def symbolic_to_polynomial(f, vars):
# Rewrite a symbolic expression as a polynomial over SR in a given
# list of variables.
poly = f.polynomial(QQ)
allvars = poly.variables()
indices = []
for x in allvars:
try:
indices.append(vars.index(x))
except ValueError:
indices.append(None)
R = PolynomialRing(SR, len(vars), vars)
res = R.zero()
for coeff, alpha in zip(poly.coefficients(), poly.exponents()):
if type(alpha) == int:
# Once again, univariate polynomials receive special treatment
# in Sage.
alpha = [alpha]
term = R(coeff)
for i, e in enumerate(alpha):
if not e:
continue
if indices[i] is None:
term *= SR(allvars[i]**e)
else:
term *= R.gen(indices[i])**e
res += term
return res
