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, k, m
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _t, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Mult(frac(one, Exp(two, frac(_t, two))), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))))), InSet(k, _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\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\frac{1}{2^{\frac{t}{2}}} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\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: 40 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	46, 8
6	Operation	operator: 42 operands: 9
7	Operation	operator: 40 operands: 10
8	Operation	operator: 11 operands: 12
9	ExprTuple	25, 13
10	ExprTuple	14, 15
11	Literal
12	ExprTuple	16, 17
13	Operation	operator: 40 operands: 18
14	Operation	operator: 36 operands: 19
15	Operation	operator: 42 operands: 20
16	Literal
17	Operation	operator: 21 operands: 22
18	ExprTuple	48, 44, 45, 23, 46
19	ExprTuple	34, 24
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	39, 27
23	Literal
24	Operation	operator: 42 operands: 28
25	Literal
26	Operation	operator: 30 operand: 33
27	Operation	operator: 30 operand: 34
28	ExprTuple	48, 32
29	ExprTuple	33
30	Literal
31	ExprTuple	34
32	Operation	operator: 36 operands: 35
33	Operation	operator: 36 operands: 37
34	Literal
35	ExprTuple	49, 48
36	Literal
37	ExprTuple	38, 39
38	Operation	operator: 40 operands: 41
39	Operation	operator: 42 operands: 43
40	Literal
41	ExprTuple	48, 44, 45, 46, 47
42	Literal
43	ExprTuple	48, 49
44	Literal
45	Literal
46	Variable
47	Variable
48	Literal
49	Literal