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 Exp, Interval, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _pos_domain, _two_pow__t_minus_one

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

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