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