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, M, i, n
from proveit.core_expr_types import a_1_to_n, a_i, v_i
from proveit.linear_algebra import Hspace, OrthoNormBases, ScalarMult, VecSum
from proveit.logic import Equals, Exists, InSet, Set
from proveit.numbers import Complex, Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult
from proveit.physics.quantum.algebra import v_1_to_n_kets

# build up the expression from sub-expressions
expr = Conditional(Exists(instance_param_or_params = [a_1_to_n], instance_expr = Equals(M, VecSum(index_or_indices = [i], summand = ScalarMult(a_i, Qmult(Ket(v_i), Bra(v_i))), domain = Interval(one, n))), domain = Complex).with_wrapping(), InSet(Set(v_1_to_n_kets), OrthoNormBases(Hspace)))

# 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\{\begin{array}{l}\exists_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{C}}~\\
\left(M = \left(\sum_{i=1}^{n} \left(a_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right)\end{array} \textrm{ if } \left\{\left\{\lvert v_{1} \rangle, \lvert v_{2} \rangle, \ldots, \lvert v_{n} \rangle\right\}\right\} \in \textrm{O.N.Bases}\left(\mathcal{H}\right)\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 47 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 9 body: 10
7	Operation	operator: 24 operand: 17
8	Operation	operator: 12 operand: 18
9	ExprTuple	14
10	Conditional	value: 15 condition: 16
11	ExprTuple	17
12	Literal
13	ExprTuple	18
14	ExprRange	lambda_map: 19 start_index: 61 end_index: 62
15	Operation	operator: 20 operands: 21
16	Operation	operator: 22 operands: 23
17	Operation	operator: 24 operands: 25
18	Variable
19	Lambda	parameter: 53 body: 42
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28
24	Literal
25	ExprTuple	29
26	Variable
27	Operation	operator: 30 operand: 34
28	ExprRange	lambda_map: 32 start_index: 61 end_index: 62
29	ExprRange	lambda_map: 33 start_index: 61 end_index: 62
30	Literal
31	ExprTuple	34
32	Lambda	parameter: 53 body: 35
33	Lambda	parameter: 53 body: 36
34	Lambda	parameter: 69 body: 37
35	Operation	operator: 47 operands: 38
36	Operation	operator: 63 operand: 44
37	Conditional	value: 40 condition: 41
38	ExprTuple	42, 43
39	ExprTuple	44
40	Operation	operator: 45 operands: 46
41	Operation	operator: 47 operands: 48
42	IndexedVar	variable: 54 index: 53
43	Literal
44	IndexedVar	variable: 67 index: 53
45	Literal
46	ExprTuple	50, 51
47	Literal
48	ExprTuple	69, 52
49	ExprTuple	53
50	IndexedVar	variable: 54 index: 69
51	Operation	operator: 55 operands: 56
52	Operation	operator: 57 operands: 58
53	Variable
54	Variable
55	Literal
56	ExprTuple	59, 60
57	Literal
58	ExprTuple	61, 62
59	Operation	operator: 63 operand: 66
60	Operation	operator: 64 operand: 66
61	Literal
62	Variable
63	Literal
64	Literal
65	ExprTuple	66
66	IndexedVar	variable: 67 index: 69
67	Variable
68	ExprTuple	69
69	Variable

Expression of type Conditional¶

from the theory of proveit.physics.quantum.algebra¶

Expression of type Conditional ¶

from the theory of proveit.physics.quantum.algebra ¶