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, e, frac, i, pi, subtract, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Exp(Exp(e, Mult(two, pi, i, subtract(_phase, frac(m, _two_pow_t)))), k), 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 \left(\varphi - \frac{m}{2^{t}}\right)})^{k} \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: 36 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 36 operands: 9
7	Variable
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	Operation	operator: 16 operands: 17
14	Literal
15	Operation	operator: 23 operands: 18
16	Literal
17	ExprTuple	38, 19, 20, 21
18	ExprTuple	35, 22
19	Literal
20	Literal
21	Operation	operator: 23 operands: 24
22	Operation	operator: 29 operand: 28
23	Literal
24	ExprTuple	26, 27
25	ExprTuple	28
26	Literal
27	Operation	operator: 29 operand: 31
28	Literal
29	Literal
30	ExprTuple	31
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Variable
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Literal
39	Literal