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, Mult, Neg, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _alpha_m, _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Equals(_alpha_m, Mult(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, k))), domain = _m_domain))), InSet(m, _m_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(m \mapsto \left\{\alpha_{m} = \left(\frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right)\right)\right) \textrm{ if } m \in \{0~\ldotp \ldotp~2^{t} - 1\}\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: 24 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	59, 28
8	Operation	operator: 10 operand: 59
9	Operation	operator: 52 operands: 12
10	Literal
11	ExprTuple	59
12	ExprTuple	13, 14
13	Operation	operator: 45 operands: 15
14	Operation	operator: 16 operand: 18
15	ExprTuple	51, 50
16	Literal
17	ExprTuple	18
18	Lambda	parameter: 58 body: 20
19	ExprTuple	58
20	Conditional	value: 21 condition: 22
21	Operation	operator: 52 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	58, 28
26	Operation	operator: 54 operands: 29
27	Operation	operator: 54 operands: 30
28	Operation	operator: 31 operands: 32
29	ExprTuple	34, 33
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	36, 37
33	Operation	operator: 47 operand: 42
34	Literal
35	Operation	operator: 52 operands: 39
36	Literal
37	Operation	operator: 40 operands: 41
38	ExprTuple	42
39	ExprTuple	60, 56, 57, 43, 58
40	Literal
41	ExprTuple	50, 44
42	Operation	operator: 45 operands: 46
43	Literal
44	Operation	operator: 47 operand: 51
45	Literal
46	ExprTuple	49, 50
47	Literal
48	ExprTuple	51
49	Operation	operator: 52 operands: 53
50	Operation	operator: 54 operands: 55
51	Literal
52	Literal
53	ExprTuple	60, 56, 57, 58, 59
54	Literal
55	ExprTuple	60, 61
56	Literal
57	Literal
58	Variable
59	Variable
60	Literal
61	Literal