Expression of type Conditional

from the theory of proveit.physics.quantum.QFT

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, l, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, Interval, Mult, Neg, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform

# build up the expression from sub-expressions
sub_expr1 = Exp(two, n)
sub_expr2 = Interval(zero, subtract(sub_expr1, one))
expr = Conditional(Equals(Qmult(NumBra(l, n), InverseFourierTransform(n), NumKet(k, n)), Mult(frac(one, Exp(two, frac(n, two))), Exp(e, frac(Neg(Mult(two, pi, i, k, l)), sub_expr1)))), And(InSet(k, sub_expr2), InSet(l, sub_expr2)))

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\{\left({_{n}}\langle l \rvert \thinspace {\mathrm {FT}}^{\dag}_{n} \thinspace \lvert k \rangle_{n}\right) = \left(\frac{1}{2^{\frac{n}{2}}} \cdot \mathsf{e}^{\frac{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot l\right)}{2^{n}}}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{n} - 1\} ,  l \in \{0~\ldotp \ldotp~2^{n} - 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	9, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 56 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	17, 18, 19
13	ExprTuple	20, 21
14	ExprTuple	61, 22
15	Literal
16	ExprTuple	62, 22
17	Operation	operator: 23 operands: 24
18	Operation	operator: 25 operand: 54
19	Operation	operator: 27 operands: 28
20	Operation	operator: 46 operands: 29
21	Operation	operator: 49 operands: 30
22	Operation	operator: 31 operands: 32
23	Literal
24	ExprTuple	62, 54
25	Literal
26	ExprTuple	54
27	Literal
28	ExprTuple	61, 54
29	ExprTuple	55, 33
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	36, 37
33	Operation	operator: 49 operands: 38
34	Literal
35	Operation	operator: 46 operands: 39
36	Literal
37	Operation	operator: 40 operands: 41
38	ExprTuple	58, 42
39	ExprTuple	43, 44
40	Literal
41	ExprTuple	44, 45
42	Operation	operator: 46 operands: 47
43	Operation	operator: 51 operand: 53
44	Operation	operator: 49 operands: 50
45	Operation	operator: 51 operand: 55
46	Literal
47	ExprTuple	54, 58
48	ExprTuple	53
49	Literal
50	ExprTuple	58, 54
51	Literal
52	ExprTuple	55
53	Operation	operator: 56 operands: 57
54	Variable
55	Literal
56	Literal
57	ExprTuple	58, 59, 60, 61, 62
58	Literal
59	Literal
60	Literal
61	Variable
62	Variable