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__u_Akl_v, circuit__u_Akl_v__psi_m
from proveit.statistics import Prob

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

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{
\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} \\
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \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	18
12	ExprRange	lambda_map: 17 start_index: 76 end_index: 21
13	ExprTuple	22
14	ExprTuple	18, 19
15	ExprRange	lambda_map: 20 start_index: 76 end_index: 21
16	ExprTuple	22, 23
17	Lambda	parameter: 66 body: 24
18	ExprRange	lambda_map: 25 start_index: 76 end_index: 77
19	ExprRange	lambda_map: 26 start_index: 76 end_index: 78
20	Lambda	parameter: 66 body: 28
21	Variable
22	ExprRange	lambda_map: 29 start_index: 76 end_index: 77
23	ExprRange	lambda_map: 30 start_index: 76 end_index: 78
24	ExprTuple	33
25	Lambda	parameter: 70 body: 31
26	Lambda	parameter: 70 body: 32
27	ExprTuple	66
28	ExprTuple	33, 34
29	Lambda	parameter: 70 body: 35
30	Lambda	parameter: 70 body: 36
31	Operation	operator: 42 operands: 37
32	Operation	operator: 42 operands: 38
33	ExprRange	lambda_map: 39 start_index: 76 end_index: 77
34	ExprRange	lambda_map: 40 start_index: 76 end_index: 78
35	Operation	operator: 42 operands: 41
36	Operation	operator: 42 operands: 43
37	NamedExprs	element: 44 targets: 50
38	NamedExprs	element: 45 targets: 52
39	Lambda	parameter: 70 body: 46
40	Lambda	parameter: 70 body: 48
41	NamedExprs	element: 49 targets: 50
42	Literal
43	NamedExprs	element: 51 targets: 52
44	Operation	operator: 54 operands: 53
45	Operation	operator: 54 operands: 62
46	IndexedVar	variable: 55 indices: 56
47	ExprTuple	70
48	Operation	operator: 57 operands: 58
49	Operation	operator: 61 operands: 59
50	Operation	operator: 63 operands: 60
51	Operation	operator: 61 operands: 62
52	Operation	operator: 63 operands: 64
53	NamedExprs	state: 65 part: 70
54	Literal
55	Variable
56	ExprTuple	66, 70
57	Literal
58	NamedExprs	operation: 67
59	NamedExprs	state: 68 part: 70
60	ExprTuple	76, 77
61	Literal
62	NamedExprs	state: 69 part: 70
63	Literal
64	ExprTuple	71, 72
65	Variable
66	Variable
67	Literal
68	Variable
69	Variable
70	Variable
71	Operation	operator: 74 operands: 73
72	Operation	operator: 74 operands: 75
73	ExprTuple	77, 76
74	Literal
75	ExprTuple	77, 78
76	Literal
77	Variable
78	Variable