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 Add, Exp, Mult, Sum, four, 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 = Exp(_diff_l_scaled_delta_floor, two)
sub_expr3 = frac(one, Mult(four, sub_expr2))
sub_expr4 = Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _pos_domain)
expr = Equals(Add(Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain), sub_expr4), Add(Mult(frac(one, four), Sum(index_or_indices = sub_expr1, summand = frac(one, sub_expr2), domain = _neg_domain)), sub_expr4))

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}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right) = \left(\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) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{4 \cdot \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: 67 operands: 5
4	Operation	operator: 67 operands: 6
5	ExprTuple	7, 9
6	ExprTuple	8, 9
7	Operation	operator: 19 operand: 13
8	Operation	operator: 62 operands: 11
9	Operation	operator: 19 operand: 16
10	ExprTuple	13
11	ExprTuple	14, 15
12	ExprTuple	16
13	Lambda	parameter: 53 body: 17
14	Operation	operator: 33 operands: 18
15	Operation	operator: 19 operand: 22
16	Lambda	parameter: 53 body: 21
17	Conditional	value: 23 condition: 30
18	ExprTuple	79, 40
19	Literal
20	ExprTuple	22
21	Conditional	value: 23 condition: 24
22	Lambda	parameter: 53 body: 26
23	Operation	operator: 33 operands: 27
24	Operation	operator: 35 operands: 28
25	ExprTuple	53
26	Conditional	value: 29 condition: 30
27	ExprTuple	79, 31
28	ExprTuple	53, 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operands: 36
31	Operation	operator: 62 operands: 37
32	Operation	operator: 42 operands: 38
33	Literal
34	ExprTuple	79, 41
35	Literal
36	ExprTuple	53, 39
37	ExprTuple	40, 41
38	ExprTuple	52, 58
39	Operation	operator: 42 operands: 43
40	Literal
41	Operation	operator: 69 operands: 44
42	Literal
43	ExprTuple	45, 46
44	ExprTuple	47, 74
45	Operation	operator: 67 operands: 48
46	Operation	operator: 77 operand: 52
47	Operation	operator: 67 operands: 50
48	ExprTuple	51, 79
49	ExprTuple	52
50	ExprTuple	53, 54
51	Operation	operator: 77 operand: 58
52	Operation	operator: 67 operands: 56
53	Variable
54	Operation	operator: 77 operand: 60
55	ExprTuple	58
56	ExprTuple	59, 79
57	ExprTuple	60
58	Operation	operator: 69 operands: 61
59	Variable
60	Operation	operator: 62 operands: 63
61	ExprTuple	74, 64
62	Literal
63	ExprTuple	65, 66
64	Operation	operator: 67 operands: 68
65	Operation	operator: 69 operands: 70
66	Operation	operator: 71 operand: 76
67	Literal
68	ExprTuple	75, 73
69	Literal
70	ExprTuple	74, 75
71	Literal
72	ExprTuple	76
73	Operation	operator: 77 operand: 79
74	Literal
75	Literal
76	Literal
77	Literal
78	ExprTuple	79
79	Literal