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, Real, Sum, 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, 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)), Real)

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