def dup_compose(f, g, K):
"""
Evaluate functional composition ``f(g)`` in ``K[x]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x = ring("x", ZZ)
>>> R.dup_compose(x**2 + x, x - 1)
x**2 - x
"""
if len(g) <= 1:
return dup_strip([dup_eval(f, dup_LC(g, K), K)])
if not f:
return []
h = [f[0]]
for c in f[1:]:
h = dup_mul(h, g, K)
h = dup_add_term(h, c, 0, K)
return h
def dup_compose(f, g, K):
"""
Evaluate functional composition ``f(g)`` in ``K[x]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x = ring("x", ZZ)
>>> R.dup_compose(x**2 + x, x - 1)
x**2 - x
"""
if len(g) <= 1:
return dup_strip([dup_eval(f, dup_LC(g, K), K)])
if not f:
return []
h = [f[0]]
for c in f[1:]:
h = dup_mul(h, g, K)
h = dup_add_term(h, c, 0, K)
return h
def dup_compose(f, g, K):
"""
Evaluate functional composition ``f(g)`` in ``K[x]``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densetools import dup_compose
>>> f = ZZ.map([1, 1, 0])
>>> g = ZZ.map([1, -1])
>>> dup_compose(f, g, ZZ)
[1, -1, 0]
"""
if len(g) <= 1:
return dup_strip([dup_eval(f, dup_LC(g, K), K)])
if not f:
return []
h = [f[0]]
for c in f[1:]:
h = dup_mul(h, g, K)
h = dup_add_term(h, c, 0, K)
return h
def dup_compose(f, g, K):
"""
Evaluate functional composition ``f(g)`` in ``K[x]``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.densetools import dup_compose
>>> f = ZZ.map([1, 1, 0])
>>> g = ZZ.map([1, -1])
>>> dup_compose(f, g, ZZ)
[1, -1, 0]
"""
if len(g) <= 1:
return dup_strip([dup_eval(f, dup_LC(g, K), K)])
if not f:
return []
h = [f[0]]
for c in f[1:]:
h = dup_mul(h, g, K)
h = dup_add_term(h, c, 0, K)
return h
def test_dmp_add_term():
assert dmp_add_term([ZZ(1),ZZ(1),ZZ(1)], ZZ(1), 2, 0, ZZ) == \
dup_add_term([ZZ(1),ZZ(1),ZZ(1)], ZZ(1), 2, ZZ)
assert dmp_add_term(f_0, [[]], 3, 2, ZZ) == f_0
assert dmp_add_term(F_0, [[]], 3, 2, QQ) == F_0
def test_dup_add_term():
f = dup_normal([], ZZ)
assert dup_add_term(f, ZZ(0), 0, ZZ) == dup_normal([], ZZ)
assert dup_add_term(f, ZZ(1), 0, ZZ) == dup_normal([1], ZZ)
assert dup_add_term(f, ZZ(1), 1, ZZ) == dup_normal([1, 0], ZZ)
assert dup_add_term(f, ZZ(1), 2, ZZ) == dup_normal([1, 0, 0], ZZ)
f = dup_normal([1,1,1], ZZ)
assert dup_add_term(f, ZZ(1), 0, ZZ) == dup_normal([1, 1, 2], ZZ)
assert dup_add_term(f, ZZ(1), 1, ZZ) == dup_normal([1, 2, 1], ZZ)
assert dup_add_term(f, ZZ(1), 2, ZZ) == dup_normal([2, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 3, ZZ) == dup_normal([1, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 4, ZZ) == dup_normal([1, 0, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 5, ZZ) == dup_normal([1, 0, 0, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 6, ZZ) == dup_normal([1, 0, 0, 0, 1, 1, 1], ZZ)
assert dup_add_term(f,ZZ(-1), 2, ZZ) == dup_normal([1, 1], ZZ)