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Review Compton's equation for scattering

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.			1638282134 $\vec{p}_{\rm before} = \vec{p}_{\rm after}$	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.			8257621077 $\vec{p}_{\rm before} = \vec{p}_{1}$	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.			8311458118 $\vec{p}_{\rm after} = \vec{p}_{2}+\vec{p}_{electron}$	no validation is available for declarations
4	0000111556: substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	1638282134 $\vec{p}_{\rm before} = \vec{p}_{\rm after}$ 8257621077 $\vec{p}_{\rm before} = \vec{p}_{1}$		3951205425 $\vec{p}_{\rm after} = \vec{p}_{1}$	valid
5	0000111556: substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8311458118 $\vec{p}_{\rm after} = \vec{p}_{2}+\vec{p}_{electron}$ 3951205425 $\vec{p}_{\rm after} = \vec{p}_{1}$		8139187332 $\vec{p}_{1} = \vec{p}_{2}+\vec{p}_{electron}$	LHS diff is pdg0002097 + pdg0004299 - pdg0006029 RHS diff is -pdg0002097 - pdg0004299 + pdg0006029
6	0000111282: subtract X from both sides number of inputs: 1; feeds: 1; outputs: 1 Subtract $#1$ from both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8139187332 $\vec{p}_{1} = \vec{p}_{2}+\vec{p}_{electron}$	0002338514 $\vec{p}_{2}$	5530148480 $\vec{p}_{1}-\vec{p}_{2} = \vec{p}_{electron}$	valid
7	0000111268: swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.	5530148480 $\vec{p}_{1}-\vec{p}_{2} = \vec{p}_{electron}$		7917051060 $\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}$	valid
8	0000111253: multiply expr 1 by expr 2 number of inputs: 2; feeds: 0; outputs: 1 Multiply Eq.~\ref{eq:#1} by Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	7917051060 $\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}$ 7917051060 $\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}$		6742123016 $\vec{p}_{electron}\cdot\vec{p}_{electron} = ( \vec{p}_{1}\cdot\vec{p}_{1})+( \vec{p}_{2}\cdot\vec{p}_{2})-2( \vec{p}_{1}\cdot\vec{p}_{2})$	Not evaluated due to missing term in SymPy

Symbols used in Compton's equation for scattering

0000006029: $ \vec{p}_1 $
0000002097: $ \vec{p}_2 $
0000005493: $ \vec{p}_{\rm after} $
0000001302: $ \vec{p}_{\rm before} $
0000004299: $ \vec{p}_{\rm electron} $

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timing of Neo4j queries:

0.003 seconds for pdg_app/to_review_derivation d4cd425b-6e07-4ab9-8de5-51cdf8493f58
0.003 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivationcab700e3-51b7-4138-9737-53c94533dfa9
0.008 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_IDcab700e3-51b7-4138-9737-53c94533dfa9
0.008 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUTcab700e3-51b7-4138-9737-53c94533dfa9
0.007 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEEDcab700e3-51b7-4138-9737-53c94533dfa9
0.007 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUTcab700e3-51b7-4138-9737-53c94533dfa9
0.006 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_stepcab700e3-51b7-4138-9737-53c94533dfa9
0.004 seconds for pdg_app/ d4cd425b-6e07-4ab9-8de5-51cdf8493f58

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.			1638282134 \(\vec{p}_{\rm before} = \vec{p}_{\rm after}\)	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.			8257621077 \(\vec{p}_{\rm before} = \vec{p}_{1}\)	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.			8311458118 \(\vec{p}_{\rm after} = \vec{p}_{2}+\vec{p}_{electron}\)	no validation is available for declarations
4	0000111556: substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	1638282134 \(\vec{p}_{\rm before} = \vec{p}_{\rm after}\) 8257621077 \(\vec{p}_{\rm before} = \vec{p}_{1}\)		3951205425 \(\vec{p}_{\rm after} = \vec{p}_{1}\)	valid
5	0000111556: substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8311458118 \(\vec{p}_{\rm after} = \vec{p}_{2}+\vec{p}_{electron}\) 3951205425 \(\vec{p}_{\rm after} = \vec{p}_{1}\)		8139187332 \(\vec{p}_{1} = \vec{p}_{2}+\vec{p}_{electron}\)	LHS diff is pdg0002097 + pdg0004299 - pdg0006029 RHS diff is -pdg0002097 - pdg0004299 + pdg0006029
6	0000111282: subtract X from both sides number of inputs: 1; feeds: 1; outputs: 1 Subtract $#1$ from both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	8139187332 \(\vec{p}_{1} = \vec{p}_{2}+\vec{p}_{electron}\)	0002338514 \(\vec{p}_{2}\)	5530148480 \(\vec{p}_{1}-\vec{p}_{2} = \vec{p}_{electron}\)	valid
7	0000111268: swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.	5530148480 \(\vec{p}_{1}-\vec{p}_{2} = \vec{p}_{electron}\)		7917051060 \(\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}\)	valid
8	0000111253: multiply expr 1 by expr 2 number of inputs: 2; feeds: 0; outputs: 1 Multiply Eq.~\ref{eq:#1} by Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.	7917051060 \(\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}\) 7917051060 \(\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}\)		6742123016 \(\vec{p}_{electron}\cdot\vec{p}_{electron} = ( \vec{p}_{1}\cdot\vec{p}_{1})+( \vec{p}_{2}\cdot\vec{p}_{2})-2( \vec{p}_{1}\cdot\vec{p}_{2})\)	Not evaluated due to missing term in SymPy