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, D, ExprTuple, Lambda, U, V, n
from proveit.linear_algebra import Diagonal, MatrixSpace, Unitary
from proveit.logic import Equals, Exists, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult

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

\left(A \mapsto \left\{\exists_{D \in \textrm{D}\left(n\right)}~\left[\exists_{U, V \in \textrm{U}\left(n\right)}~\left(A = \left(U \thinspace D \thinspace V\right)\right)\right] \textrm{ if } A \in \mathbb{C}^{n \times 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: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operand: 8
5	Operation	operator: 38 operands: 7
6	ExprTuple	8
7	ExprTuple	31, 9
8	Lambda	parameter: 40 body: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	40
11	Conditional	value: 14 condition: 15
12	Literal
13	NamedExprs	field: 16 rows: 46 columns: 46
14	Operation	operator: 17 operand: 20
15	Operation	operator: 38 operands: 19
16	Literal
17	Literal
18	ExprTuple	20
19	ExprTuple	40, 21
20	Lambda	parameters: 22 body: 23
21	Operation	operator: 24 operand: 46
22	ExprTuple	41, 42
23	Conditional	value: 25 condition: 26
24	Literal
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Operation	operator: 35 operands: 36
33	Operation	operator: 38 operands: 37
34	Operation	operator: 38 operands: 39
35	Literal
36	ExprTuple	41, 40, 42
37	ExprTuple	41, 43
38	Literal
39	ExprTuple	42, 43
40	Variable
41	Variable
42	Variable
43	Operation	operator: 44 operand: 46
44	Literal
45	ExprTuple	46
46	Variable