Expression of type Equals

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 e, l
from proveit.logic import Equals
from proveit.numbers import Abs, Add, Exp, Interval, Neg, Sum, one, subtract, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha, _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Exp(Abs(_rel_indexed_alpha), two)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one))))

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) = \left(\sum_{l = -2^{t - 1} + 1}^{-e - 1} \left|\alpha_{b_{\textit{f}} \oplus l}\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',)
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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 47 body: 10
9	Lambda	parameter: 47 body: 12
10	Conditional	value: 14 condition: 13
11	ExprTuple	47
12	Conditional	value: 14 condition: 15
13	Operation	operator: 18 operands: 16
14	Operation	operator: 50 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	47, 20
17	ExprTuple	21, 52
18	Literal
19	ExprTuple	47, 22
20	Operation	operator: 26 operands: 23
21	Operation	operator: 24 operand: 29
22	Operation	operator: 26 operands: 27
23	ExprTuple	30, 28
24	Literal
25	ExprTuple	29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 58 operand: 37
29	Operation	operator: 33 operand: 38
30	Operation	operator: 54 operands: 35
31	Operation	operator: 54 operands: 36
32	ExprTuple	37
33	Literal
34	ExprTuple	38
35	ExprTuple	39, 60
36	ExprTuple	40, 57
37	Operation	operator: 54 operands: 41
38	Operation	operator: 42 operands: 43
39	Operation	operator: 58 operand: 48
40	Operation	operator: 58 operand: 49
41	ExprTuple	49, 60
42	Literal
43	ExprTuple	46, 47
44	ExprTuple	48
45	ExprTuple	49
46	Literal
47	Variable
48	Operation	operator: 50 operands: 51
49	Variable
50	Literal
51	ExprTuple	52, 53
52	Literal
53	Operation	operator: 54 operands: 55
54	Literal
55	ExprTuple	56, 57
56	Literal
57	Operation	operator: 58 operand: 60
58	Literal
59	ExprTuple	60
60	Literal