Expression of type Conditional

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, l
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _rel_indexed_alpha, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Equals(_rel_indexed_alpha, Mult(frac(one, _two_pow_t), frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t)))))))), And(InSet(l, _full_domain), NotEquals(l, zero)))

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\{\alpha_{b_{\textit{f}} \oplus l} = \left(\frac{1}{2^{t}} \cdot \frac{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)}}\right) \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} ,  l \neq 0\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 11 operand: 18
8	Operation	operator: 67 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	Literal
12	ExprTuple	18
13	ExprTuple	19, 20
14	Literal
15	ExprTuple	79, 21
16	Literal
17	ExprTuple	79, 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 76 operands: 25
20	Operation	operator: 76 operands: 26
21	Operation	operator: 27 operands: 28
22	Literal
23	Literal
24	ExprTuple	78, 79
25	ExprTuple	66, 80
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 43
29	Operation	operator: 60 operands: 32
30	Operation	operator: 60 operands: 33
31	Operation	operator: 60 operands: 34
32	ExprTuple	66, 35
33	ExprTuple	66, 36
34	ExprTuple	37, 66
35	Operation	operator: 70 operand: 41
36	Operation	operator: 70 operand: 42
37	Operation	operator: 70 operand: 43
38	ExprTuple	41
39	ExprTuple	42
40	ExprTuple	43
41	Operation	operator: 81 operands: 44
42	Operation	operator: 81 operands: 45
43	Operation	operator: 81 operands: 46
44	ExprTuple	48, 47
45	ExprTuple	48, 49
46	ExprTuple	83, 50
47	Operation	operator: 67 operands: 51
48	Literal
49	Operation	operator: 67 operands: 52
50	Operation	operator: 60 operands: 53
51	ExprTuple	83, 55, 56, 54
52	ExprTuple	83, 55, 56, 57
53	ExprTuple	84, 58
54	Operation	operator: 60 operands: 59
55	Literal
56	Literal
57	Operation	operator: 60 operands: 61
58	Operation	operator: 70 operand: 66
59	ExprTuple	63, 64
60	Literal
61	ExprTuple	72, 65
62	ExprTuple	66
63	Operation	operator: 67 operands: 68
64	Operation	operator: 70 operand: 79
65	Operation	operator: 70 operand: 73
66	Literal
67	Literal
68	ExprTuple	80, 72
69	ExprTuple	79
70	Literal
71	ExprTuple	73
72	Operation	operator: 74 operand: 78
73	Operation	operator: 76 operands: 77
74	Literal
75	ExprTuple	78
76	Literal
77	ExprTuple	79, 80
78	Literal
79	Variable
80	Operation	operator: 81 operands: 82
81	Literal
82	ExprTuple	83, 84
83	Literal
84	Literal