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.core_expr_types import Len
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(Len(operands = [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()]), Len(operands = [ExprRange(sub_expr1, sub_expr1, 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(\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)|, |\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, 7
4	Literal
5	ExprTuple	8
6	Operation	operator: 17 operands: 9
7	ExprRange	lambda_map: 10 start_index: 11 end_index: 41
8	ExprRange	lambda_map: 12 start_index: 71 end_index: 75
9	NamedExprs	state: 13
10	Lambda	parameter: 72 body: 14
11	Operation	operator: 67 operands: 15
12	Lambda	parameter: 72 body: 72
13	Operation	operator: 37 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	70, 65
16	ExprTuple	24, 19
17	Literal
18	NamedExprs	state: 20
19	Operation	operator: 28 operands: 21
20	Operation	operator: 37 operands: 22
21	ExprTuple	32, 23
22	ExprTuple	24, 25
23	Operation	operator: 37 operands: 26
24	Operation	operator: 45 operands: 27
25	Operation	operator: 28 operands: 29
26	ExprTuple	30, 43
27	ExprTuple	71, 31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 62 operands: 34
31	Operation	operator: 62 operands: 35
32	Operation	operator: 48 operand: 41
33	Operation	operator: 37 operands: 38
34	ExprTuple	51, 39
35	ExprTuple	65, 40
36	ExprTuple	41
37	Literal
38	ExprTuple	42, 43
39	Operation	operator: 54 operands: 44
40	Operation	operator: 45 operands: 46
41	Literal
42	Operation	operator: 62 operands: 47
43	Operation	operator: 48 operand: 71
44	ExprTuple	65, 57, 58, 50, 60
45	Literal
46	ExprTuple	71, 65
47	ExprTuple	51, 52
48	Literal
49	ExprTuple	71
50	Operation	operator: 62 operands: 53
51	Literal
52	Operation	operator: 54 operands: 55
53	ExprTuple	65, 56
54	Literal
55	ExprTuple	65, 57, 58, 59, 60
56	Operation	operator: 73 operand: 64
57	Literal
58	Literal
59	Operation	operator: 62 operands: 63
60	Literal
61	ExprTuple	64
62	Literal
63	ExprTuple	65, 66
64	Operation	operator: 67 operands: 68
65	Literal
66	Operation	operator: 73 operand: 72
67	Literal
68	ExprTuple	70, 71
69	ExprTuple	72
70	Operation	operator: 73 operand: 75
71	Literal
72	Variable
73	Literal
74	ExprTuple	75
75	Variable