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, ExprRange, IndexedVar, Variable, i, lambda_, m, n
from proveit.core_expr_types import a_i, b_i, lambda_i
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import And, Equals, InSet
from proveit.numbers import Interval, Min, RealNonNeg, one
from proveit.physics.quantum import Ket, Qmult, var_ket_psi

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Min(m, n)
expr = Conditional(Equals(var_ket_psi, VecSum(index_or_indices = [i], summand = ScalarMult(lambda_i, Qmult(Ket(a_i), Ket(b_i))), domain = Interval(one, sub_expr2))), And(ExprRange(sub_expr1, InSet(IndexedVar(lambda_, sub_expr1), RealNonNeg), one, sub_expr2)))

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\{\lvert \psi \rangle = \left(\sum_{i=1}^{{\rm Min}\left(m, n\right)} \left(\lambda_{i} \cdot \left(\lvert a_{i} \rangle \thinspace \lvert b_{i} \rangle\right)\right)\right) \textrm{ if } \left(\lambda_{1} \in \mathbb{R}^{\ge 0}\right) \land  \left(\lambda_{2} \in \mathbb{R}^{\ge 0}\right) \land  \ldots \land  \left(\lambda_{{\rm Min}\left(m, n\right)} \in \mathbb{R}^{\ge 0}\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: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Variable
8	Operation	operator: 10 operand: 13
9	ExprRange	lambda_map: 12 start_index: 37 end_index: 38
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 29 body: 14
13	Lambda	parameter: 51 body: 15
14	Operation	operator: 23 operands: 16
15	Conditional	value: 17 condition: 18
16	ExprTuple	19, 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	IndexedVar	variable: 30 index: 29
20	Literal
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	51, 28
25	ExprTuple	29
26	IndexedVar	variable: 30 index: 51
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Variable
30	Variable
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37, 38
35	Operation	operator: 40 operand: 44
36	Operation	operator: 40 operand: 45
37	Literal
38	Operation	operator: 42 operands: 43
39	ExprTuple	44
40	Literal
41	ExprTuple	45
42	Literal
43	ExprTuple	46, 47
44	IndexedVar	variable: 48 index: 51
45	IndexedVar	variable: 49 index: 51
46	Variable
47	Variable
48	Variable
49	Variable
50	ExprTuple	51
51	Variable