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

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, four)
sub_expr3 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = ExprTuple(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 = _pos_domain))), Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain), Variable("_a", latex_format = r"{_{-}a}"))))

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) + {_{-}a}\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: 62 operands: 3
2	Operation	operator: 62 operands: 4
3	ExprTuple	6, 5
4	ExprTuple	6, 7
5	Operation	operator: 72 operands: 8
6	Operation	operator: 33 operands: 9
7	Operation	operator: 72 operands: 10
8	ExprTuple	11, 12
9	ExprTuple	80, 13
10	ExprTuple	14, 15
11	Operation	operator: 18 operand: 20
12	Operation	operator: 18 operand: 21
13	Literal
14	Operation	operator: 18 operand: 22
15	Variable
16	ExprTuple	20
17	ExprTuple	21
18	Literal
19	ExprTuple	22
20	Lambda	parameter: 52 body: 23
21	Lambda	parameter: 52 body: 24
22	Lambda	parameter: 52 body: 26
23	Conditional	value: 27 condition: 30
24	Conditional	value: 27 condition: 28
25	ExprTuple	52
26	Conditional	value: 29 condition: 30
27	Operation	operator: 33 operands: 31
28	Operation	operator: 35 operands: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operands: 36
31	ExprTuple	80, 37
32	ExprTuple	52, 38
33	Literal
34	ExprTuple	80, 39
35	Literal
36	ExprTuple	52, 40
37	Operation	operator: 68 operands: 41
38	Operation	operator: 44 operands: 42
39	Operation	operator: 68 operands: 43
40	Operation	operator: 44 operands: 45
41	ExprTuple	46, 74
42	ExprTuple	55, 60
43	ExprTuple	52, 74
44	Literal
45	ExprTuple	47, 48
46	Operation	operator: 72 operands: 49
47	Operation	operator: 72 operands: 50
48	Operation	operator: 78 operand: 55
49	ExprTuple	52, 53
50	ExprTuple	54, 80
51	ExprTuple	55
52	Variable
53	Operation	operator: 78 operand: 59
54	Operation	operator: 78 operand: 60
55	Operation	operator: 72 operands: 58
56	ExprTuple	59
57	ExprTuple	60
58	ExprTuple	61, 80
59	Operation	operator: 62 operands: 63
60	Operation	operator: 68 operands: 64
61	Variable
62	Literal
63	ExprTuple	65, 66
64	ExprTuple	74, 67
65	Operation	operator: 68 operands: 69
66	Operation	operator: 70 operand: 75
67	Operation	operator: 72 operands: 73
68	Literal
69	ExprTuple	74, 76
70	Literal
71	ExprTuple	75
72	Literal
73	ExprTuple	76, 77
74	Literal
75	Literal
76	Literal
77	Operation	operator: 78 operand: 80
78	Literal
79	ExprTuple	80
80	Literal