Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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 ExprTuple, Lambda, l, m
from proveit.logic import Bijections, InSet
from proveit.numbers import Add, Mod
from proveit.physics.quantum.QPE import _Omega, _b_floor, _full_domain, _m_domain, _phase_est_circuit, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(InSet(Lambda(l, Mod(Add(_b_floor, l), _two_pow_t)), Bijections(_full_domain, _m_domain)), InSet(Lambda(m, _phase_est_circuit), Bijections(_m_domain, _Omega)))

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(\left[l \mapsto \left(\left(b_{\textit{f}} + l\right) ~\textup{mod}~ 2^{t}\right)\right] \in \left[\{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~2^{t} - 1\}\right], \left[m \mapsto \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)\right] \in \left[\{0~\ldotp \ldotp~2^{t} - 1\} \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Lambda	parameter: 44 body: 11
7	Operation	operator: 15 operands: 12
8	Lambda	parameter: 119 body: 14
9	Operation	operator: 15 operands: 16
10	ExprTuple	44
11	Operation	operator: 17 operands: 18
12	ExprTuple	19, 22
13	ExprTuple	119
14	Operation	operator: 20 operands: 21
15	Literal
16	ExprTuple	22, 23
17	Literal
18	ExprTuple	24, 63
19	Operation	operator: 98 operands: 25
20	Literal
21	ExprTuple	26, 27, 28, 29
22	Operation	operator: 98 operands: 30
23	Literal
24	Operation	operator: 115 operands: 31
25	ExprTuple	32, 75
26	ExprTuple	33, 34
27	ExprTuple	35, 36
28	ExprTuple	37, 38
29	ExprTuple	39, 40
30	ExprTuple	41, 42
31	ExprTuple	43, 44
32	Operation	operator: 115 operands: 45
33	ExprRange	lambda_map: 46 start_index: 124 end_index: 120
34	ExprRange	lambda_map: 47 start_index: 124 end_index: 121
35	ExprRange	lambda_map: 48 start_index: 124 end_index: 120
36	ExprRange	lambda_map: 48 start_index: 107 end_index: 108
37	ExprRange	lambda_map: 49 start_index: 124 end_index: 120
38	ExprRange	lambda_map: 50 start_index: 124 end_index: 121
39	ExprRange	lambda_map: 51 start_index: 124 end_index: 120
40	ExprRange	lambda_map: 52 start_index: 124 end_index: 121
41	Literal
42	Operation	operator: 115 operands: 53
43	Literal
44	Variable
45	ExprTuple	54, 124
46	Lambda	parameter: 106 body: 55
47	Lambda	parameter: 106 body: 56
48	Lambda	parameter: 106 body: 57
49	Lambda	parameter: 106 body: 58
50	Lambda	parameter: 106 body: 59
51	Lambda	parameter: 106 body: 60
52	Lambda	parameter: 106 body: 62
53	ExprTuple	63, 117
54	Operation	operator: 122 operand: 75
55	Operation	operator: 90 operands: 65
56	Operation	operator: 72 operands: 66
57	Operation	operator: 72 operands: 67
58	Operation	operator: 68 operands: 69
59	Operation	operator: 91 operands: 70
60	Operation	operator: 72 operands: 71
61	ExprTuple	106
62	Operation	operator: 72 operands: 73
63	Operation	operator: 86 operands: 74
64	ExprTuple	75
65	NamedExprs	state: 76
66	NamedExprs	element: 77 targets: 85
67	NamedExprs	element: 78 targets: 79
68	Literal
69	NamedExprs	basis: 80
70	NamedExprs	operation: 81
71	NamedExprs	element: 82 targets: 83
72	Literal
73	NamedExprs	element: 84 targets: 85
74	ExprTuple	100, 120
75	Operation	operator: 86 operands: 87
76	Operation	operator: 88 operand: 102
77	Operation	operator: 90 operands: 97
78	Operation	operator: 91 operands: 92
79	Operation	operator: 98 operands: 93
80	Literal
81	Literal
82	Operation	operator: 96 operands: 94
83	Operation	operator: 98 operands: 95
84	Operation	operator: 96 operands: 97
85	Operation	operator: 98 operands: 99
86	Literal
87	ExprTuple	100, 101
88	Literal
89	ExprTuple	102
90	Literal
91	Literal
92	NamedExprs	operation: 103 part: 106
93	ExprTuple	124, 108
94	NamedExprs	state: 104 part: 106
95	ExprTuple	124, 120
96	Literal
97	NamedExprs	state: 105 part: 106
98	Literal
99	ExprTuple	107, 108
100	Literal
101	Operation	operator: 115 operands: 109
102	Literal
103	Operation	operator: 110 operands: 111
104	Operation	operator: 112 operands: 113
105	Literal
106	Variable
107	Operation	operator: 115 operands: 114
108	Operation	operator: 115 operands: 116
109	ExprTuple	120, 117
110	Literal
111	ExprTuple	118, 120
112	Literal
113	ExprTuple	119, 120
114	ExprTuple	120, 124
115	Literal
116	ExprTuple	120, 121
117	Operation	operator: 122 operand: 124
118	Literal
119	Variable
120	Literal
121	Literal
122	Literal
123	ExprTuple	124
124	Literal