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, 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 = ExprTuple(Lambda(l, 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(l \mapsto \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..\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: 81 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 13 operand: 20
10	Operation	operator: 69 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	Literal
14	ExprTuple	20
15	ExprTuple	21, 22
16	Literal
17	ExprTuple	81, 23
18	Literal
19	ExprTuple	81, 24
20	Operation	operator: 25 operands: 26
21	Operation	operator: 78 operands: 27
22	Operation	operator: 78 operands: 28
23	Operation	operator: 29 operands: 30
24	Literal
25	Literal
26	ExprTuple	80, 81
27	ExprTuple	68, 82
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 45
31	Operation	operator: 62 operands: 34
32	Operation	operator: 62 operands: 35
33	Operation	operator: 62 operands: 36
34	ExprTuple	68, 37
35	ExprTuple	68, 38
36	ExprTuple	39, 68
37	Operation	operator: 72 operand: 43
38	Operation	operator: 72 operand: 44
39	Operation	operator: 72 operand: 45
40	ExprTuple	43
41	ExprTuple	44
42	ExprTuple	45
43	Operation	operator: 83 operands: 46
44	Operation	operator: 83 operands: 47
45	Operation	operator: 83 operands: 48
46	ExprTuple	50, 49
47	ExprTuple	50, 51
48	ExprTuple	85, 52
49	Operation	operator: 69 operands: 53
50	Literal
51	Operation	operator: 69 operands: 54
52	Operation	operator: 62 operands: 55
53	ExprTuple	85, 57, 58, 56
54	ExprTuple	85, 57, 58, 59
55	ExprTuple	86, 60
56	Operation	operator: 62 operands: 61
57	Literal
58	Literal
59	Operation	operator: 62 operands: 63
60	Operation	operator: 72 operand: 68
61	ExprTuple	65, 66
62	Literal
63	ExprTuple	74, 67
64	ExprTuple	68
65	Operation	operator: 69 operands: 70
66	Operation	operator: 72 operand: 81
67	Operation	operator: 72 operand: 75
68	Literal
69	Literal
70	ExprTuple	82, 74
71	ExprTuple	81
72	Literal
73	ExprTuple	75
74	Operation	operator: 76 operand: 80
75	Operation	operator: 78 operands: 79
76	Literal
77	ExprTuple	80
78	Literal
79	ExprTuple	81, 82
80	Literal
81	Variable
82	Operation	operator: 83 operands: 84
83	Literal
84	ExprTuple	85, 86
85	Literal
86	Literal