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 Equals, 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(Equals(Exp(e, Neg(frac(Mult(two, pi, i, k, Mod(m, _two_pow_t)), _two_pow_t))), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _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}}} = \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	40, 9
7	Operation	operator: 45 operands: 10
8	Operation	operator: 45 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	15, 14
11	ExprTuple	15, 16
12	Literal
13	ExprTuple	17, 18
14	Operation	operator: 29 operand: 23
15	Literal
16	Operation	operator: 29 operand: 24
17	Literal
18	Operation	operator: 21 operands: 22
19	ExprTuple	23
20	ExprTuple	24
21	Literal
22	ExprTuple	44, 25
23	Operation	operator: 27 operands: 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operand: 33
26	ExprTuple	31, 44
27	Literal
28	ExprTuple	32, 44
29	Literal
30	ExprTuple	33
31	Operation	operator: 35 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	47, 38, 39, 40, 37
35	Literal
36	ExprTuple	47, 38, 39, 40, 43
37	Operation	operator: 41 operands: 42
38	Literal
39	Literal
40	Variable
41	Literal
42	ExprTuple	43, 44
43	Variable
44	Operation	operator: 45 operands: 46
45	Literal
46	ExprTuple	47, 48
47	Literal
48	Literal