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 A, B, Conditional, ExprRange, IndexedVar, Variable, a, b, i, n
from proveit.core_expr_types import a_i, b_i, v_i
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import And, Equals, 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 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [i]
sub_expr3 = Interval(one, n)
sub_expr4 = Qmult(Ket(v_i), Bra(v_i))
expr = Conditional(And(Equals(A, VecSum(index_or_indices = sub_expr2, summand = ScalarMult(a_i, sub_expr4), domain = sub_expr3)), Equals(B, VecSum(index_or_indices = sub_expr2, summand = ScalarMult(b_i, sub_expr4), domain = sub_expr3))).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, n), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, n)))

# 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}{c} \left(A = \left(\sum_{i=1}^{n} \left(a_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right) \land  \\ \left(B = \left(\sum_{i=1}^{n} \left(b_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right) \end{array} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{n} \in \mathbb{C}\right), \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{n} \in \mathbb{C}\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 11 operands: 10
7	Operation	operator: 11 operands: 12
8	ExprRange	lambda_map: 13 start_index: 55 end_index: 56
9	ExprRange	lambda_map: 14 start_index: 55 end_index: 56
10	ExprTuple	15, 16
11	Literal
12	ExprTuple	17, 18
13	Lambda	parameter: 37 body: 19
14	Lambda	parameter: 37 body: 20
15	Variable
16	Operation	operator: 22 operand: 26
17	Variable
18	Operation	operator: 22 operand: 27
19	Operation	operator: 41 operands: 24
20	Operation	operator: 41 operands: 25
21	ExprTuple	26
22	Literal
23	ExprTuple	27
24	ExprTuple	28, 30
25	ExprTuple	29, 30
26	Lambda	parameter: 63 body: 31
27	Lambda	parameter: 63 body: 32
28	IndexedVar	variable: 47 index: 37
29	IndexedVar	variable: 48 index: 37
30	Literal
31	Conditional	value: 34 condition: 36
32	Conditional	value: 35 condition: 36
33	ExprTuple	37
34	Operation	operator: 39 operands: 38
35	Operation	operator: 39 operands: 40
36	Operation	operator: 41 operands: 42
37	Variable
38	ExprTuple	43, 45
39	Literal
40	ExprTuple	44, 45
41	Literal
42	ExprTuple	63, 46
43	IndexedVar	variable: 47 index: 63
44	IndexedVar	variable: 48 index: 63
45	Operation	operator: 49 operands: 50
46	Operation	operator: 51 operands: 52
47	Variable
48	Variable
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	55, 56
53	Operation	operator: 57 operand: 60
54	Operation	operator: 58 operand: 60
55	Literal
56	Variable
57	Literal
58	Literal
59	ExprTuple	60
60	IndexedVar	variable: 61 index: 63
61	Variable
62	ExprTuple	63
63	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 ¶