def test_dup_decompose():
assert dup_decompose([1], ZZ) == [[1]]
assert dup_decompose([1, 0], ZZ) == [[1, 0]]
assert dup_decompose([1, 0, 0, 0], ZZ) == [[1, 0, 0, 0]]
assert dup_decompose([1, 0, 0, 0, 0], ZZ) == [[1, 0, 0], [1, 0, 0]]
assert dup_decompose(
[1, 0, 0, 0, 0, 0, 0], ZZ) == [[1, 0, 0, 0], [1, 0, 0]]
assert dup_decompose([7, 0, 0, 0, 1], ZZ) == [[7, 0, 1], [1, 0, 0]]
assert dup_decompose([4, 0, 3, 0, 2], ZZ) == [[4, 3, 2], [1, 0, 0]]
f = [1, 0, 20, 0, 150, 0, 500, 0, 625, -2, 0, -10, 9]
assert dup_decompose(f, ZZ) == [[1, 0, 0, -2, 9], [1, 0, 5, 0]]
f = [2, 0, 40, 0, 300, 0, 1000, 0, 1250, -4, 0, -20, 18]
assert dup_decompose(f, ZZ) == [[2, 0, 0, -4, 18], [1, 0, 5, 0]]
f = [1, 0, 20, -8, 150, -120, 524, -600, 865, -1034, 600, -170, 29]
assert dup_decompose(f, ZZ) == [[1, -8, 24, -34, 29], [1, 0, 5, 0]]
f = [DMP([6, 0, -42], ZZ), DMP([48, 0, 96], ZZ), DMP([144, 648, 288], ZZ),
DMP([624, 864, 384], ZZ), DMP([108, 312, 432, 192], ZZ)]
assert dup_decompose(f, ZZ['a']) == [f]
def decompose(f):
"""Computes functional decomposition of `f`. """
if not f.lev:
return map(f.per, dup_decompose(f.rep, f.dom))
else:
raise ValueError('univariate polynomial expected')
def test_dup_decompose():
assert dup_decompose([1], ZZ) == [[1]]
assert dup_decompose([1, 0], ZZ) == [[1, 0]]
assert dup_decompose([1, 0, 0, 0], ZZ) == [[1, 0, 0, 0]]
assert dup_decompose([1, 0, 0, 0, 0], ZZ) == [[1, 0, 0], [1, 0, 0]]
assert dup_decompose([1, 0, 0, 0, 0, 0, 0], ZZ) == [[1, 0, 0, 0],
[1, 0, 0]]
assert dup_decompose([7, 0, 0, 0, 1], ZZ) == [[7, 0, 1], [1, 0, 0]]
assert dup_decompose([4, 0, 3, 0, 2], ZZ) == [[4, 3, 2], [1, 0, 0]]
f = [1, 0, 20, 0, 150, 0, 500, 0, 625, -2, 0, -10, 9]
assert dup_decompose(f, ZZ) == [[1, 0, 0, -2, 9], [1, 0, 5, 0]]
f = [2, 0, 40, 0, 300, 0, 1000, 0, 1250, -4, 0, -20, 18]
assert dup_decompose(f, ZZ) == [[2, 0, 0, -4, 18], [1, 0, 5, 0]]
f = [1, 0, 20, -8, 150, -120, 524, -600, 865, -1034, 600, -170, 29]
assert dup_decompose(f, ZZ) == [[1, -8, 24, -34, 29], [1, 0, 5, 0]]
R, t = ring("t", ZZ)
f = [
6 * t**2 - 42, 48 * t**2 + 96, 144 * t**2 + 648 * t + 288,
624 * t**2 + 864 * t + 384, 108 * t**3 + 312 * t**2 + 432 * t + 192
]
assert dup_decompose(f, R.to_domain()) == [f]
def test_dup_decompose():
assert dup_decompose([1], ZZ) == [[1]]
assert dup_decompose([1, 0], ZZ) == [[1, 0]]
assert dup_decompose([1, 0, 0, 0], ZZ) == [[1, 0, 0, 0]]
assert dup_decompose([1, 0, 0, 0, 0], ZZ) == [[1, 0, 0], [1, 0, 0]]
assert dup_decompose(
[1, 0, 0, 0, 0, 0, 0], ZZ) == [[1, 0, 0, 0], [1, 0, 0]]
assert dup_decompose([7, 0, 0, 0, 1], ZZ) == [[7, 0, 1], [1, 0, 0]]
assert dup_decompose([4, 0, 3, 0, 2], ZZ) == [[4, 3, 2], [1, 0, 0]]
f = [1, 0, 20, 0, 150, 0, 500, 0, 625, -2, 0, -10, 9]
assert dup_decompose(f, ZZ) == [[1, 0, 0, -2, 9], [1, 0, 5, 0]]
f = [2, 0, 40, 0, 300, 0, 1000, 0, 1250, -4, 0, -20, 18]
assert dup_decompose(f, ZZ) == [[2, 0, 0, -4, 18], [1, 0, 5, 0]]
f = [1, 0, 20, -8, 150, -120, 524, -600, 865, -1034, 600, -170, 29]
assert dup_decompose(f, ZZ) == [[1, -8, 24, -34, 29], [1, 0, 5, 0]]
R, t = ring("t", ZZ)
f = [6*t**2 - 42,
48*t**2 + 96,
144*t**2 + 648*t + 288,
624*t**2 + 864*t + 384,
108*t**3 + 312*t**2 + 432*t + 192]
assert dup_decompose(f, R.to_domain()) == [f]
def decompose(f):
"""Computes functional decomposition of `f`. """
if not f.lev:
return map(f.per, dup_decompose(f.rep, f.dom))
else:
raise ValueError('univariate polynomial expected')
def test_dup_decompose():
assert dup_decompose([1], ZZ) == [[1]]
assert dup_decompose([1, 0], ZZ) == [[1, 0]]
assert dup_decompose([1, 0, 0, 0], ZZ) == [[1, 0, 0, 0]]
assert dup_decompose([1, 0, 0, 0, 0], ZZ) == [[1, 0, 0], [1, 0, 0]]
assert dup_decompose([1, 0, 0, 0, 0, 0, 0], ZZ) == [[1, 0, 0, 0],
[1, 0, 0]]
assert dup_decompose([7, 0, 0, 0, 1], ZZ) == [[7, 0, 1], [1, 0, 0]]
assert dup_decompose([4, 0, 3, 0, 2], ZZ) == [[4, 3, 2], [1, 0, 0]]
f = [1, 0, 20, 0, 150, 0, 500, 0, 625, -2, 0, -10, 9]
assert dup_decompose(f, ZZ) == [[1, 0, 0, -2, 9], [1, 0, 5, 0]]
f = [2, 0, 40, 0, 300, 0, 1000, 0, 1250, -4, 0, -20, 18]
assert dup_decompose(f, ZZ) == [[2, 0, 0, -4, 18], [1, 0, 5, 0]]
f = [1, 0, 20, -8, 150, -120, 524, -600, 865, -1034, 600, -170, 29]
assert dup_decompose(f, ZZ) == [[1, -8, 24, -34, 29], [1, 0, 5, 0]]
f = [
DMP([6, 0, -42], ZZ),
DMP([48, 0, 96], ZZ),
DMP([144, 648, 288], ZZ),
DMP([624, 864, 384], ZZ),
DMP([108, 312, 432, 192], ZZ)
]
assert dup_decompose(f, ZZ['a']) == [f]
