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, e, l
from proveit.numbers import Abs, Add, Exp, Sum, two
from proveit.physics.quantum.QPE import Pfail, _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(Pfail(e), Add(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(\left[P_{\rm fail}\right]\left(e\right), \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)\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: 3 operand: 46
2	Operation	operator: 53 operands: 5
3	Literal
4	ExprTuple	46
5	ExprTuple	6, 7
6	Operation	operator: 9 operand: 11
7	Operation	operator: 9 operand: 12
8	ExprTuple	11
9	Literal
10	ExprTuple	12
11	Lambda	parameter: 48 body: 13
12	Lambda	parameter: 48 body: 15
13	Conditional	value: 17 condition: 16
14	ExprTuple	48
15	Conditional	value: 17 condition: 18
16	Operation	operator: 21 operands: 19
17	Operation	operator: 49 operands: 20
18	Operation	operator: 21 operands: 22
19	ExprTuple	48, 23
20	ExprTuple	24, 51
21	Literal
22	ExprTuple	48, 25
23	Operation	operator: 29 operands: 26
24	Operation	operator: 27 operand: 33
25	Operation	operator: 29 operands: 30
26	ExprTuple	31, 32
27	Literal
28	ExprTuple	33
29	Literal
30	ExprTuple	39, 45
31	Operation	operator: 53 operands: 34
32	Operation	operator: 57 operand: 39
33	Operation	operator: 36 operand: 40
34	ExprTuple	38, 59
35	ExprTuple	39
36	Literal
37	ExprTuple	40
38	Operation	operator: 57 operand: 45
39	Operation	operator: 53 operands: 42
40	Operation	operator: 43 operands: 44
41	ExprTuple	45
42	ExprTuple	46, 59
43	Literal
44	ExprTuple	47, 48
45	Operation	operator: 49 operands: 50
46	Variable
47	Literal
48	Variable
49	Literal
50	ExprTuple	51, 52
51	Literal
52	Operation	operator: 53 operands: 54
53	Literal
54	ExprTuple	55, 56
55	Literal
56	Operation	operator: 57 operand: 59
57	Literal
58	ExprTuple	59
59	Literal