Expression of type Sum

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 _rel_indexed_alpha, _two_pow__t_minus_one

# build up the expression from sub-expressions
expr = Sum(index_or_indices = [l], summand = Exp(Abs(_rel_indexed_alpha), two), domain = Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), 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())

\sum_{l = -2^{t - 1} + 1}^{-e - 1} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 32 body: 5
4	ExprTuple	32
5	Conditional	value: 6 condition: 7
6	Operation	operator: 35 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 37
9	Literal
10	ExprTuple	32, 12
11	Operation	operator: 13 operand: 17
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 20 operand: 24
18	Operation	operator: 39 operands: 22
19	Operation	operator: 39 operands: 23
20	Literal
21	ExprTuple	24
22	ExprTuple	25, 45
23	ExprTuple	26, 42
24	Operation	operator: 27 operands: 28
25	Operation	operator: 43 operand: 33
26	Operation	operator: 43 operand: 34
27	Literal
28	ExprTuple	31, 32
29	ExprTuple	33
30	ExprTuple	34
31	Literal
32	Variable
33	Operation	operator: 35 operands: 36
34	Variable
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Literal
42	Operation	operator: 43 operand: 45
43	Literal
44	ExprTuple	45
45	Literal