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 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 = Exp(_diff_l_scaled_delta_floor, two)
expr = Add(Mult(frac(one, four), Sum(index_or_indices = sub_expr1, summand = frac(one, sub_expr2), domain = _neg_domain)), Sum(index_or_indices = sub_expr1, summand = frac(one, Mult(four, 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(\frac{1}{4} \cdot \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)\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\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: 58 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 53 operands: 4
3	Operation	operator: 10 operand: 8
4	ExprTuple	6, 7
5	ExprTuple	8
6	Operation	operator: 24 operands: 9
7	Operation	operator: 10 operand: 13
8	Lambda	parameter: 44 body: 12
9	ExprTuple	70, 31
10	Literal
11	ExprTuple	13
12	Conditional	value: 14 condition: 15
13	Lambda	parameter: 44 body: 17
14	Operation	operator: 24 operands: 18
15	Operation	operator: 26 operands: 19
16	ExprTuple	44
17	Conditional	value: 20 condition: 21
18	ExprTuple	70, 22
19	ExprTuple	44, 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 53 operands: 28
23	Operation	operator: 33 operands: 29
24	Literal
25	ExprTuple	70, 32
26	Literal
27	ExprTuple	44, 30
28	ExprTuple	31, 32
29	ExprTuple	43, 49
30	Operation	operator: 33 operands: 34
31	Literal
32	Operation	operator: 60 operands: 35
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	38, 65
36	Operation	operator: 58 operands: 39
37	Operation	operator: 68 operand: 43
38	Operation	operator: 58 operands: 41
39	ExprTuple	42, 70
40	ExprTuple	43
41	ExprTuple	44, 45
42	Operation	operator: 68 operand: 49
43	Operation	operator: 58 operands: 47
44	Variable
45	Operation	operator: 68 operand: 51
46	ExprTuple	49
47	ExprTuple	50, 70
48	ExprTuple	51
49	Operation	operator: 60 operands: 52
50	Variable
51	Operation	operator: 53 operands: 54
52	ExprTuple	65, 55
53	Literal
54	ExprTuple	56, 57
55	Operation	operator: 58 operands: 59
56	Operation	operator: 60 operands: 61
57	Operation	operator: 62 operand: 67
58	Literal
59	ExprTuple	66, 64
60	Literal
61	ExprTuple	65, 66
62	Literal
63	ExprTuple	67
64	Operation	operator: 68 operand: 70
65	Literal
66	Literal
67	Literal
68	Literal
69	ExprTuple	70
70	Literal