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, j, n
from proveit.core_expr_types import v_i, w_j
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(j, Conditional(Qmult(Bra(w_j), A, Ket(v_i), Ket(w_j), Bra(v_i)), InSet(j, Interval(one, n))))

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())

j \mapsto \left\{\langle w_{j} \rvert \thinspace A \thinspace \lvert v_{i} \rangle \thinspace \lvert w_{j} \rangle \thinspace \langle v_{i} \rvert \textrm{ if } j \in \{1~\ldotp \ldotp~n\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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