Expression of type Equals

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

# build up the expression from sub-expressions
expr = 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)))

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())

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)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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