002321: $ \omega $
0000003141: $ \pi $
0000004201: $ f $
0000006235: $ f $
0000005321: $ k $
0000009491: $ T $
0000001357: $ v $

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timing of Neo4j queries:

0.007 seconds for pdg_app/to_review_derivation 1084bd46-e763-49da-b93c-66813506fe87
0.015 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivationa34f0e4b-15c8-4cb3-abec-912f005ab6fa
0.006 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_IDa34f0e4b-15c8-4cb3-abec-912f005ab6fa
0.006 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUTa34f0e4b-15c8-4cb3-abec-912f005ab6fa
0.003 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEEDa34f0e4b-15c8-4cb3-abec-912f005ab6fa
0.003 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUTa34f0e4b-15c8-4cb3-abec-912f005ab6fa
0.008 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_stepa34f0e4b-15c8-4cb3-abec-912f005ab6fa
0.005 seconds for pdg_app/ 1084bd46-e763-49da-b93c-66813506fe87

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.			5900595848 \(k = \frac{\omega}{v}\)	no validation is available for declarations
2	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			0404050504 \(\lambda = \frac{v}{f}\)	no validation is available for declarations
3	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			3131211131 \(\omega = 2 \pi f\)	no validation is available for declarations
4	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			3131111133 \(T = 1 / f\)	no validation is available for declarations
5	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	5900595848 \(k = \frac{\omega}{v}\) 3132131132 \(\omega = \frac{2\pi}{T}\)		0934990943 \(k = \frac{2 \pi}{v T}\)	LHS diff is pdg0002321 - pdg0005321 RHS diff is 2pdg0003141(pdg0001357 - 1)/(pdg0001357*pdg0009491)
6	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	0404050504 \(\lambda = \frac{v}{f}\) 3131111133 \(T = 1 / f\)		1293923844 \(\lambda = v T\)	LHS diff is -pdg0001115 + pdg0009491 RHS diff is -pdg0001357*pdg0009491 + 1/pdg0004201
7	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	0934990943 \(k = \frac{2 \pi}{v T}\) 1293923844 \(\lambda = v T\)		3121513111 \(k = \frac{2 \pi}{\lambda}\)	LHS diff is pdg0001115 - pdg0005321 RHS diff is pdg0001357pdg0009491 - 2pdg0003141/pdg0001115
8	0000111182: multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	3131111133 \(T = 1 / f\)	0005749291 \(f\)	2131616531 \(T f = 1\)	LHS arithmetic error. Diff: pdg0009491*(-pdg0004201 + pdg0006235)
9	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	2131616531 \(T f = 1\)	0008837284 \(T\)	2113211456 \(f = 1/T\)	valid
10	0000111634: substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	3131211131 \(\omega = 2 \pi f\) 2113211456 \(f = 1/T\)		3132131132 \(\omega = \frac{2\pi}{T}\)	LHS diff is -pdg0002321 + pdg0004201 RHS diff is (1 - 2*pdg0003141)/pdg0009491
11	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	3121513111 \(k = \frac{2 \pi}{\lambda}\)			no validation is available for declarations