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, Mod, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _two_pow_t

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