Expression of type Mult

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, Exp(_diff_l_scaled_delta_floor, two))
expr = Mult(frac(one, four), 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())

\frac{1}{4} \cdot \left(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\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: 49 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 21 operands: 4
3	Operation	operator: 54 operands: 5
4	ExprTuple	66, 6
5	ExprTuple	7, 8
6	Literal
7	Operation	operator: 10 operand: 12
8	Operation	operator: 10 operand: 13
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 40 body: 14
13	Lambda	parameter: 40 body: 16
14	Conditional	value: 18 condition: 17
15	ExprTuple	40
16	Conditional	value: 18 condition: 19
17	Operation	operator: 23 operands: 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	40, 25
21	Literal
22	ExprTuple	66, 26
23	Literal
24	ExprTuple	40, 27
25	Operation	operator: 30 operands: 28
26	Operation	operator: 56 operands: 29
27	Operation	operator: 30 operands: 31
28	ExprTuple	32, 33
29	ExprTuple	34, 61
30	Literal
31	ExprTuple	39, 45
32	Operation	operator: 54 operands: 35
33	Operation	operator: 64 operand: 39
34	Operation	operator: 54 operands: 37
35	ExprTuple	38, 66
36	ExprTuple	39
37	ExprTuple	40, 41
38	Operation	operator: 64 operand: 45
39	Operation	operator: 54 operands: 43
40	Variable
41	Operation	operator: 64 operand: 47
42	ExprTuple	45
43	ExprTuple	46, 66
44	ExprTuple	47
45	Operation	operator: 56 operands: 48
46	Variable
47	Operation	operator: 49 operands: 50
48	ExprTuple	61, 51
49	Literal
50	ExprTuple	52, 53
51	Operation	operator: 54 operands: 55
52	Operation	operator: 56 operands: 57
53	Operation	operator: 58 operand: 63
54	Literal
55	ExprTuple	62, 60
56	Literal
57	ExprTuple	61, 62
58	Literal
59	ExprTuple	63
60	Operation	operator: 64 operand: 66
61	Literal
62	Literal
63	Literal
64	Literal
65	ExprTuple	66
66	Literal