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 e, l
from proveit.numbers import Abs, Add, Exp, Interval, Neg, Sum, one, subtract, two
from proveit.physics.quantum.QPE import _pos_domain, _rel_indexed_alpha, _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Exp(Abs(_rel_indexed_alpha), two)
expr = Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one))), 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}^{-e - 1} \left|\alpha_{b_{\textit{f}} \oplus l}\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: 51 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: 46 body: 9
8	Lambda	parameter: 46 body: 11
9	Conditional	value: 13 condition: 12
10	ExprTuple	46
11	Conditional	value: 13 condition: 14
12	Operation	operator: 17 operands: 15
13	Operation	operator: 47 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	46, 19
16	ExprTuple	20, 49
17	Literal
18	ExprTuple	46, 21
19	Operation	operator: 25 operands: 22
20	Operation	operator: 23 operand: 29
21	Operation	operator: 25 operands: 26
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29
25	Literal
26	ExprTuple	30, 43
27	Operation	operator: 51 operands: 31
28	Operation	operator: 51 operands: 32
29	Operation	operator: 33 operand: 38
30	Operation	operator: 51 operands: 35
31	ExprTuple	36, 57
32	ExprTuple	37, 54
33	Literal
34	ExprTuple	38
35	ExprTuple	44, 57
36	Operation	operator: 55 operand: 43
37	Operation	operator: 55 operand: 44
38	Operation	operator: 41 operands: 42
39	ExprTuple	43
40	ExprTuple	44
41	Literal
42	ExprTuple	45, 46
43	Operation	operator: 47 operands: 48
44	Variable
45	Literal
46	Variable
47	Literal
48	ExprTuple	49, 50
49	Literal
50	Operation	operator: 51 operands: 52
51	Literal
52	ExprTuple	53, 54
53	Literal
54	Operation	operator: 55 operand: 57
55	Literal
56	ExprTuple	57
57	Literal