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, W, i, j, m, n
from proveit.core_expr_types import v_i, w_1_to_n, w_j
from proveit.linear_algebra import OrthoNormBases, VecSum
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult
from proveit.physics.quantum.algebra import w_1_to_n_kets

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([w_1_to_n], Conditional(Equals(A, VecSum(index_or_indices = [i], summand = VecSum(index_or_indices = [j], summand = Qmult(Bra(w_j), A, Ket(v_i), Ket(w_j), Bra(v_i)), domain = Interval(one, n)), domain = Interval(one, m))), InSet(w_1_to_n_kets, OrthoNormBases(W)))))

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(\left(w_{1}, w_{2}, \ldots, w_{n}\right) \mapsto \left\{A = \left(\sum_{i=1}^{m} \left(\sum_{j=1}^{n} \left(\langle w_{j} \rvert \thinspace A \thinspace \lvert v_{i} \rangle \thinspace \lvert w_{j} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right) \textrm{ if } \left\{\lvert w_{1} \rangle, \lvert w_{2} \rangle, \ldots, \lvert w_{n} \rangle\right\} \in \textrm{O.N.Bases}\left(W\right)\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	parameters: 2 body: 3
2	ExprTuple	4
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 59 end_index: 60
5	Operation	operator: 8 operands: 9
6	Operation	operator: 43 operands: 10
7	Lambda	parameter: 40 body: 33
8	Literal
9	ExprTuple	46, 11
10	ExprTuple	12, 13
11	Operation	operator: 27 operand: 19
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operand: 21
14	ExprTuple	19
15	Literal
16	ExprTuple	20
17	Literal
18	ExprTuple	21
19	Lambda	parameter: 66 body: 22
20	ExprRange	lambda_map: 23 start_index: 59 end_index: 60
21	Variable
22	Conditional	value: 24 condition: 25
23	Lambda	parameter: 40 body: 26
24	Operation	operator: 27 operand: 31
25	Operation	operator: 43 operands: 29
26	Operation	operator: 51 operand: 33
27	Literal
28	ExprTuple	31
29	ExprTuple	66, 32
30	ExprTuple	33
31	Lambda	parameter: 65 body: 34
32	Operation	operator: 55 operands: 35
33	IndexedVar	variable: 61 index: 40
34	Conditional	value: 37 condition: 38
35	ExprTuple	59, 39
36	ExprTuple	40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 43 operands: 44
39	Variable
40	Variable
41	Literal
42	ExprTuple	45, 46, 47, 48, 49
43	Literal
44	ExprTuple	65, 50
45	Operation	operator: 53 operand: 57
46	Variable
47	Operation	operator: 51 operand: 58
48	Operation	operator: 51 operand: 57
49	Operation	operator: 53 operand: 58
50	Operation	operator: 55 operands: 56
51	Literal
52	ExprTuple	57
53	Literal
54	ExprTuple	58
55	Literal
56	ExprTuple	59, 60
57	IndexedVar	variable: 61 index: 65
58	IndexedVar	variable: 63 index: 66
59	Literal
60	Variable
61	Variable
62	ExprTuple	65
63	Variable
64	ExprTuple	66
65	Variable
66	Variable