Expression of type Add

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 l
from proveit.numbers import Add, Exp, 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 = 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))

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(\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)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 49 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operand: 7
3	Operation	operator: 5 operand: 8
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Lambda	parameter: 35 body: 9
8	Lambda	parameter: 35 body: 11
9	Conditional	value: 13 condition: 12
10	ExprTuple	35
11	Conditional	value: 13 condition: 14
12	Operation	operator: 18 operands: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	35, 20
16	Literal
17	ExprTuple	61, 21
18	Literal
19	ExprTuple	35, 22
20	Operation	operator: 25 operands: 23
21	Operation	operator: 51 operands: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	27, 28
24	ExprTuple	29, 56
25	Literal
26	ExprTuple	34, 40
27	Operation	operator: 49 operands: 30
28	Operation	operator: 59 operand: 34
29	Operation	operator: 49 operands: 32
30	ExprTuple	33, 61
31	ExprTuple	34
32	ExprTuple	35, 36
33	Operation	operator: 59 operand: 40
34	Operation	operator: 49 operands: 38
35	Variable
36	Operation	operator: 59 operand: 42
37	ExprTuple	40
38	ExprTuple	41, 61
39	ExprTuple	42
40	Operation	operator: 51 operands: 43
41	Variable
42	Operation	operator: 44 operands: 45
43	ExprTuple	56, 46
44	Literal
45	ExprTuple	47, 48
46	Operation	operator: 49 operands: 50
47	Operation	operator: 51 operands: 52
48	Operation	operator: 53 operand: 58
49	Literal
50	ExprTuple	57, 55
51	Literal
52	ExprTuple	56, 57
53	Literal
54	ExprTuple	58
55	Operation	operator: 59 operand: 61
56	Literal
57	Literal
58	Literal
59	Literal
60	ExprTuple	61
61	Literal