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 Conditional, ExprTuple, Lambda, e, l
from proveit.logic import Equals, InSet
from proveit.numbers import Abs, Add, Exp, Sum, two
from proveit.physics.quantum.QPE import Pfail, _e_domain, _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(Lambda(e, Conditional(Equals(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))), InSet(e, _e_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(e \mapsto \left\{\left[P_{\rm fail}\right]\left(e\right) = \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)\right) \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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