Expression of type ExprTuple

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, ExprTuple, Lambda, U, n
from proveit.linear_algebra import Adj, MatrixSpace, Unitary
from proveit.logic import Equals, Exists, Forall, InSet
from proveit.numbers import Complex, NaturalPos, sqrt
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [A], instance_expr = Exists(instance_param_or_params = [U], instance_expr = Equals(A, Qmult(sqrt(Qmult(A, Adj(A))), U)), domain = Unitary(n)), domain = MatrixSpace(field = Complex, rows = n, columns = n)), InSet(n, NaturalPos))))

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())

\left(n \mapsto \left\{\forall_{A \in \mathbb{C}^{n \times n}}~\left[\exists_{U \in \textrm{U}\left(n\right)}~\left(A = \left(\sqrt{\left(A \thinspace A^{\dagger}\right)} \thinspace U\right)\right)\right] \textrm{ if } n \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 36 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 27 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	36, 9
8	Lambda	parameter: 50 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operand: 16
12	Operation	operator: 27 operands: 15
13	Literal
14	ExprTuple	16
15	ExprTuple	50, 17
16	Lambda	parameter: 35 body: 19
17	Operation	operator: 20 operands: 21
18	ExprTuple	35
19	Conditional	value: 22 condition: 23
20	Literal
21	NamedExprs	field: 24 rows: 36 columns: 36
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	50, 29
27	Literal
28	ExprTuple	35, 30
29	Operation	operator: 41 operands: 31
30	Operation	operator: 32 operand: 36
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36
34	Operation	operator: 37 operands: 38
35	Variable
36	Variable
37	Literal
38	ExprTuple	39, 40
39	Operation	operator: 41 operands: 42
40	Operation	operator: 43 operands: 44
41	Literal
42	ExprTuple	50, 45
43	Literal
44	ExprTuple	46, 47
45	Operation	operator: 48 operand: 50
46	Literal
47	Literal
48	Literal
49	ExprTuple	50
50	Variable