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 ExprTuple, k, l, n
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform

# build up the expression from sub-expressions
expr = ExprTuple(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)), Exp(two, n)))))

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({_{n}}\langle l \rvert \thinspace {\mathrm {FT}}^{\dag}_{n} \thinspace \lvert k \rangle_{n}, \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)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 36 operands: 5
3	Literal
4	ExprTuple	6, 7, 8
5	ExprTuple	9, 10
6	Operation	operator: 11 operands: 12
7	Operation	operator: 13 operand: 35
8	Operation	operator: 15 operands: 16
9	Operation	operator: 28 operands: 17
10	Operation	operator: 32 operands: 18
11	Literal
12	ExprTuple	42, 35
13	Literal
14	ExprTuple	35
15	Literal
16	ExprTuple	41, 35
17	ExprTuple	19, 20
18	ExprTuple	21, 22
19	Literal
20	Operation	operator: 32 operands: 23
21	Literal
22	Operation	operator: 28 operands: 24
23	ExprTuple	38, 25
24	ExprTuple	26, 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operand: 34
27	Operation	operator: 32 operands: 33
28	Literal
29	ExprTuple	35, 38
30	Literal
31	ExprTuple	34
32	Literal
33	ExprTuple	38, 35
34	Operation	operator: 36 operands: 37
35	Variable
36	Literal
37	ExprTuple	38, 39, 40, 41, 42
38	Literal
39	Literal
40	Literal
41	Variable
42	Variable