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Expression of type Lambda

from the theory of proveit.linear_algebra.matrices.exponentiation

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, Conditional, Lambda, m, n
from proveit.linear_algebra import MatrixExp, Unitary
from proveit.logic import InSet
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Unitary(n)
expr = Lambda(A, Conditional(InSet(MatrixExp(A, m), sub_expr1), InSet(A, sub_expr1)))
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())
A \mapsto \left\{A^{m} \in \textrm{U}\left(n\right) \textrm{ if } A \in \textrm{U}\left(n\right)\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 14
body: 2
1ExprTuple14
2Conditionalvalue: 3
condition: 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple14, 9
8Operationoperator: 10
operands: 11
9Operationoperator: 12
operand: 16
10Literal
11ExprTuple14, 15
12Literal
13ExprTuple16
14Variable
15Variable
16Variable