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 Conditional, ConditionalSet, ExprRange, ExprTuple, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import MatrixExp
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, Exp, Interval, Neg, one, two, zero
from proveit.physics.quantum import CONTROL
from proveit.physics.quantum.QPE import _U, _s
from proveit.physics.quantum.circuits import Gate, Igate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Add(t, one)
sub_expr4 = Add(sub_expr1, t)
expr = ExprTuple(Len(operands = [ExprRange(sub_expr1, [ExprRange(sub_expr2, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(sub_expr3)), Equals(sub_expr4, sub_expr2)), Conditional(Igate, NotEquals(sub_expr4, sub_expr2))), one, t).with_case_simplification(), ExprRange(sub_expr2, MultiQubitElem(element = Gate(operation = MatrixExp(_U, Exp(two, Neg(sub_expr1))), part = sub_expr2), targets = Interval(sub_expr3, Add(t, _s))), one, _s)], Add(Neg(t), one), zero).with_decreasing_order()]), Len(operands = [ExprRange(sub_expr2, sub_expr2, one, t)]))

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(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 1}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 1}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 1}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right), \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 2}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 2}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{t - 2}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right), \ldots, \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{0}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{0}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{0}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right)\right)|, |\left(1, 2, \ldots, t\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
4	Literal
5	ExprTuple	7
6	ExprRange	lambda_map: 8 start_index: 9 end_index: 10
7	ExprRange	lambda_map: 11 start_index: 68 end_index: 67
8	Lambda	parameter: 71 body: 12
9	Operation	operator: 63 operands: 13
10	Literal
11	Lambda	parameter: 50 body: 50
12	ExprTuple	14, 15
13	ExprTuple	16, 68
14	ExprRange	lambda_map: 17 start_index: 68 end_index: 67
15	ExprRange	lambda_map: 18 start_index: 68 end_index: 59
16	Operation	operator: 69 operand: 67
17	Lambda	parameter: 50 body: 20
18	Lambda	parameter: 50 body: 22
19	ExprTuple	67
20	Operation	operator: 23 operands: 24
21	ExprTuple	50
22	Operation	operator: 37 operands: 25
23	Literal
24	ExprTuple	26, 27
25	NamedExprs	element: 28 targets: 29
26	Conditional	value: 30 condition: 31
27	Conditional	value: 32 condition: 33
28	Operation	operator: 40 operands: 34
29	Operation	operator: 35 operands: 36
30	Operation	operator: 37 operands: 38
31	Operation	operator: 39 operands: 43
32	Operation	operator: 40 operands: 41
33	Operation	operator: 42 operands: 43
34	NamedExprs	operation: 44 part: 50
35	Literal
36	ExprTuple	60, 45
37	Literal
38	NamedExprs	element: 46 targets: 47
39	Literal
40	Literal
41	NamedExprs	operation: 48
42	Literal
43	ExprTuple	49, 50
44	Operation	operator: 51 operands: 52
45	Operation	operator: 63 operands: 53
46	Literal
47	Operation	operator: 54 operand: 60
48	Literal
49	Operation	operator: 63 operands: 56
50	Variable
51	Literal
52	ExprTuple	57, 58
53	ExprTuple	67, 59
54	Literal
55	ExprTuple	60
56	ExprTuple	71, 67
57	Literal
58	Operation	operator: 61 operands: 62
59	Literal
60	Operation	operator: 63 operands: 64
61	Literal
62	ExprTuple	65, 66
63	Literal
64	ExprTuple	67, 68
65	Literal
66	Operation	operator: 69 operand: 71
67	Variable
68	Literal
69	Literal
70	ExprTuple	71
71	Variable