def _gcd_monom(f, g):
ring = f.ring
ground_gcd = ring.domain.gcd
ground_quo = ring.domain.quo
mf, cf = list(f.terms())[0]
_mgcd, _cgcd = mf, cf
for mg, cg in g.terms():
_mgcd = monomial_gcd(_mgcd, mg)
_cgcd = ground_gcd(_cgcd, cg)
h = f.new([(_mgcd, _cgcd)])
cff = f.new([(monomial_ldiv(mf, _mgcd), ground_quo(cf, _cgcd))])
cfg = f.new([(monomial_ldiv(mg, _mgcd), ground_quo(cg, _cgcd)) for mg, cg in g.terms()])
return h, cff, cfg
def diff(f, x):
"""Computes partial derivative in ``x``.
Examples
========
>>> from sympy.polys.rings import ring
>>> from sympy.polys.domains import ZZ
>>> _, x, y = ring("x,y", ZZ)
>>> p = x + x**2*y**3
>>> p.diff(x)
2*x*y**3 + 1
"""
ring = f.ring
i = list(ring.gens).index(x)
m = ring.monomial_basis(i)
g = ring.zero
for expv, coeff in f.terms():
if expv[i]:
e = monomial_ldiv(expv, m)
g[e] = coeff*expv[i]
return g
