Expression of type Add

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.numbers import Add, Exp, Sum, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = [l]
expr = Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), 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 = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{l^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{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',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 53 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operand: 7
3	Operation	operator: 5 operand: 8
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Lambda	parameter: 39 body: 9
8	Lambda	parameter: 39 body: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	39
11	Conditional	value: 14 condition: 15
12	Operation	operator: 18 operands: 16
13	Operation	operator: 20 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	ExprTuple	65, 22
17	ExprTuple	39, 23
18	Literal
19	ExprTuple	65, 24
20	Literal
21	ExprTuple	39, 25
22	Operation	operator: 55 operands: 26
23	Operation	operator: 29 operands: 27
24	Operation	operator: 55 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprTuple	39, 60
27	ExprTuple	31, 32
28	ExprTuple	33, 60
29	Literal
30	ExprTuple	38, 44
31	Operation	operator: 53 operands: 34
32	Operation	operator: 63 operand: 38
33	Operation	operator: 53 operands: 36
34	ExprTuple	37, 65
35	ExprTuple	38
36	ExprTuple	39, 40
37	Operation	operator: 63 operand: 44
38	Operation	operator: 53 operands: 42
39	Variable
40	Operation	operator: 63 operand: 46
41	ExprTuple	44
42	ExprTuple	45, 65
43	ExprTuple	46
44	Operation	operator: 55 operands: 47
45	Variable
46	Operation	operator: 48 operands: 49
47	ExprTuple	60, 50
48	Literal
49	ExprTuple	51, 52
50	Operation	operator: 53 operands: 54
51	Operation	operator: 55 operands: 56
52	Operation	operator: 57 operand: 62
53	Literal
54	ExprTuple	61, 59
55	Literal
56	ExprTuple	60, 61
57	Literal
58	ExprTuple	62
59	Operation	operator: 63 operand: 65
60	Literal
61	Literal
62	Literal
63	Literal
64	ExprTuple	65
65	Literal