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(Mult(sub_expr2, Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain)), Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr2, sub_expr3), domain = _neg_domain)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \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 = -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) \end{array} \end{array}

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.	()	(2)	('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: 48 operands: 5
4	Operation	operator: 9 operand: 8
5	ExprTuple	18, 7
6	ExprTuple	8
7	Operation	operator: 9 operand: 12
8	Lambda	parameter: 39 body: 11
9	Literal
10	ExprTuple	12
11	Conditional	value: 13 condition: 17
12	Lambda	parameter: 39 body: 15
13	Operation	operator: 48 operands: 16
14	ExprTuple	39
15	Conditional	value: 19 condition: 17
16	ExprTuple	18, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 23 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	ExprTuple	39, 25
22	ExprTuple	65, 26
23	Literal
24	ExprTuple	65, 27
25	Operation	operator: 28 operands: 29
26	Literal
27	Operation	operator: 55 operands: 30
28	Literal
29	ExprTuple	31, 32
30	ExprTuple	33, 60
31	Operation	operator: 53 operands: 34
32	Operation	operator: 63 operand: 38
33	Operation	operator: 53 operands: 36
34	ExprTuple	37, 65
35	ExprTuple	38
36	ExprTuple	39, 40
37	Operation	operator: 63 operand: 44
38	Operation	operator: 53 operands: 42
39	Variable
40	Operation	operator: 63 operand: 46
41	ExprTuple	44
42	ExprTuple	45, 65
43	ExprTuple	46
44	Operation	operator: 55 operands: 47
45	Variable
46	Operation	operator: 48 operands: 49
47	ExprTuple	60, 50
48	Literal
49	ExprTuple	51, 52
50	Operation	operator: 53 operands: 54
51	Operation	operator: 55 operands: 56
52	Operation	operator: 57 operand: 62
53	Literal
54	ExprTuple	61, 59
55	Literal
56	ExprTuple	60, 61
57	Literal
58	ExprTuple	62
59	Operation	operator: 63 operand: 65
60	Literal
61	Literal
62	Literal
63	Literal
64	ExprTuple	65
65	Literal