def pow(f, n):
"""Raise `f` to a non-negative power `n`. """
if isinstance(n, int):
if n < 0:
F, n = dup_invert(f.rep, f.mod, f.dom), -n
else:
F = f.rep
return f.per(dup_rem(dup_pow(F, n, f.dom), f.mod, f.dom))
else:
raise TypeError("`int` expected, got %s" % type(n))
def pow(f, n):
"""Raise `f` to a non-negative power `n`. """
if isinstance(n, int):
if n < 0:
F, n = dup_invert(f.rep, f.mod, f.dom), -n
else:
F = f.rep
return f.per(dup_rem(dup_pow(F, n, f.dom), f.mod, f.dom))
else:
raise TypeError("`int` expected, got %s" % type(n))
def test_dmp_pow():
assert dmp_pow([[]], 0, 1, ZZ) == [[ZZ(1)]]
assert dmp_pow([[]], 0, 1, QQ) == [[QQ(1)]]
assert dmp_pow([[]], 1, 1, ZZ) == [[]]
assert dmp_pow([[]], 7, 1, ZZ) == [[]]
assert dmp_pow([[ZZ(1)]], 0, 1, ZZ) == [[ZZ(1)]]
assert dmp_pow([[ZZ(1)]], 1, 1, ZZ) == [[ZZ(1)]]
assert dmp_pow([[ZZ(1)]], 7, 1, ZZ) == [[ZZ(1)]]
assert dmp_pow([[QQ(3,7)]], 0, 1, QQ) == [[QQ(1,1)]]
assert dmp_pow([[QQ(3,7)]], 1, 1, QQ) == [[QQ(3,7)]]
assert dmp_pow([[QQ(3,7)]], 7, 1, QQ) == [[QQ(2187,823543)]]
f = dup_normal([2,0,0,1,7], ZZ)
assert dmp_pow(f, 2, 0, ZZ) == dup_pow(f, 2, ZZ)
def test_dup_pow():
assert dup_pow([], 0, ZZ) == [ZZ(1)]
assert dup_pow([], 0, QQ) == [QQ(1)]
assert dup_pow([], 1, ZZ) == []
assert dup_pow([], 7, ZZ) == []
assert dup_pow([ZZ(1)], 0, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(1)], 1, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(1)], 7, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(3)], 0, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(3)], 1, ZZ) == [ZZ(3)]
assert dup_pow([ZZ(3)], 7, ZZ) == [ZZ(2187)]
assert dup_pow([QQ(1,1)], 0, QQ) == [QQ(1,1)]
assert dup_pow([QQ(1,1)], 1, QQ) == [QQ(1,1)]
assert dup_pow([QQ(1,1)], 7, QQ) == [QQ(1,1)]
assert dup_pow([QQ(3,7)], 0, QQ) == [QQ(1,1)]
assert dup_pow([QQ(3,7)], 1, QQ) == [QQ(3,7)]
assert dup_pow([QQ(3,7)], 7, QQ) == [QQ(2187,823543)]
f = dup_normal([2,0,0,1,7], ZZ)
assert dup_pow(f, 0, ZZ) == dup_normal([1], ZZ)
assert dup_pow(f, 1, ZZ) == dup_normal([2,0,0,1,7], ZZ)
assert dup_pow(f, 2, ZZ) == dup_normal([4,0,0,4,28,0,1,14,49], ZZ)
assert dup_pow(f, 3, ZZ) == dup_normal([8,0,0,12,84,0,6,84,294,1,21,147,343], ZZ)
def test_dup_ext_factor():
h = [QQ(1), QQ(0), QQ(1)]
K = QQ.algebraic_field(I)
assert dup_ext_factor([], K) == (ANP([], h, QQ), [])
f = [ANP([QQ(1)], h, QQ), ANP([QQ(1)], h, QQ)]
assert dup_ext_factor(f, K) == (ANP([QQ(1)], h, QQ), [(f, 1)])
g = [ANP([QQ(2)], h, QQ), ANP([QQ(2)], h, QQ)]
assert dup_ext_factor(g, K) == (ANP([QQ(2)], h, QQ), [(f, 1)])
f = [
ANP([QQ(7)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1, 1)], h, QQ)
]
g = [
ANP([QQ(1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1, 7)], h, QQ)
]
assert dup_ext_factor(f, K) == (ANP([QQ(7)], h, QQ), [(g, 1)])
f = [
ANP([QQ(1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1)], h, QQ)
]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ)], 1),
])
f = [
ANP([QQ(1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1)], h, QQ)
]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ)], 1),
])
h = [QQ(1), QQ(0), QQ(-2)]
K = QQ.algebraic_field(sqrt(2))
f = [
ANP([QQ(1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ),
ANP([QQ(1, 1)], h, QQ)
]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ), ANP([QQ(1)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ), ANP([QQ(1)], h, QQ)], 1),
])
