Expression of type ExprTuple

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 ExprTuple, 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)
sub_expr3 = frac(one, Mult(four, sub_expr2))
sub_expr4 = Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _pos_domain)
expr = ExprTuple(Add(Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain), sub_expr4), Add(Mult(frac(one, four), Sum(index_or_indices = sub_expr1, summand = frac(one, sub_expr2), domain = _neg_domain)), sub_expr4))

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(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\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), \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)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 65 operands: 3
2	Operation	operator: 65 operands: 4
3	ExprTuple	5, 7
4	ExprTuple	6, 7
5	Operation	operator: 17 operand: 11
6	Operation	operator: 60 operands: 9
7	Operation	operator: 17 operand: 14
8	ExprTuple	11
9	ExprTuple	12, 13
10	ExprTuple	14
11	Lambda	parameter: 51 body: 15
12	Operation	operator: 31 operands: 16
13	Operation	operator: 17 operand: 20
14	Lambda	parameter: 51 body: 19
15	Conditional	value: 21 condition: 28
16	ExprTuple	77, 38
17	Literal
18	ExprTuple	20
19	Conditional	value: 21 condition: 22
20	Lambda	parameter: 51 body: 24
21	Operation	operator: 31 operands: 25
22	Operation	operator: 33 operands: 26
23	ExprTuple	51
24	Conditional	value: 27 condition: 28
25	ExprTuple	77, 29
26	ExprTuple	51, 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Operation	operator: 60 operands: 35
30	Operation	operator: 40 operands: 36
31	Literal
32	ExprTuple	77, 39
33	Literal
34	ExprTuple	51, 37
35	ExprTuple	38, 39
36	ExprTuple	50, 56
37	Operation	operator: 40 operands: 41
38	Literal
39	Operation	operator: 67 operands: 42
40	Literal
41	ExprTuple	43, 44
42	ExprTuple	45, 72
43	Operation	operator: 65 operands: 46
44	Operation	operator: 75 operand: 50
45	Operation	operator: 65 operands: 48
46	ExprTuple	49, 77
47	ExprTuple	50
48	ExprTuple	51, 52
49	Operation	operator: 75 operand: 56
50	Operation	operator: 65 operands: 54
51	Variable
52	Operation	operator: 75 operand: 58
53	ExprTuple	56
54	ExprTuple	57, 77
55	ExprTuple	58
56	Operation	operator: 67 operands: 59
57	Variable
58	Operation	operator: 60 operands: 61
59	ExprTuple	72, 62
60	Literal
61	ExprTuple	63, 64
62	Operation	operator: 65 operands: 66
63	Operation	operator: 67 operands: 68
64	Operation	operator: 69 operand: 74
65	Literal
66	ExprTuple	73, 71
67	Literal
68	ExprTuple	72, 73
69	Literal
70	ExprTuple	74
71	Operation	operator: 75 operand: 77
72	Literal
73	Literal
74	Literal
75	Literal
76	ExprTuple	77
77	Literal