def test_dmp_diff_in():
assert dmp_diff_in(f_6, 2, 1, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 1, 3, ZZ), 2, 3, ZZ), 0, 1, 3, ZZ)
assert dmp_diff_in(f_6, 3, 1, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 1, 3, ZZ), 3, 3, ZZ), 0, 1, 3, ZZ)
assert dmp_diff_in(f_6, 2, 2, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 2, 3, ZZ), 2, 3, ZZ), 0, 2, 3, ZZ)
assert dmp_diff_in(f_6, 3, 2, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 2, 3, ZZ), 3, 3, ZZ), 0, 2, 3, ZZ)
def test_dmp_diff_in():
assert dmp_diff_in(f_6, 2, 1, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 1, 3, ZZ), 2, 3, ZZ), 0, 1, 3, ZZ)
assert dmp_diff_in(f_6, 3, 1, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 1, 3, ZZ), 3, 3, ZZ), 0, 1, 3, ZZ)
assert dmp_diff_in(f_6, 2, 2, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 2, 3, ZZ), 2, 3, ZZ), 0, 2, 3, ZZ)
assert dmp_diff_in(f_6, 3, 2, 3, ZZ) == \
dmp_swap(dmp_diff(dmp_swap(f_6, 0, 2, 3, ZZ), 3, 3, ZZ), 0, 2, 3, ZZ)
def dmp_sqf_part(f, u, K):
"""
Returns square-free part of a polynomial in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dmp_sqf_part(x**3 + 2*x**2*y + x*y**2)
x**2 + x*y
"""
if not u:
return dup_sqf_part(f, K)
if K.is_FiniteField:
return dmp_gf_sqf_part(f, u, K)
if dmp_zero_p(f, u):
return f
if K.is_negative(dmp_ground_LC(f, u, K)):
f = dmp_neg(f, u, K)
gcd = f
for i in range(u+1):
gcd = dmp_gcd(gcd, dmp_diff_in(f, 1, i, u, K), u, K)
sqf = dmp_quo(f, gcd, u, K)
if K.is_Field:
return dmp_ground_monic(sqf, u, K)
else:
return dmp_ground_primitive(sqf, u, K)[1]
def diff(f, m=1, j=0):
"""Computes `m`-th order derivative of `f` in `x_j`. """
if not isinstance(m, int):
raise TypeError("`int` expected, got %s" % type(m))
if not isinstance(j, int):
raise TypeError("`int` expected, got %s" % type(j))
return f.per(dmp_diff_in(f.rep, m, j, f.lev, f.dom))
def diff(f, m=1, j=0):
"""Computes `m`-th order derivative of `f` in `x_j`. """
if not isinstance(m, int):
raise TypeError("`int` expected, got %s" % type(m))
if not isinstance(j, int):
raise TypeError("`int` expected, got %s" % type(j))
return f.per(dmp_diff_in(f.rep, m, j, f.lev, f.dom))