f = [ANP([QQ(1, 1)], h, QQ), ANP([2, 0], h, QQ), ANP([QQ(2, 1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 2),
])
assert dup_ext_factor(dup_pow(f, 3, K), K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 6),
])
f = dup_mul_ground(f, ANP([QQ(2, 1)], h, QQ), K)
assert dup_ext_factor(f, K) == \
(ANP([QQ(2,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 2),
])
assert dup_ext_factor(dup_pow(f, 3, K), K) == \
(ANP([QQ(8,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 6),
])
h = [QQ(1, 1), QQ(0, 1), QQ(1, 1)]
K = QQ.algebraic_field(I)
f = [ANP([QQ(4, 1)], h, QQ), ANP([], h, QQ), ANP([QQ(9, 1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(4,1)], h, QQ), [
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(3,2), QQ(0,1)], h, QQ)], 1),
])
f = [
ANP([QQ(4, 1)], h, QQ),
ANP([QQ(8, 1)], h, QQ),
ANP([QQ(77, 1)], h, QQ),
ANP([QQ(18, 1)], h, QQ),
ANP([QQ(153, 1)], h, QQ)
]
assert dup_ext_factor(f, K) == \
(ANP([QQ(4,1)], h, QQ), [
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(4,1), QQ(1,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(4,1), QQ(1,1)], h, QQ)], 1),
])
def test_dup_ext_factor():
h = [QQ(1),QQ(0),QQ(1)]
K = QQ.algebraic_field(I)
assert dup_ext_factor([], K) == (ANP([], h, QQ), [])
f = [ANP([QQ(1)], h, QQ), ANP([QQ(1)], h, QQ)]
assert dup_ext_factor(f, K) == (ANP([QQ(1)], h, QQ), [(f, 1)])
g = [ANP([QQ(2)], h, QQ), ANP([QQ(2)], h, QQ)]
assert dup_ext_factor(g, K) == (ANP([QQ(2)], h, QQ), [(f, 1)])
f = [ANP([QQ(7)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1,1)], h, QQ)]
g = [ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1,7)], h, QQ)]
assert dup_ext_factor(f, K) == (ANP([QQ(7)], h, QQ), [(g, 1)])
f = [ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ)], 1),
])
f = [ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ)], 1),
])
h = [QQ(1),QQ(0),QQ(-2)]
K = QQ.algebraic_field(sqrt(2))
f = [ANP([QQ(1)], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([], h, QQ), ANP([QQ(1,1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1)], h, QQ), [
([ANP([QQ(1)], h, QQ), ANP([QQ(-1),QQ(0)], h, QQ), ANP([QQ(1)], h, QQ)], 1),
([ANP([QQ(1)], h, QQ), ANP([QQ( 1),QQ(0)], h, QQ), ANP([QQ(1)], h, QQ)], 1),
])
f = [ANP([QQ(1,1)], h, QQ), ANP([2,0], h, QQ), ANP([QQ(2,1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 2),
])
assert dup_ext_factor(dup_pow(f, 3, K), K) == \
(ANP([QQ(1,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 6),
])
f = dup_mul_ground(f, ANP([QQ(2,1)], h, QQ), K)
assert dup_ext_factor(f, K) == \
(ANP([QQ(2,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 2),
])
assert dup_ext_factor(dup_pow(f, 3, K), K) == \
(ANP([QQ(8,1)], h, QQ), [
([ANP([1], h, QQ), ANP([1,0], h, QQ)], 6),
])
h = [QQ(1,1), QQ(0,1), QQ(1,1)]
K = QQ.algebraic_field(I)
f = [ANP([QQ(4,1)], h, QQ), ANP([], h, QQ), ANP([QQ(9,1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(4,1)], h, QQ), [
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(3,2), QQ(0,1)], h, QQ)], 1),
])
f = [ANP([QQ(4,1)], h, QQ), ANP([QQ(8,1)], h, QQ), ANP([QQ(77,1)], h, QQ), ANP([QQ(18,1)], h, QQ), ANP([QQ(153,1)], h, QQ)]
assert dup_ext_factor(f, K) == \
(ANP([QQ(4,1)], h, QQ), [
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(4,1), QQ(1,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([-QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(3,2), QQ(0,1)], h, QQ)], 1),
([ANP([QQ(1,1)], h, QQ), ANP([ QQ(4,1), QQ(1,1)], h, QQ)], 1),
])