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 Abs, Add, Exp, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Exp(Abs(_rel_indexed_alpha), two)
sub_expr3 = Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _pos_domain)
expr = ExprTuple(Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), sub_expr3), Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two))), domain = _neg_domain), sub_expr3))

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)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right), \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}} \left|\alpha_{b_{\textit{f}} \oplus l}\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: 68 operands: 3
2	Operation	operator: 68 operands: 4
3	ExprTuple	5, 7
4	ExprTuple	6, 7
5	Operation	operator: 10 operand: 12
6	Operation	operator: 10 operand: 13
7	Operation	operator: 10 operand: 14
8	ExprTuple	12
9	ExprTuple	13
10	Literal
11	ExprTuple	14
12	Lambda	parameter: 61 body: 15
13	Lambda	parameter: 61 body: 16
14	Lambda	parameter: 61 body: 18
15	Conditional	value: 21 condition: 20
16	Conditional	value: 19 condition: 20
17	ExprTuple	61
18	Conditional	value: 21 condition: 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 27 operands: 25
21	Operation	operator: 73 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	ExprTuple	82, 29
25	ExprTuple	61, 30
26	ExprTuple	31, 79
27	Literal
28	ExprTuple	61, 32
29	Operation	operator: 66 operands: 33
30	Operation	operator: 37 operands: 34
31	Operation	operator: 35 operand: 43
32	Operation	operator: 37 operands: 38
33	ExprTuple	39, 40
34	ExprTuple	41, 42
35	Literal
36	ExprTuple	43
37	Literal
38	ExprTuple	51, 59
39	Literal
40	Operation	operator: 73 operands: 44
41	Operation	operator: 68 operands: 45
42	Operation	operator: 77 operand: 51
43	Operation	operator: 47 operand: 52
44	ExprTuple	49, 79
45	ExprTuple	50, 82
46	ExprTuple	51
47	Literal
48	ExprTuple	52
49	Operation	operator: 68 operands: 53
50	Operation	operator: 77 operand: 59
51	Operation	operator: 68 operands: 55
52	Operation	operator: 56 operands: 57
53	ExprTuple	61, 58
54	ExprTuple	59
55	ExprTuple	60, 82
56	Literal
57	ExprTuple	81, 61
58	Operation	operator: 77 operand: 64
59	Operation	operator: 73 operands: 63
60	Variable
61	Variable
62	ExprTuple	64
63	ExprTuple	79, 65
64	Operation	operator: 66 operands: 67
65	Operation	operator: 68 operands: 69
66	Literal
67	ExprTuple	70, 71
68	Literal
69	ExprTuple	80, 72
70	Operation	operator: 73 operands: 74
71	Operation	operator: 75 operand: 81
72	Operation	operator: 77 operand: 82
73	Literal
74	ExprTuple	79, 80
75	Literal
76	ExprTuple	81
77	Literal
78	ExprTuple	82
79	Literal
80	Literal
81	Literal
82	Literal