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, two_pow_t

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

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(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right),\left(\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)\right), \left(\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)\right), \ldots, \left(\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)\right)\right)|, |\left(1, 2, \ldots, \left(t + 1\right)\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: 37 operands: 9
7	ExprRange	lambda_map: 10 start_index: 11 end_index: 41
8	ExprRange	lambda_map: 12 start_index: 53 end_index: 13
9	ExprTuple	23, 14
10	Lambda	parameter: 68 body: 15
11	Operation	operator: 17 operands: 16
12	Lambda	parameter: 68 body: 68
13	Operation	operator: 17 operands: 18
14	Operation	operator: 28 operands: 19
15	Operation	operator: 37 operands: 20
16	ExprTuple	21, 53
17	Literal
18	ExprTuple	57, 53
19	ExprTuple	32, 22
20	ExprTuple	23, 24
21	Operation	operator: 66 operand: 57
22	Operation	operator: 37 operands: 26
23	Operation	operator: 45 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprTuple	57
26	ExprTuple	30, 43
27	ExprTuple	53, 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	64, 40
36	ExprTuple	41
37	Literal
38	ExprTuple	42, 43
39	Operation	operator: 55 operands: 44
40	Operation	operator: 45 operands: 46
41	Literal
42	Operation	operator: 62 operands: 47
43	Operation	operator: 48 operand: 53
44	ExprTuple	64, 58, 59, 50, 61
45	Literal
46	ExprTuple	53, 64
47	ExprTuple	51, 52
48	Literal
49	ExprTuple	53
50	Operation	operator: 62 operands: 54
51	Literal
52	Operation	operator: 55 operands: 56
53	Literal
54	ExprTuple	64, 57
55	Literal
56	ExprTuple	64, 58, 59, 60, 61
57	Variable
58	Literal
59	Literal
60	Operation	operator: 62 operands: 63
61	Literal
62	Literal
63	ExprTuple	64, 65
64	Literal
65	Operation	operator: 66 operand: 68
66	Literal
67	ExprTuple	68
68	Variable