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 series_valuation(series, prime, prec=30):
"""Compute the Gauss norm of the given Laurent series, with prime
identifying the valuation. For practical reasons, we use a simple
heuristic to determine if this valuation is bounded: We look at
prec terms, and unless the minimal valuation occurs in the first
two thirds of these, we say that we have unbounded valuation."""
assert is_LaurentSeries(series)
deg = series.valuation()
trunc = series.truncate(prec - deg)
coeffs = [valuation(c, prime) for c in list(trunc)]
allmin = apply(min, coeffs)
end = (2 * len(coeffs)) // 3
startmin = apply(min, coeffs[:end])
if startmin > allmin:
return -infinity
else:
return allmin
