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
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Mult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), Exp(e, Mult(two, pi, i, _phase, k))), InSet(k, Interval(zero, subtract(two_pow_t, one))))

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 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: 19 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	26, 8
6	Operation	operator: 29 operands: 9
7	Operation	operator: 29 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: 19 operands: 18
14	Literal
15	Operation	operator: 19 operands: 20
16	Literal
17	Operation	operator: 21 operands: 22
18	ExprTuple	33, 23, 24, 25, 27
19	Literal
20	ExprTuple	33, 23, 24, 25, 26
21	Literal
22	ExprTuple	27, 28
23	Literal
24	Literal
25	Literal
26	Variable
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operand: 35
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35
33	Literal
34	Variable
35	Literal