Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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