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, j, k, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, Interval, Mult, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import FourierTransform
# 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(k, n), FourierTransform(n), NumKet(j, n)), Qmult(frac(one, Exp(two, frac(n, two))), Exp(e, frac(Mult(two, pi, i, j, k), sub_expr1)))), And(InSet(j, sub_expr2), InSet(k, sub_expr2)))
# 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")
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
stored_expr.style_options()
# display the expression information
stored_expr.expr_info()