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 ExprRange, ExprTuple, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _ket_u, _phase, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(ExprRange(sub_expr1, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(Neg(t), one), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(t, one), Add(t, _s))), one, _s).with_wrapping_at(2,6))

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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\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	ExprRange	lambda_map: 3 start_index: 4 end_index: 43
2	ExprRange	lambda_map: 5 start_index: 53 end_index: 37
3	Lambda	parameter: 66 body: 6
4	Operation	operator: 31 operands: 7
5	Lambda	parameter: 66 body: 8
6	Operation	operator: 18 operands: 9
7	ExprTuple	10, 53
8	Operation	operator: 11 operands: 12
9	NamedExprs	state: 13
10	Operation	operator: 64 operand: 36
11	Literal
12	NamedExprs	element: 15 targets: 16
13	Operation	operator: 40 operands: 17
14	ExprTuple	36
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	22, 23
18	Literal
19	NamedExprs	state: 24 part: 66
20	Literal
21	ExprTuple	25, 26
22	Operation	operator: 46 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprTuple	53, 33
28	Literal
29	ExprTuple	34, 35
30	ExprTuple	36, 53
31	Literal
32	ExprTuple	36, 37
33	Operation	operator: 60 operands: 38
34	Operation	operator: 49 operand: 43
35	Operation	operator: 40 operands: 41
36	Variable
37	Literal
38	ExprTuple	62, 42
39	ExprTuple	43
40	Literal
41	ExprTuple	44, 45
42	Operation	operator: 46 operands: 47
43	Literal
44	Operation	operator: 60 operands: 48
45	Operation	operator: 49 operand: 53
46	Literal
47	ExprTuple	53, 62
48	ExprTuple	51, 52
49	Literal
50	ExprTuple	53
51	Literal
52	Operation	operator: 54 operands: 55
53	Literal
54	Literal
55	ExprTuple	62, 56, 57, 58, 59
56	Literal
57	Literal
58	Operation	operator: 60 operands: 61
59	Literal
60	Literal
61	ExprTuple	62, 63
62	Literal
63	Operation	operator: 64 operand: 66
64	Literal
65	ExprTuple	66
66	Variable