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, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase
from proveit.physics.quantum.circuits import Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Neg(t)
sub_expr3 = frac(one, sqrt(two))
expr = ExprTuple(Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(sub_expr2, one))), _phase)), ket1)))), ExprRange(sub_expr1, Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(sub_expr2, two), zero).with_decreasing_order())

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^{-\left(-t + 1\right)} \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}, \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 - 3} \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}\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: 10 operands: 3
2	ExprRange	lambda_map: 4 start_index: 5 end_index: 34
3	NamedExprs	state: 6
4	Lambda	parameter: 65 body: 7
5	Operation	operator: 60 operands: 8
6	Operation	operator: 30 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprTuple	63, 58
9	ExprTuple	17, 12
10	Literal
11	NamedExprs	state: 13
12	Operation	operator: 21 operands: 14
13	Operation	operator: 30 operands: 15
14	ExprTuple	25, 16
15	ExprTuple	17, 18
16	Operation	operator: 30 operands: 19
17	Operation	operator: 38 operands: 20
18	Operation	operator: 21 operands: 22
19	ExprTuple	23, 36
20	ExprTuple	64, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 55 operands: 27
24	Operation	operator: 55 operands: 28
25	Operation	operator: 41 operand: 34
26	Operation	operator: 30 operands: 31
27	ExprTuple	44, 32
28	ExprTuple	58, 33
29	ExprTuple	34
30	Literal
31	ExprTuple	35, 36
32	Operation	operator: 47 operands: 37
33	Operation	operator: 38 operands: 39
34	Literal
35	Operation	operator: 55 operands: 40
36	Operation	operator: 41 operand: 64
37	ExprTuple	58, 50, 51, 43, 53
38	Literal
39	ExprTuple	64, 58
40	ExprTuple	44, 45
41	Literal
42	ExprTuple	64
43	Operation	operator: 55 operands: 46
44	Literal
45	Operation	operator: 47 operands: 48
46	ExprTuple	58, 49
47	Literal
48	ExprTuple	58, 50, 51, 52, 53
49	Operation	operator: 66 operand: 57
50	Literal
51	Literal
52	Operation	operator: 55 operands: 56
53	Literal
54	ExprTuple	57
55	Literal
56	ExprTuple	58, 59
57	Operation	operator: 60 operands: 61
58	Literal
59	Operation	operator: 66 operand: 65
60	Literal
61	ExprTuple	63, 64
62	ExprTuple	65
63	Operation	operator: 66 operand: 68
64	Literal
65	Variable
66	Literal
67	ExprTuple	68
68	Variable