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, Variable, k, l
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Mult, e, frac, i, pi, subtract, two
from proveit.physics.quantum.QPE import _b_floor, _m_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Exp(Exp(e, Mult(two, pi, i, subtract(Variable("_a", latex_format = r"{_{-}a}"), frac(Add(_b_floor, l), _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({_{-}a} - \frac{b_{\textit{f}} + l}{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: 37 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 37 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: 35 operands: 18
16	Literal
17	ExprTuple	41, 19, 20, 21
18	ExprTuple	34, 22
19	Literal
20	Literal
21	Operation	operator: 35 operands: 23
22	Operation	operator: 28 operand: 27
23	ExprTuple	25, 26
24	ExprTuple	27
25	Variable
26	Operation	operator: 28 operand: 30
27	Literal
28	Literal
29	ExprTuple	30
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	Operation	operator: 35 operands: 36
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42
39	Literal
40	Variable
41	Literal
42	Literal