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, e, l
from proveit.numbers import Add, Exp, Interval, Mult, Sum, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain, _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, four)
sub_expr3 = frac(one, Exp(l, two))
sub_expr4 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = ExprTuple(Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = sub_expr4, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr4, domain = _pos_domain))), Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = Interval(e, subtract(_two_pow__t_minus_one, 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(\frac{1}{4} \cdot \left(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right), \frac{1}{4} \cdot \left(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{l^{2}}\right) + \left(\sum_{l = e}^{2^{t - 1} - 1} \frac{1}{l^{2}}\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: 71 operands: 3
2	Operation	operator: 71 operands: 4
3	ExprTuple	6, 5
4	ExprTuple	6, 7
5	Operation	operator: 81 operands: 8
6	Operation	operator: 38 operands: 9
7	Operation	operator: 81 operands: 10
8	ExprTuple	11, 12
9	ExprTuple	89, 13
10	ExprTuple	14, 15
11	Operation	operator: 19 operand: 21
12	Operation	operator: 19 operand: 22
13	Literal
14	Operation	operator: 19 operand: 23
15	Operation	operator: 19 operand: 24
16	ExprTuple	21
17	ExprTuple	22
18	ExprTuple	23
19	Literal
20	ExprTuple	24
21	Lambda	parameter: 61 body: 25
22	Lambda	parameter: 61 body: 26
23	Lambda	parameter: 61 body: 27
24	Lambda	parameter: 61 body: 29
25	Conditional	value: 30 condition: 32
26	Conditional	value: 30 condition: 31
27	Conditional	value: 33 condition: 32
28	ExprTuple	61
29	Conditional	value: 33 condition: 34
30	Operation	operator: 38 operands: 35
31	Operation	operator: 40 operands: 36
32	Operation	operator: 40 operands: 37
33	Operation	operator: 38 operands: 39
34	Operation	operator: 40 operands: 41
35	ExprTuple	89, 42
36	ExprTuple	61, 43
37	ExprTuple	61, 44
38	Literal
39	ExprTuple	89, 45
40	Literal
41	ExprTuple	61, 46
42	Operation	operator: 77 operands: 47
43	Operation	operator: 51 operands: 48
44	Operation	operator: 51 operands: 49
45	Operation	operator: 77 operands: 50
46	Operation	operator: 51 operands: 52
47	ExprTuple	53, 83
48	ExprTuple	64, 69
49	ExprTuple	54, 55
50	ExprTuple	61, 83
51	Literal
52	ExprTuple	70, 56
53	Operation	operator: 81 operands: 57
54	Operation	operator: 81 operands: 58
55	Operation	operator: 87 operand: 64
56	Operation	operator: 81 operands: 60
57	ExprTuple	61, 62
58	ExprTuple	63, 89
59	ExprTuple	64
60	ExprTuple	69, 86
61	Variable
62	Operation	operator: 87 operand: 68
63	Operation	operator: 87 operand: 69
64	Operation	operator: 81 operands: 67
65	ExprTuple	68
66	ExprTuple	69
67	ExprTuple	70, 89
68	Operation	operator: 71 operands: 72
69	Operation	operator: 77 operands: 73
70	Variable
71	Literal
72	ExprTuple	74, 75
73	ExprTuple	83, 76
74	Operation	operator: 77 operands: 78
75	Operation	operator: 79 operand: 84
76	Operation	operator: 81 operands: 82
77	Literal
78	ExprTuple	83, 85
79	Literal
80	ExprTuple	84
81	Literal
82	ExprTuple	85, 86
83	Literal
84	Literal
85	Literal
86	Operation	operator: 87 operand: 89
87	Literal
88	ExprTuple	89
89	Literal