def dmp_inner_gcd(f, g, u, K):
"""
Computes polynomial GCD and cofactors of ``f`` and ``g`` in ``K[X]``.
Returns ``(h, cff, cfg)`` such that ``a = gcd(f, g)``,
``cff = quo(f, h)``, and ``cfg = quo(g, h)``.
**Examples**
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_inner_gcd
>>> f = ZZ.map([[1], [2, 0], [1, 0, 0]])
>>> g = ZZ.map([[1], [1, 0], []])
>>> dmp_inner_gcd(f, g, 1, ZZ)
([[1], [1, 0]], [[1], [1, 0]], [[1], []])
"""
if not u:
return dup_inner_gcd(f, g, K)
J, (f, g) = dmp_multi_deflate((f, g), u, K)
h, cff, cfg = _dmp_inner_gcd(f, g, u, K)
return (dmp_inflate(h, J, u, K),
dmp_inflate(cff, J, u, K),
dmp_inflate(cfg, J, u, K))
def dmp_inner_gcd(f, g, u, K):
"""
Computes polynomial GCD and cofactors of `f` and `g` in `K[X]`.
Returns ``(h, cff, cfg)`` such that ``a = gcd(f, g)``,
``cff = quo(f, h)``, and ``cfg = quo(g, h)``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y, = ring("x,y", ZZ)
>>> f = x**2 + 2*x*y + y**2
>>> g = x**2 + x*y
>>> R.dmp_inner_gcd(f, g)
(x + y, x + y, x)
"""
if not u:
return dup_inner_gcd(f, g, K)
J, (f, g) = dmp_multi_deflate((f, g), u, K)
h, cff, cfg = _dmp_inner_gcd(f, g, u, K)
return (dmp_inflate(h, J, u, K),
dmp_inflate(cff, J, u, K),
dmp_inflate(cfg, J, u, K))
def dmp_inner_gcd(f, g, u, K):
"""
Computes polynomial GCD and cofactors of `f` and `g` in `K[X]`.
Returns ``(h, cff, cfg)`` such that ``a = gcd(f, g)``,
``cff = quo(f, h)``, and ``cfg = quo(g, h)``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y, = ring("x,y", ZZ)
>>> f = x**2 + 2*x*y + y**2
>>> g = x**2 + x*y
>>> R.dmp_inner_gcd(f, g)
(x + y, x + y, x)
"""
if not u:
return dup_inner_gcd(f, g, K)
J, (f, g) = dmp_multi_deflate((f, g), u, K)
h, cff, cfg = _dmp_inner_gcd(f, g, u, K)
return (dmp_inflate(h, J, u, K),
dmp_inflate(cff, J, u, K),
dmp_inflate(cfg, J, u, K))
def dmp_inner_gcd(f, g, u, K):
"""
Computes polynomial GCD and cofactors of `f` and `g` in `K[X]`.
Returns ``(h, cff, cfg)`` such that ``a = gcd(f, g)``,
``cff = quo(f, h)``, and ``cfg = quo(g, h)``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_inner_gcd
>>> f = ZZ.map([[1], [2, 0], [1, 0, 0]])
>>> g = ZZ.map([[1], [1, 0], []])
>>> dmp_inner_gcd(f, g, 1, ZZ)
([[1], [1, 0]], [[1], [1, 0]], [[1], []])
"""
if not u:
return dup_inner_gcd(f, g, K)
J, (f, g) = dmp_multi_deflate((f, g), u, K)
h, cff, cfg = _dmp_inner_gcd(f, g, u, K)
return (dmp_inflate(h, J, u, K), dmp_inflate(cff, J, u,
K), dmp_inflate(cfg, J, u, K))
def test_dmp_multi_deflate():
assert dmp_multi_deflate(([[]],), 1, ZZ) == \
((1, 1), ([[]],))
assert dmp_multi_deflate(([[]], [[]]), 1, ZZ) == \
((1, 1), ([[]], [[]]))
assert dmp_multi_deflate(([[1]], [[]]), 1, ZZ) == \
((1, 1), ([[1]], [[]]))
assert dmp_multi_deflate(([[1]], [[2]]), 1, ZZ) == \
((1, 1), ([[1]], [[2]]))
assert dmp_multi_deflate(([[1]], [[2,0]]), 1, ZZ) == \
((1, 1), ([[1]], [[2, 0]]))
assert dmp_multi_deflate(([[2,0]], [[2,0]]), 1, ZZ) == \
((1, 1), ([[2, 0]], [[2, 0]]))
assert dmp_multi_deflate(([[2]], [[2,0,0]]), 1, ZZ) == ((1, 2), ([[2]], [[2, 0]]))
assert dmp_multi_deflate(([[2,0,0]], [[2,0,0]]), 1, ZZ) == ((1, 2), ([[2, 0]], [[2, 0]]))
assert dmp_multi_deflate(([2,0,0], [1,0,4,0,1]), 0, ZZ) == \
((2,), ([2, 0], [1, 4, 1]))
f = [[1, 0, 0], [], [1, 0], [], [1]]
g = [[1, 0, 1, 0], [], [1]]
assert dmp_multi_deflate((f,), 1, ZZ) == \
((2, 1), ([[1, 0, 0], [1, 0], [1]],))
assert dmp_multi_deflate((f, g), 1, ZZ) == \
((2, 1), ([[1, 0, 0], [1, 0], [1]],
[[1, 0, 1, 0], [1]]))