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 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))
sub_expr4 = Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _pos_domain)
sub_expr5 = Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain)
expr = ExprTuple(Add(Mult(sub_expr2, sub_expr5), Mult(sub_expr2, sub_expr4)), Mult(sub_expr2, Add(sub_expr5, sub_expr4)))

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}{4} \cdot \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)\right) + \left(\frac{1}{4} \cdot \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}{\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)\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: 61 operands: 3
2	Operation	operator: 56 operands: 4
3	ExprTuple	5, 6
4	ExprTuple	11, 7
5	Operation	operator: 56 operands: 8
6	Operation	operator: 56 operands: 9
7	Operation	operator: 61 operands: 10
8	ExprTuple	11, 12
9	ExprTuple	11, 13
10	ExprTuple	12, 13
11	Operation	operator: 28 operands: 14
12	Operation	operator: 16 operand: 19
13	Operation	operator: 16 operand: 20
14	ExprTuple	73, 18
15	ExprTuple	19
16	Literal
17	ExprTuple	20
18	Literal
19	Lambda	parameter: 47 body: 21
20	Lambda	parameter: 47 body: 23
21	Conditional	value: 25 condition: 24
22	ExprTuple	47
23	Conditional	value: 25 condition: 26
24	Operation	operator: 30 operands: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	47, 32
28	Literal
29	ExprTuple	73, 33
30	Literal
31	ExprTuple	47, 34
32	Operation	operator: 37 operands: 35
33	Operation	operator: 63 operands: 36
34	Operation	operator: 37 operands: 38
35	ExprTuple	39, 40
36	ExprTuple	41, 68
37	Literal
38	ExprTuple	46, 52
39	Operation	operator: 61 operands: 42
40	Operation	operator: 71 operand: 46
41	Operation	operator: 61 operands: 44
42	ExprTuple	45, 73
43	ExprTuple	46
44	ExprTuple	47, 48
45	Operation	operator: 71 operand: 52
46	Operation	operator: 61 operands: 50
47	Variable
48	Operation	operator: 71 operand: 54
49	ExprTuple	52
50	ExprTuple	53, 73
51	ExprTuple	54
52	Operation	operator: 63 operands: 55
53	Variable
54	Operation	operator: 56 operands: 57
55	ExprTuple	68, 58
56	Literal
57	ExprTuple	59, 60
58	Operation	operator: 61 operands: 62
59	Operation	operator: 63 operands: 64
60	Operation	operator: 65 operand: 70
61	Literal
62	ExprTuple	69, 67
63	Literal
64	ExprTuple	68, 69
65	Literal
66	ExprTuple	70
67	Operation	operator: 71 operand: 73
68	Literal
69	Literal
70	Literal
71	Literal
72	ExprTuple	73
73	Literal