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, Neg, Sum, e, frac, i, one, pi, 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 = 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, 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} \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 \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: 64 body: 3
2	ExprTuple	64
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 29 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	64, 11
9	Operation	operator: 12 operand: 15
10	Operation	operator: 57 operands: 14
11	Literal
12	Literal
13	ExprTuple	15
14	ExprTuple	16, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 50 operands: 20
17	Operation	operator: 21 operand: 23
18	Literal
19	ExprTuple	64, 55
20	ExprTuple	56, 55
21	Literal
22	ExprTuple	23
23	Lambda	parameter: 63 body: 25
24	ExprTuple	63
25	Conditional	value: 26 condition: 27
26	Operation	operator: 57 operands: 28
27	Operation	operator: 29 operands: 30
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	63, 33
31	Operation	operator: 59 operands: 34
32	Operation	operator: 59 operands: 35
33	Operation	operator: 36 operands: 37
34	ExprTuple	39, 38
35	ExprTuple	39, 40
36	Literal
37	ExprTuple	41, 42
38	Operation	operator: 52 operand: 47
39	Literal
40	Operation	operator: 57 operands: 44
41	Literal
42	Operation	operator: 45 operands: 46
43	ExprTuple	47
44	ExprTuple	65, 61, 62, 48, 63
45	Literal
46	ExprTuple	55, 49
47	Operation	operator: 50 operands: 51
48	Literal
49	Operation	operator: 52 operand: 56
50	Literal
51	ExprTuple	54, 55
52	Literal
53	ExprTuple	56
54	Operation	operator: 57 operands: 58
55	Operation	operator: 59 operands: 60
56	Literal
57	Literal
58	ExprTuple	65, 61, 62, 63, 64
59	Literal
60	ExprTuple	65, 66
61	Literal
62	Literal
63	Variable
64	Variable
65	Literal
66	Literal