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(Mult(two, sub_expr3), sub_expr2)), Add(Mult(frac(one, two), sub_expr3), Mult(sub_expr1, sub_expr2))).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(\left(2 \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) + \frac{1}{e^{2}}\right)\right) =  \\ \left(\left(\frac{1}{2} \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) + \left(\frac{1}{4} \cdot \frac{1}{e^{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: 17 operands: 5
4	Operation	operator: 53 operands: 6
5	ExprTuple	15, 7
6	ExprTuple	8, 9
7	Operation	operator: 53 operands: 10
8	Operation	operator: 17 operands: 11
9	Operation	operator: 17 operands: 12
10	ExprTuple	13, 16
11	ExprTuple	14, 22
12	ExprTuple	15, 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 33 operands: 19
15	Operation	operator: 33 operands: 20
16	Operation	operator: 33 operands: 21
17	Literal
18	ExprTuple	51, 22
19	ExprTuple	59, 51
20	ExprTuple	59, 23
21	ExprTuple	59, 24
22	Operation	operator: 25 operand: 28
23	Literal
24	Operation	operator: 49 operands: 27
25	Literal
26	ExprTuple	28
27	ExprTuple	47, 51
28	Lambda	parameter: 42 body: 30
29	ExprTuple	42
30	Conditional	value: 31 condition: 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	59, 37
35	Literal
36	ExprTuple	42, 38
37	Operation	operator: 49 operands: 39
38	Operation	operator: 40 operands: 41
39	ExprTuple	42, 51
40	Literal
41	ExprTuple	43, 44
42	Variable
43	Operation	operator: 53 operands: 45
44	Operation	operator: 53 operands: 46
45	ExprTuple	47, 59
46	ExprTuple	48, 56
47	Variable
48	Operation	operator: 49 operands: 50
49	Literal
50	ExprTuple	51, 52
51	Literal
52	Operation	operator: 53 operands: 54
53	Literal
54	ExprTuple	55, 56
55	Literal
56	Operation	operator: 57 operand: 59
57	Literal
58	ExprTuple	59
59	Literal