Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

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, U, n
from proveit.linear_algebra import Adj, Unitary
from proveit.logic import Equals, InSet
from proveit.numbers import sqrt
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Lambda(U, Conditional(Equals(A, Qmult(U, sqrt(Qmult(Adj(A), A)))), InSet(U, Unitary(n))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

U \mapsto \left\{A = \left(U \thinspace \sqrt{\left(A^{\dagger} \thinspace A\right)}\right) \textrm{ if } U \in \textrm{U}\left(n\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 14 body: 2
1	ExprTuple	14
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	30, 9
7	Literal
8	ExprTuple	14, 10
9	Operation	operator: 21 operands: 11
10	Operation	operator: 12 operand: 16
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16
14	Variable
15	Operation	operator: 17 operands: 18
16	Variable
17	Literal
18	ExprTuple	19, 20
19	Operation	operator: 21 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 30
23	Literal
24	ExprTuple	26, 27
25	Operation	operator: 28 operand: 30
26	Literal
27	Literal
28	Literal
29	ExprTuple	30
30	Variable