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, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, 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}^{-\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} \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: 32 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	38, 8
6	Operation	operator: 34 operands: 9
7	Operation	operator: 34 operands: 10
8	Operation	operator: 11 operands: 12
9	ExprTuple	14, 13
10	ExprTuple	14, 15
11	Literal
12	ExprTuple	16, 17
13	Operation	operator: 27 operand: 22
14	Literal
15	Operation	operator: 32 operands: 19
16	Literal
17	Operation	operator: 20 operands: 21
18	ExprTuple	22
19	ExprTuple	40, 36, 37, 23, 38
20	Literal
21	ExprTuple	30, 24
22	Operation	operator: 25 operands: 26
23	Literal
24	Operation	operator: 27 operand: 31
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Literal
32	Literal
33	ExprTuple	40, 36, 37, 38, 39
34	Literal
35	ExprTuple	40, 41
36	Literal
37	Literal
38	Variable
39	Variable
40	Literal
41	Literal