Theorem output_prod_operator_repr of type Forall ¶

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

In [1]:

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.algebra import output_prod_operator_repr

In [2]:

# check that the built expression is the same as the stored expression
assert output_prod_operator_repr.expr == stored_expr
assert output_prod_operator_repr.expr._style_id == stored_expr._style_id
print("Passed sanity check: output_prod_operator_repr matches stored_expr")

Passed sanity check: output_prod_operator_repr matches stored_expr

In [3]:

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{V, W \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{A \in \mathcal{L}\left(V, W\right)}~\left[\forall_{m, n \in \mathbb{N}^+}~\left[\begin{array}{l}\forall_{v_{1}, v_{2}, \ldots, v_{m}~|~\left\{\lvert v_{1} \rangle, \lvert v_{2} \rangle, \ldots, \lvert v_{m} \rangle\right\} \in \textrm{O.N.Bases}\left(V\right)}~\\
\left[\begin{array}{l}\forall_{w_{1}, w_{2}, \ldots, w_{n}~|~\left\{\lvert w_{1} \rangle, \lvert w_{2} \rangle, \ldots, \lvert w_{n} \rangle\right\} \in \textrm{O.N.Bases}\left(W\right)}~\\
\left(A = \left(\sum_{i=1}^{m} \left(\sum_{j=1}^{n} \left(\langle w_{j} \rvert \thinspace A \thinspace \lvert v_{i} \rangle \thinspace \lvert w_{j} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right)\end{array}\right]\end{array}\right]\right]\right]

In [4]:

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

In [5]:

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Operation	operator: 44 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 26 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 44 operand: 8
5	Operation	operator: 30 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 102 body: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	102
12	Conditional	value: 16 condition: 17
13	ExprTuple	58, 18
14	Literal
15	ExprTuple	76, 18
16	Operation	operator: 44 operand: 21
17	Operation	operator: 99 operands: 20
18	Literal
19	ExprTuple	21
20	ExprTuple	102, 22
21	Lambda	parameters: 23 body: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	95, 116
24	Conditional	value: 27 condition: 28
25	Literal
26	ExprTuple	58, 76
27	Operation	operator: 44 operand: 32
28	Operation	operator: 30 operands: 31
29	ExprTuple	32
30	Literal
31	ExprTuple	33, 34
32	Lambda	parameters: 35 body: 36
33	Operation	operator: 99 operands: 37
34	Operation	operator: 99 operands: 38
35	ExprTuple	39
36	Conditional	value: 40 condition: 41
37	ExprTuple	95, 42
38	ExprTuple	116, 42
39	ExprRange	lambda_map: 43 start_index: 115 end_index: 95
40	Operation	operator: 44 operand: 47
41	Operation	operator: 99 operands: 46
42	Literal
43	Lambda	parameter: 96 body: 77
44	Literal
45	ExprTuple	47
46	ExprTuple	48, 49
47	Lambda	parameters: 50 body: 51
48	Operation	operator: 69 operands: 52
49	Operation	operator: 71 operand: 58
50	ExprTuple	54
51	Conditional	value: 55 condition: 56
52	ExprTuple	57
53	ExprTuple	58
54	ExprRange	lambda_map: 59 start_index: 115 end_index: 116
55	Operation	operator: 60 operands: 61
56	Operation	operator: 99 operands: 62
57	ExprRange	lambda_map: 63 start_index: 115 end_index: 95
58	Variable
59	Lambda	parameter: 96 body: 89
60	Literal
61	ExprTuple	102, 64
62	ExprTuple	65, 66
63	Lambda	parameter: 96 body: 67
64	Operation	operator: 83 operand: 74
65	Operation	operator: 69 operands: 70
66	Operation	operator: 71 operand: 76
67	Operation	operator: 107 operand: 77
68	ExprTuple	74
69	Literal
70	ExprTuple	75
71	Literal
72	ExprTuple	76
73	ExprTuple	77
74	Lambda	parameter: 122 body: 78
75	ExprRange	lambda_map: 79 start_index: 115 end_index: 116
76	Variable
77	IndexedVar	variable: 119 index: 96
78	Conditional	value: 80 condition: 81
79	Lambda	parameter: 96 body: 82
80	Operation	operator: 83 operand: 87
81	Operation	operator: 99 operands: 85
82	Operation	operator: 107 operand: 89
83	Literal
84	ExprTuple	87
85	ExprTuple	122, 88
86	ExprTuple	89
87	Lambda	parameter: 121 body: 90
88	Operation	operator: 111 operands: 91
89	IndexedVar	variable: 117 index: 96
90	Conditional	value: 93 condition: 94
91	ExprTuple	115, 95
92	ExprTuple	96
93	Operation	operator: 97 operands: 98
94	Operation	operator: 99 operands: 100
95	Variable
96	Variable
97	Literal
98	ExprTuple	101, 102, 103, 104, 105
99	Literal
100	ExprTuple	121, 106
101	Operation	operator: 109 operand: 113
102	Variable
103	Operation	operator: 107 operand: 114
104	Operation	operator: 107 operand: 113
105	Operation	operator: 109 operand: 114
106	Operation	operator: 111 operands: 112
107	Literal
108	ExprTuple	113
109	Literal
110	ExprTuple	114
111	Literal
112	ExprTuple	115, 116
113	IndexedVar	variable: 117 index: 121
114	IndexedVar	variable: 119 index: 122
115	Literal
116	Variable
117	Variable
118	ExprTuple	121
119	Variable
120	ExprTuple	122
121	Variable
122	Variable