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, Sum, two
from proveit.physics.quantum.QPE import _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)
expr = ExprTuple(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())

\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}, \sum_{l = e + 1}^{2^{t - 1}} \left|\alpha_{b_{\textit{f}} \oplus l}\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: 43 body: 8
7	Lambda	parameter: 43 body: 10
8	Conditional	value: 12 condition: 11
9	ExprTuple	43
10	Conditional	value: 12 condition: 13
11	Operation	operator: 16 operands: 14
12	Operation	operator: 44 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	43, 18
15	ExprTuple	19, 46
16	Literal
17	ExprTuple	43, 20
18	Operation	operator: 24 operands: 21
19	Operation	operator: 22 operand: 28
20	Operation	operator: 24 operands: 25
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28
24	Literal
25	ExprTuple	34, 40
26	Operation	operator: 48 operands: 29
27	Operation	operator: 52 operand: 34
28	Operation	operator: 31 operand: 35
29	ExprTuple	33, 54
30	ExprTuple	34
31	Literal
32	ExprTuple	35
33	Operation	operator: 52 operand: 40
34	Operation	operator: 48 operands: 37
35	Operation	operator: 38 operands: 39
36	ExprTuple	40
37	ExprTuple	41, 54
38	Literal
39	ExprTuple	42, 43
40	Operation	operator: 44 operands: 45
41	Variable
42	Literal
43	Variable
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Operation	operator: 48 operands: 49
48	Literal
49	ExprTuple	50, 51
50	Literal
51	Operation	operator: 52 operand: 54
52	Literal
53	ExprTuple	54
54	Literal