def ll_common_denominator(f):
"""For a polynomial f with fractional coefficients, write out the
polynomial such that there is only a single denominator."""
# f should be a polynomial
if not is_Polynomial(f):
return ll_raw(f)
# first determine the lcm of the denominators of the coefficients
cd = reduce(lcm, [c.denominator() for c in f])
if is_Polynomial(cd) and cd.degree() > 0:
return "\\frac{" + ll_raw(cd * f) + "}{" + ll_raw(factor(cd)) + "}"
else:
return ll_raw(f)
def gauss_valuation(poly, prime, prec=30):
"""Compute the Gauss norm of the given polynomial, with prime
identifying the valuation."""
if is_Polynomial(poly):
return min([valuation(c, prime) for c in poly])
if is_LaurentSeries(poly):
return series_valuation(poly, prime, prec)
else:
# in case we just get a constant
return valuation(poly, prime)
def poly_reduced_degree(poly, prime):
if is_Polynomial(poly):
i = poly.degree()
v = 1
while v > 0 and i >= 0:
v = valuation(poly[i], prime)
i -= 1
return i+1
elif valuation(poly, prime) > 0:
return -infinity
else:
return 0
def m(poly_or_vector, *args):
if is_Polynomial(poly_or_vector):
return f(poly_or_vector.coefficients(), *args)
else:
return f(poly_or_vector, *args)
