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 Abs, Add, Exp, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
sub_expr1 = [l]
expr = Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two))), domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = Exp(Abs(_rel_indexed_alpha), 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}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \left|\alpha_{b_{\textit{f}} \oplus l}\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: 61 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: 54 body: 9
8	Lambda	parameter: 54 body: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	54
11	Conditional	value: 14 condition: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 20 operands: 18
14	Operation	operator: 66 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	ExprTuple	75, 22
18	ExprTuple	54, 23
19	ExprTuple	24, 72
20	Literal
21	ExprTuple	54, 25
22	Operation	operator: 59 operands: 26
23	Operation	operator: 30 operands: 27
24	Operation	operator: 28 operand: 36
25	Operation	operator: 30 operands: 31
26	ExprTuple	32, 33
27	ExprTuple	34, 35
28	Literal
29	ExprTuple	36
30	Literal
31	ExprTuple	44, 52
32	Literal
33	Operation	operator: 66 operands: 37
34	Operation	operator: 61 operands: 38
35	Operation	operator: 70 operand: 44
36	Operation	operator: 40 operand: 45
37	ExprTuple	42, 72
38	ExprTuple	43, 75
39	ExprTuple	44
40	Literal
41	ExprTuple	45
42	Operation	operator: 61 operands: 46
43	Operation	operator: 70 operand: 52
44	Operation	operator: 61 operands: 48
45	Operation	operator: 49 operands: 50
46	ExprTuple	54, 51
47	ExprTuple	52
48	ExprTuple	53, 75
49	Literal
50	ExprTuple	74, 54
51	Operation	operator: 70 operand: 57
52	Operation	operator: 66 operands: 56
53	Variable
54	Variable
55	ExprTuple	57
56	ExprTuple	72, 58
57	Operation	operator: 59 operands: 60
58	Operation	operator: 61 operands: 62
59	Literal
60	ExprTuple	63, 64
61	Literal
62	ExprTuple	73, 65
63	Operation	operator: 66 operands: 67
64	Operation	operator: 68 operand: 74
65	Operation	operator: 70 operand: 75
66	Literal
67	ExprTuple	72, 73
68	Literal
69	ExprTuple	74
70	Literal
71	ExprTuple	75
72	Literal
73	Literal
74	Literal
75	Literal