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 ExprRange, IndexedVar, Variable, a, c, l
from proveit.numbers import Exp, Mult, Sum, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Sum(index_or_indices = [l], summand = Mult(IndexedVar(a, one), frac(one, Exp(_diff_l_scaled_delta_floor, two)), ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, zero)), 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())

\sum_{l = e + 1}^{2^{t - 1}} \left(a_{1} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right)

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: 38 body: 5
4	ExprTuple	38
5	Conditional	value: 6 condition: 7
6	Operation	operator: 46 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12, 13
9	Literal
10	ExprTuple	38, 14
11	IndexedVar	variable: 15 index: 45
12	Operation	operator: 16 operands: 17
13	ExprRange	lambda_map: 18 start_index: 45 end_index: 19
14	Operation	operator: 20 operands: 21
15	Variable
16	Literal
17	ExprTuple	45, 22
18	Lambda	parameter: 32 body: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 50 operands: 26
23	IndexedVar	variable: 27 index: 32
24	Operation	operator: 36 operands: 29
25	Operation	operator: 50 operands: 30
26	ExprTuple	31, 54
27	Variable
28	ExprTuple	32
29	ExprTuple	33, 45
30	ExprTuple	54, 34
31	Operation	operator: 36 operands: 35
32	Variable
33	Variable
34	Operation	operator: 36 operands: 37
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	55, 40
38	Variable
39	Operation	operator: 42 operand: 44
40	Operation	operator: 42 operand: 45
41	ExprTuple	44
42	Literal
43	ExprTuple	45
44	Operation	operator: 46 operands: 47
45	Literal
46	Literal
47	ExprTuple	48, 49
48	Operation	operator: 50 operands: 51
49	Operation	operator: 52 operand: 56
50	Literal
51	ExprTuple	54, 55
52	Literal
53	ExprTuple	56
54	Literal
55	Literal
56	Literal