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 e, l
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Mult, Sum, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = frac(one, four)
sub_expr2 = frac(one, Exp(e, two))
sub_expr3 = Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))
expr = Equals(Mult(sub_expr1, Add(sub_expr3, Add(sub_expr2, sub_expr3))), Mult(sub_expr1, Add(Mult(two, sub_expr3), sub_expr2)))

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