Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([k, l], 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(k, l\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	64, 65
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 59 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	20, 21, 22
16	ExprTuple	23, 24
17	ExprTuple	64, 25
18	Literal
19	ExprTuple	65, 25
20	Operation	operator: 26 operands: 27
21	Operation	operator: 28 operand: 57
22	Operation	operator: 30 operands: 31
23	Operation	operator: 49 operands: 32
24	Operation	operator: 52 operands: 33
25	Operation	operator: 34 operands: 35
26	Literal
27	ExprTuple	65, 57
28	Literal
29	ExprTuple	57
30	Literal
31	ExprTuple	64, 57
32	ExprTuple	58, 36
33	ExprTuple	37, 38
34	Literal
35	ExprTuple	39, 40
36	Operation	operator: 52 operands: 41
37	Literal
38	Operation	operator: 49 operands: 42
39	Literal
40	Operation	operator: 43 operands: 44
41	ExprTuple	61, 45
42	ExprTuple	46, 47
43	Literal
44	ExprTuple	47, 48
45	Operation	operator: 49 operands: 50
46	Operation	operator: 54 operand: 56
47	Operation	operator: 52 operands: 53
48	Operation	operator: 54 operand: 58
49	Literal
50	ExprTuple	57, 61
51	ExprTuple	56
52	Literal
53	ExprTuple	61, 57
54	Literal
55	ExprTuple	58
56	Operation	operator: 59 operands: 60
57	Variable
58	Literal
59	Literal
60	ExprTuple	61, 62, 63, 64, 65
61	Literal
62	Literal
63	Literal
64	Variable
65	Variable