Expression of type ExprTuple

from the theory of proveit.physics.quantum.circuits

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
from proveit.physics.quantum.circuits import circuit__psi_m__u_Akl_v, circuit__u_Akl_v
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Prob(circuit__u_Akl_v), Prob(circuit__psi_m__u_Akl_v))

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(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert u \rangle} & \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \multiqout{3}{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \ghostqout{\lvert v \rangle}
} \end{array}\right), \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \rangle} \\
\multiqin{3}{\lvert u \rangle} & \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \multiqout{3}{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \ghostqout{\lvert v \rangle}
} \end{array}\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 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12, 13
9	Literal
10	ExprTuple	14, 15, 16
11	ExprTuple	17
12	ExprRange	lambda_map: 18 start_index: 86 end_index: 23
13	ExprTuple	19
14	ExprTuple	20, 21
15	ExprRange	lambda_map: 22 start_index: 86 end_index: 23
16	ExprTuple	24, 25
17	ExprRange	lambda_map: 26 start_index: 86 end_index: 88
18	Lambda	parameter: 77 body: 27
19	ExprRange	lambda_map: 28 start_index: 86 end_index: 88
20	ExprRange	lambda_map: 29 start_index: 86 end_index: 87
21	ExprRange	lambda_map: 30 start_index: 86 end_index: 88
22	Lambda	parameter: 77 body: 32
23	Variable
24	ExprRange	lambda_map: 33 start_index: 86 end_index: 87
25	ExprRange	lambda_map: 34 start_index: 86 end_index: 88
26	Lambda	parameter: 80 body: 35
27	ExprTuple	40
28	Lambda	parameter: 80 body: 36
29	Lambda	parameter: 80 body: 37
30	Lambda	parameter: 80 body: 38
31	ExprTuple	77
32	ExprTuple	39, 40
33	Lambda	parameter: 80 body: 41
34	Lambda	parameter: 80 body: 42
35	Operation	operator: 50 operands: 43
36	Operation	operator: 50 operands: 44
37	Operation	operator: 50 operands: 45
38	Operation	operator: 50 operands: 46
39	ExprRange	lambda_map: 47 start_index: 86 end_index: 87
40	ExprRange	lambda_map: 48 start_index: 86 end_index: 88
41	Operation	operator: 50 operands: 49
42	Operation	operator: 50 operands: 51
43	NamedExprs	element: 54 targets: 52
44	NamedExprs	element: 60 targets: 52
45	NamedExprs	element: 53 targets: 59
46	NamedExprs	element: 54 targets: 61
47	Lambda	parameter: 80 body: 55
48	Lambda	parameter: 80 body: 57
49	NamedExprs	element: 58 targets: 59
50	Literal
51	NamedExprs	element: 60 targets: 61
52	Operation	operator: 73 operands: 62
53	Operation	operator: 63 operands: 69
54	Operation	operator: 63 operands: 64
55	Operation	operator: 65 operands: 66
56	ExprTuple	80
57	IndexedVar	variable: 67 indices: 68
58	Operation	operator: 71 operands: 69
59	Operation	operator: 73 operands: 70
60	Operation	operator: 71 operands: 72
61	Operation	operator: 73 operands: 74
62	ExprTuple	86, 88
63	Literal
64	NamedExprs	state: 75 part: 80
65	Literal
66	NamedExprs	operation: 76
67	Variable
68	ExprTuple	77, 80
69	NamedExprs	state: 78 part: 80
70	ExprTuple	86, 87
71	Literal
72	NamedExprs	state: 79 part: 80
73	Literal
74	ExprTuple	81, 82
75	Variable
76	Literal
77	Variable
78	Variable
79	Variable
80	Variable
81	Operation	operator: 84 operands: 83
82	Operation	operator: 84 operands: 85
83	ExprTuple	87, 86
84	Literal
85	ExprTuple	87, 88
86	Literal
87	Variable
88	Variable