Expression of type InSet

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.logic import InSet
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 = InSet(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)\right) \in \mathbb{R}

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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 21 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 52 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 8 operand: 10
6	Operation	operator: 8 operand: 11
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	Lambda	parameter: 38 body: 12
11	Lambda	parameter: 38 body: 14
12	Conditional	value: 16 condition: 15
13	ExprTuple	38
14	Conditional	value: 16 condition: 17
15	Operation	operator: 21 operands: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	38, 23
19	Literal
20	ExprTuple	64, 24
21	Literal
22	ExprTuple	38, 25
23	Operation	operator: 28 operands: 26
24	Operation	operator: 54 operands: 27
25	Operation	operator: 28 operands: 29
26	ExprTuple	30, 31
27	ExprTuple	32, 59
28	Literal
29	ExprTuple	37, 43
30	Operation	operator: 52 operands: 33
31	Operation	operator: 62 operand: 37
32	Operation	operator: 52 operands: 35
33	ExprTuple	36, 64
34	ExprTuple	37
35	ExprTuple	38, 39
36	Operation	operator: 62 operand: 43
37	Operation	operator: 52 operands: 41
38	Variable
39	Operation	operator: 62 operand: 45
40	ExprTuple	43
41	ExprTuple	44, 64
42	ExprTuple	45
43	Operation	operator: 54 operands: 46
44	Variable
45	Operation	operator: 47 operands: 48
46	ExprTuple	59, 49
47	Literal
48	ExprTuple	50, 51
49	Operation	operator: 52 operands: 53
50	Operation	operator: 54 operands: 55
51	Operation	operator: 56 operand: 61
52	Literal
53	ExprTuple	60, 58
54	Literal
55	ExprTuple	59, 60
56	Literal
57	ExprTuple	61
58	Operation	operator: 62 operand: 64
59	Literal
60	Literal
61	Literal
62	Literal
63	ExprTuple	64
64	Literal