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, Mult, Sum, four, 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]
sub_expr2 = frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two)))
expr = Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = 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 = -2^{t - 1} + 1}^{-\left(e + 1\right)} \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}} \frac{1}{4 \cdot \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: 48 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: 42 body: 9
8	Lambda	parameter: 42 body: 11
9	Conditional	value: 13 condition: 12
10	ExprTuple	42
11	Conditional	value: 13 condition: 14
12	Operation	operator: 18 operands: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	42, 20
16	Literal
17	ExprTuple	61, 21
18	Literal
19	ExprTuple	42, 22
20	Operation	operator: 25 operands: 23
21	Operation	operator: 50 operands: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	27, 28
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	35, 40
27	Operation	operator: 48 operands: 31
28	Operation	operator: 55 operand: 35
29	Literal
30	Operation	operator: 57 operands: 33
31	ExprTuple	34, 61
32	ExprTuple	35
33	ExprTuple	36, 62
34	Operation	operator: 55 operand: 40
35	Operation	operator: 48 operands: 38
36	Operation	operator: 48 operands: 39
37	ExprTuple	40
38	ExprTuple	41, 61
39	ExprTuple	42, 43
40	Operation	operator: 57 operands: 44
41	Variable
42	Variable
43	Operation	operator: 55 operand: 47
44	ExprTuple	62, 46
45	ExprTuple	47
46	Operation	operator: 48 operands: 49
47	Operation	operator: 50 operands: 51
48	Literal
49	ExprTuple	63, 52
50	Literal
51	ExprTuple	53, 54
52	Operation	operator: 55 operand: 61
53	Operation	operator: 57 operands: 58
54	Operation	operator: 59 operand: 64
55	Literal
56	ExprTuple	61
57	Literal
58	ExprTuple	62, 63
59	Literal
60	ExprTuple	64
61	Literal
62	Literal
63	Literal
64	Literal