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, i, n
from proveit.core_expr_types import x_1_to_n, x_i
from proveit.linear_algebra import HilbertSpaces, Hspace, Identity, OrthoNormBases, VecSum
from proveit.logic import Equals, Forall, InClass, InSet
from proveit.numbers import Interval, NaturalPos, one
from proveit.physics.quantum import Bra, Ket, Qmult
from proveit.physics.quantum.algebra import x_1_to_n_kets

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(VecSum(index_or_indices = [i], summand = Qmult(Ket(x_i), Bra(x_i)), domain = Interval(one, n)), Identity(Hspace)), condition = InSet(x_1_to_n_kets, OrthoNormBases(Hspace))).with_wrapping(), domain = NaturalPos), InClass(Hspace, HilbertSpaces))

# 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\{\forall_{n \in \mathbb{N}^+}~\left[\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~\left\{\lvert x_{1} \rangle, \lvert x_{2} \rangle, \ldots, \lvert x_{n} \rangle\right\} \in \textrm{O.N.Bases}\left(\mathcal{H}\right)}~\\
\left(\left(\sum_{i=1}^{n} \left(\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert\right)\right) = I_{\mathcal{H}}\right)\end{array}\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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: 12 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	39, 7
6	Lambda	parameter: 62 body: 9
7	Literal
8	ExprTuple	62
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operand: 15
11	Operation	operator: 47 operands: 14
12	Literal
13	ExprTuple	15
14	ExprTuple	62, 16
15	Lambda	parameters: 17 body: 18
16	Literal
17	ExprTuple	19
18	Conditional	value: 20 condition: 21
19	ExprRange	lambda_map: 22 start_index: 61 end_index: 62
20	Operation	operator: 23 operands: 24
21	Operation	operator: 47 operands: 25
22	Lambda	parameter: 63 body: 53
23	Literal
24	ExprTuple	26, 27
25	ExprTuple	28, 29
26	Operation	operator: 30 operand: 37
27	Operation	operator: 32 operand: 39
28	Operation	operator: 33 operands: 34
29	Operation	operator: 35 operand: 39
30	Literal
31	ExprTuple	37
32	Literal
33	Literal
34	ExprTuple	38
35	Literal
36	ExprTuple	39
37	Lambda	parameter: 66 body: 40
38	ExprRange	lambda_map: 41 start_index: 61 end_index: 62
39	Variable
40	Conditional	value: 42 condition: 43
41	Lambda	parameter: 63 body: 44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 54 operand: 53
45	Literal
46	ExprTuple	50, 51
47	Literal
48	ExprTuple	66, 52
49	ExprTuple	53
50	Operation	operator: 54 operand: 60
51	Operation	operator: 55 operand: 60
52	Operation	operator: 57 operands: 58
53	IndexedVar	variable: 64 index: 63
54	Literal
55	Literal
56	ExprTuple	60
57	Literal
58	ExprTuple	61, 62
59	ExprTuple	63
60	IndexedVar	variable: 64 index: 66
61	Literal
62	Variable
63	Variable
64	Variable
65	ExprTuple	66
66	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 ¶