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, k, m
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Integer, Mult, Sum, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _alpha_m_mod_two_pow_t, _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Equals(_alpha_m_mod_two_pow_t, Mult(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Exp(Exp(e, Mult(two, pi, i, subtract(_phase, frac(m, _two_pow_t)))), k), domain = _m_domain))), InSet(m, Integer))))

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(m \mapsto \left\{\alpha_{m ~\textup{mod}~ 2^{t}} = \left(\frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\varphi - \frac{m}{2^{t}}\right)})^{k}\right)\right) \textrm{ if } m \in \mathbb{Z}\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: 58 body: 3
2	ExprTuple	58
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 28 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	58, 11
9	Operation	operator: 12 operand: 15
10	Operation	operator: 40 operands: 14
11	Literal
12	Literal
13	ExprTuple	15
14	ExprTuple	16, 17
15	Operation	operator: 18 operands: 57
16	Operation	operator: 56 operands: 19
17	Operation	operator: 20 operand: 22
18	Literal
19	ExprTuple	52, 59
20	Literal
21	ExprTuple	22
22	Lambda	parameter: 31 body: 24
23	ExprTuple	31
24	Conditional	value: 25 condition: 26
25	Operation	operator: 60 operands: 27
26	Operation	operator: 28 operands: 29
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 60 operands: 33
31	Variable
32	Operation	operator: 34 operands: 35
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38, 39
36	Literal
37	Operation	operator: 40 operands: 41
38	Literal
39	Operation	operator: 47 operands: 42
40	Literal
41	ExprTuple	62, 43, 44, 45
42	ExprTuple	59, 46
43	Literal
44	Literal
45	Operation	operator: 47 operands: 48
46	Operation	operator: 53 operand: 52
47	Literal
48	ExprTuple	50, 51
49	ExprTuple	52
50	Literal
51	Operation	operator: 53 operand: 55
52	Literal
53	Literal
54	ExprTuple	55
55	Operation	operator: 56 operands: 57
56	Literal
57	ExprTuple	58, 59
58	Variable
59	Operation	operator: 60 operands: 61
60	Literal
61	ExprTuple	62, 63
62	Literal
63	Literal