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 l
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, four)
sub_expr3 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr2, sub_expr3), domain = _neg_domain), Mult(sub_expr2, Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_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)} \left(\frac{1}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right) = \left(\frac{1}{4} \cdot \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)\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: 10 operand: 7
4	Operation	operator: 47 operands: 6
5	ExprTuple	7
6	ExprTuple	17, 8
7	Lambda	parameter: 37 body: 9
8	Operation	operator: 10 operand: 13
9	Conditional	value: 12 condition: 19
10	Literal
11	ExprTuple	13
12	Operation	operator: 47 operands: 14
13	Lambda	parameter: 37 body: 16
14	ExprTuple	17, 18
15	ExprTuple	37
16	Conditional	value: 18 condition: 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	65, 25
21	Literal
22	ExprTuple	65, 26
23	Literal
24	ExprTuple	37, 27
25	Literal
26	Operation	operator: 53 operands: 28
27	Operation	operator: 29 operands: 30
28	ExprTuple	31, 59
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 57 operands: 34
32	Operation	operator: 57 operands: 35
33	Operation	operator: 63 operand: 40
34	ExprTuple	37, 38
35	ExprTuple	39, 65
36	ExprTuple	40
37	Variable
38	Operation	operator: 63 operand: 44
39	Operation	operator: 63 operand: 45
40	Operation	operator: 57 operands: 43
41	ExprTuple	44
42	ExprTuple	45
43	ExprTuple	46, 65
44	Operation	operator: 47 operands: 48
45	Operation	operator: 53 operands: 49
46	Variable
47	Literal
48	ExprTuple	50, 51
49	ExprTuple	59, 52
50	Operation	operator: 53 operands: 54
51	Operation	operator: 55 operand: 60
52	Operation	operator: 57 operands: 58
53	Literal
54	ExprTuple	59, 61
55	Literal
56	ExprTuple	60
57	Literal
58	ExprTuple	61, 62
59	Literal
60	Literal
61	Literal
62	Operation	operator: 63 operand: 65
63	Literal
64	ExprTuple	65
65	Literal