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 ExprTuple, l
from proveit.numbers import Abs, Add, Exp, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Exp(Abs(_rel_indexed_alpha), two)
sub_expr3 = frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two)))
expr = ExprTuple(Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _pos_domain)), Add(Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _pos_domain)))

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(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right), \left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\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: 70 operands: 3
2	Operation	operator: 70 operands: 4
3	ExprTuple	5, 6
4	ExprTuple	7, 8
5	Operation	operator: 12 operand: 14
6	Operation	operator: 12 operand: 15
7	Operation	operator: 12 operand: 16
8	Operation	operator: 12 operand: 17
9	ExprTuple	14
10	ExprTuple	15
11	ExprTuple	16
12	Literal
13	ExprTuple	17
14	Lambda	parameter: 64 body: 18
15	Lambda	parameter: 64 body: 19
16	Lambda	parameter: 64 body: 20
17	Lambda	parameter: 64 body: 22
18	Conditional	value: 23 condition: 24
19	Conditional	value: 23 condition: 26
20	Conditional	value: 25 condition: 24
21	ExprTuple	64
22	Conditional	value: 25 condition: 26
23	Operation	operator: 79 operands: 27
24	Operation	operator: 31 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprTuple	33, 84
28	ExprTuple	64, 34
29	Literal
30	ExprTuple	83, 35
31	Literal
32	ExprTuple	64, 36
33	Operation	operator: 37 operand: 43
34	Operation	operator: 41 operands: 39
35	Operation	operator: 72 operands: 40
36	Operation	operator: 41 operands: 42
37	Literal
38	ExprTuple	43
39	ExprTuple	44, 45
40	ExprTuple	46, 47
41	Literal
42	ExprTuple	55, 62
43	Operation	operator: 48 operand: 53
44	Operation	operator: 70 operands: 50
45	Operation	operator: 77 operand: 55
46	Literal
47	Operation	operator: 79 operands: 52
48	Literal
49	ExprTuple	53
50	ExprTuple	54, 83
51	ExprTuple	55
52	ExprTuple	56, 84
53	Operation	operator: 57 operands: 58
54	Operation	operator: 77 operand: 62
55	Operation	operator: 70 operands: 60
56	Operation	operator: 70 operands: 61
57	Literal
58	ExprTuple	86, 64
59	ExprTuple	62
60	ExprTuple	63, 83
61	ExprTuple	64, 65
62	Operation	operator: 79 operands: 66
63	Variable
64	Variable
65	Operation	operator: 77 operand: 69
66	ExprTuple	84, 68
67	ExprTuple	69
68	Operation	operator: 70 operands: 71
69	Operation	operator: 72 operands: 73
70	Literal
71	ExprTuple	85, 74
72	Literal
73	ExprTuple	75, 76
74	Operation	operator: 77 operand: 83
75	Operation	operator: 79 operands: 80
76	Operation	operator: 81 operand: 86
77	Literal
78	ExprTuple	83
79	Literal
80	ExprTuple	84, 85
81	Literal
82	ExprTuple	86
83	Literal
84	Literal
85	Literal
86	Literal