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

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

\left(A, \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
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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