Expression of type Conditional

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, 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 = 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\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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