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 Abs, Exp, Real, Sum, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = InSet(Sum(index_or_indices = [l], summand = Exp(Abs(_rel_indexed_alpha), two), domain = _neg_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(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\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: 12 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 6
3	Literal
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 35 body: 8
7	ExprTuple	35
8	Conditional	value: 9 condition: 10
9	Operation	operator: 38 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 40
12	Literal
13	ExprTuple	35, 15
14	Operation	operator: 16 operand: 20
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 23 operand: 27
21	Operation	operator: 42 operands: 25
22	Operation	operator: 46 operand: 29
23	Literal
24	ExprTuple	27
25	ExprTuple	28, 48
26	ExprTuple	29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 46 operand: 36
29	Operation	operator: 42 operands: 33
30	Literal
31	ExprTuple	34, 35
32	ExprTuple	36
33	ExprTuple	37, 48
34	Literal
35	Variable
36	Operation	operator: 38 operands: 39
37	Variable
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Operation	operator: 46 operand: 48
46	Literal
47	ExprTuple	48
48	Literal