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 Conditional, ExprTuple, 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 = ExprTuple(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())

\left(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..\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: 33 body: 3
2	ExprTuple	33
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 31 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	33, 11
9	Operation	operator: 33 operand: 16
10	Operation	operator: 19 operand: 17
11	Operation	operator: 14 operands: 15
12	ExprTuple	16
13	ExprTuple	17
14	Literal
15	ExprTuple	18, 18
16	Operation	operator: 19 operand: 22
17	Lambda	parameter: 53 body: 21
18	Literal
19	Literal
20	ExprTuple	22
21	Conditional	value: 23 condition: 27
22	Lambda	parameter: 53 body: 24
23	Operation	operator: 29 operands: 25
24	Conditional	value: 26 condition: 27
25	ExprTuple	28, 35
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operand: 37
29	Literal
30	ExprTuple	37, 35
31	Literal
32	ExprTuple	53, 36
33	Variable
34	ExprTuple	37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	IndexedVar	variable: 42 index: 53
38	Literal
39	ExprTuple	43, 44
40	Literal
41	ExprTuple	45, 46
42	Variable
43	Operation	operator: 47 operand: 50
44	Operation	operator: 48 operand: 50
45	Literal
46	Variable
47	Literal
48	Literal
49	ExprTuple	50
50	IndexedVar	variable: 51 index: 53
51	Variable
52	ExprTuple	53
53	Variable