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 k, m
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _t, _two_pow_t
# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = Exp(e, Mult(two, pi, i, _phase, k))
sub_expr3 = frac(one, Exp(two, frac(_t, two)))
sub_expr4 = Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))
expr = Equals(Mult(sub_expr3, Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr2, Mult(sub_expr3, sub_expr4)), domain = _m_domain)), Mult(Exp(sub_expr3, two), Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr2, sub_expr4), domain = _m_domain)))
# 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()