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 Conditional, Function, Lambda, f, i, n
from proveit.core_expr_types import a_i, v_i
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals, Functions, InSet
from proveit.numbers import Complex, Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(one, n)
sub_expr3 = Qmult(Ket(v_i), Bra(v_i))
expr = Lambda(f, Conditional(Equals(Function(f, [VecSum(index_or_indices = sub_expr1, summand = ScalarMult(a_i, sub_expr3), domain = sub_expr2)]), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Function(f, [a_i]), sub_expr3), domain = sub_expr2)), InSet(f, Functions(Complex, Complex))))

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())

f \mapsto \left\{f\left(\sum_{i=1}^{n} \left(a_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right) = \left(\sum_{i=1}^{n} \left(f\left(a_{i}\right) \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right) \textrm{ if } f \in \left[\mathbb{C} \rightarrow \mathbb{C}\right]\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 32 body: 2
1	ExprTuple	32
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 30 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	32, 10
8	Operation	operator: 32 operand: 15
9	Operation	operator: 18 operand: 16
10	Operation	operator: 13 operands: 14
11	ExprTuple	15
12	ExprTuple	16
13	Literal
14	ExprTuple	17, 17
15	Operation	operator: 18 operand: 21
16	Lambda	parameter: 52 body: 20
17	Literal
18	Literal
19	ExprTuple	21
20	Conditional	value: 22 condition: 26
21	Lambda	parameter: 52 body: 23
22	Operation	operator: 28 operands: 24
23	Conditional	value: 25 condition: 26
24	ExprTuple	27, 34
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operand: 36
28	Literal
29	ExprTuple	36, 34
30	Literal
31	ExprTuple	52, 35
32	Variable
33	ExprTuple	36
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operands: 40
36	IndexedVar	variable: 41 index: 52
37	Literal
38	ExprTuple	42, 43
39	Literal
40	ExprTuple	44, 45
41	Variable
42	Operation	operator: 46 operand: 49
43	Operation	operator: 47 operand: 49
44	Literal
45	Variable
46	Literal
47	Literal
48	ExprTuple	49
49	IndexedVar	variable: 50 index: 52
50	Variable
51	ExprTuple	52
52	Variable