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, _pos_domain

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