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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(i, Conditional(VecSum(index_or_indices = [j], summand = Qmult(Bra(w_j), A, Ket(v_i), Ket(w_j), Bra(v_i)), domain = Interval(one, n)), InSet(i, 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(i \mapsto \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) \textrm{ if } i \in \{1~\ldotp \ldotp~m\}\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	parameter: 40 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 17 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	40, 9
8	Lambda	parameter: 39 body: 10
9	Operation	operator: 29 operands: 11
10	Conditional	value: 12 condition: 13
11	ExprTuple	33, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Variable
15	Literal
16	ExprTuple	19, 20, 21, 22, 23
17	Literal
18	ExprTuple	39, 24
19	Operation	operator: 27 operand: 31
20	Variable
21	Operation	operator: 25 operand: 32
22	Operation	operator: 25 operand: 31
23	Operation	operator: 27 operand: 32
24	Operation	operator: 29 operands: 30
25	Literal
26	ExprTuple	31
27	Literal
28	ExprTuple	32
29	Literal
30	ExprTuple	33, 34
31	IndexedVar	variable: 35 index: 39
32	IndexedVar	variable: 37 index: 40
33	Literal
34	Variable
35	Variable
36	ExprTuple	39
37	Variable
38	ExprTuple	40
39	Variable
40	Variable