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Expression of type ExprTuple

from the theory of proveit.linear_algebra.linear_maps

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Composition, Conditional, ExprTuple, Lambda, V
from proveit.linear_algebra import Commutator, VecAdd, VecNeg
from proveit.logic import And, Equals, InSet
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A, B], Conditional(Equals(Commutator(A, B), VecAdd(Composition(A, B), VecNeg(Composition(B, A)))), And(InSet(A, V), InSet(B, V)))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\left(A, B\right) \mapsto \left\{\left[A, B\right] = \left(\left(A \circ B\right) + \left(-\left(B \circ A\right)\right)\right) \textrm{ if } A \in V ,  B \in V\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 22
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12
9Operationoperator: 13
operands: 22
10Operationoperator: 14
operands: 15
11Operationoperator: 17
operands: 16
12Operationoperator: 17
operands: 18
13Literal
14Literal
15ExprTuple19, 20
16ExprTuple29, 21
17Literal
18ExprTuple28, 21
19Operationoperator: 26
operands: 22
20Operationoperator: 23
operand: 25
21Variable
22ExprTuple29, 28
23Literal
24ExprTuple25
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Variable
29Variable