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In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_axiom_expr # Load the stored axiom expression as 'stored_expr'
# import the special expression
from proveit.linear_algebra.linear_maps import commutator_def
In [2]:
# check that the built expression is the same as the stored expression
assert commutator_def.expr == stored_expr
assert commutator_def.expr._style_id == stored_expr._style_id
print("Passed sanity check: commutator_def matches stored_expr")
Passed sanity check: commutator_def matches stored_expr
In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{K}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{A, B \in V}~\left(\left[A, B\right] = \left(\left(A \circ B\right) + \left(-\left(B \circ A\right)\right)\right)\right)\right]\right]
In [4]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [5]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 10
operand: 2
1ExprTuple2
2Lambdaparameter: 21
body: 3
3Operationoperator: 10
operand: 5
4ExprTuple5
5Lambdaparameter: 38
body: 7
6ExprTuple38
7Conditionalvalue: 8
condition: 9
8Operationoperator: 10
operand: 14
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14
12Literal
13ExprTuple38, 15
14Lambdaparameters: 39
body: 16
15Operationoperator: 17
operand: 21
16Conditionalvalue: 19
condition: 20
17Literal
18ExprTuple21
19Operationoperator: 22
operands: 23
20Operationoperator: 24
operands: 25
21Variable
22Literal
23ExprTuple26, 27
24Literal
25ExprTuple28, 29
26Operationoperator: 30
operands: 39
27Operationoperator: 31
operands: 32
28Operationoperator: 34
operands: 33
29Operationoperator: 34
operands: 35
30Literal
31Literal
32ExprTuple36, 37
33ExprTuple46, 38
34Literal
35ExprTuple45, 38
36Operationoperator: 43
operands: 39
37Operationoperator: 40
operand: 42
38Variable
39ExprTuple46, 45
40Literal
41ExprTuple42
42Operationoperator: 43
operands: 44
43Literal
44ExprTuple45, 46
45Variable
46Variable