Expression of type VecSum

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.numbers import Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

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

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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