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]
expr = InSet(Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), 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}{l^{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: 23 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 56 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: 42 body: 12
11	Lambda	parameter: 42 body: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	42
14	Conditional	value: 17 condition: 18
15	Operation	operator: 21 operands: 19
16	Operation	operator: 23 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	ExprTuple	68, 25
20	ExprTuple	42, 26
21	Literal
22	ExprTuple	68, 27
23	Literal
24	ExprTuple	42, 28
25	Operation	operator: 58 operands: 29
26	Operation	operator: 32 operands: 30
27	Operation	operator: 58 operands: 31
28	Operation	operator: 32 operands: 33
29	ExprTuple	42, 63
30	ExprTuple	34, 35
31	ExprTuple	36, 63
32	Literal
33	ExprTuple	41, 47
34	Operation	operator: 56 operands: 37
35	Operation	operator: 66 operand: 41
36	Operation	operator: 56 operands: 39
37	ExprTuple	40, 68
38	ExprTuple	41
39	ExprTuple	42, 43
40	Operation	operator: 66 operand: 47
41	Operation	operator: 56 operands: 45
42	Variable
43	Operation	operator: 66 operand: 49
44	ExprTuple	47
45	ExprTuple	48, 68
46	ExprTuple	49
47	Operation	operator: 58 operands: 50
48	Variable
49	Operation	operator: 51 operands: 52
50	ExprTuple	63, 53
51	Literal
52	ExprTuple	54, 55
53	Operation	operator: 56 operands: 57
54	Operation	operator: 58 operands: 59
55	Operation	operator: 60 operand: 65
56	Literal
57	ExprTuple	64, 62
58	Literal
59	ExprTuple	63, 64
60	Literal
61	ExprTuple	65
62	Operation	operator: 66 operand: 68
63	Literal
64	Literal
65	Literal
66	Literal
67	ExprTuple	68
68	Literal