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, Function, Variable, k
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase

# build up the expression from sub-expressions
expr = Conditional(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Function(Variable("_a", latex_format = r"{_{-}a}"), [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 \varphi \cdot k} \cdot {_{-}a}\left(k\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: 18 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	25, 8
6	Operation	operator: 28 operands: 9
7	Operation	operator: 10 operand: 25
8	Operation	operator: 12 operands: 13
9	ExprTuple	14, 15
10	Variable
11	ExprTuple	25
12	Literal
13	ExprTuple	16, 17
14	Literal
15	Operation	operator: 18 operands: 19
16	Literal
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	32, 22, 23, 24, 25
20	Literal
21	ExprTuple	26, 27
22	Literal
23	Literal
24	Literal
25	Variable
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operand: 34
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34
32	Literal
33	Literal
34	Literal