Expression of type Conditional

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, W, i, j, m, n
from proveit.core_expr_types import v_i, 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 = 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\{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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 38 operands: 5
3	Literal
4	ExprTuple	41, 6
5	ExprTuple	7, 8
6	Operation	operator: 22 operand: 14
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operand: 16
9	ExprTuple	14
10	Literal
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Lambda	parameter: 61 body: 17
15	ExprRange	lambda_map: 18 start_index: 54 end_index: 55
16	Variable
17	Conditional	value: 19 condition: 20
18	Lambda	parameter: 35 body: 21
19	Operation	operator: 22 operand: 26
20	Operation	operator: 38 operands: 24
21	Operation	operator: 46 operand: 28
22	Literal
23	ExprTuple	26
24	ExprTuple	61, 27
25	ExprTuple	28
26	Lambda	parameter: 60 body: 29
27	Operation	operator: 50 operands: 30
28	IndexedVar	variable: 56 index: 35
29	Conditional	value: 32 condition: 33
30	ExprTuple	54, 34
31	ExprTuple	35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operands: 39
34	Variable
35	Variable
36	Literal
37	ExprTuple	40, 41, 42, 43, 44
38	Literal
39	ExprTuple	60, 45
40	Operation	operator: 48 operand: 52
41	Variable
42	Operation	operator: 46 operand: 53
43	Operation	operator: 46 operand: 52
44	Operation	operator: 48 operand: 53
45	Operation	operator: 50 operands: 51
46	Literal
47	ExprTuple	52
48	Literal
49	ExprTuple	53
50	Literal
51	ExprTuple	54, 55
52	IndexedVar	variable: 56 index: 60
53	IndexedVar	variable: 58 index: 61
54	Literal
55	Variable
56	Variable
57	ExprTuple	60
58	Variable
59	ExprTuple	61
60	Variable
61	Variable