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

# build up the expression from sub-expressions
sub_expr1 = [l]
expr = ExprTuple(Sum(index_or_indices = sub_expr1, summand = Exp(Abs(_rel_indexed_alpha), two), domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two))), domain = _neg_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(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}, \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)

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