def test_Domain_get_ring():
assert ZZ.has_assoc_Ring is True
assert QQ.has_assoc_Ring is True
assert ZZ[x].has_assoc_Ring is True
assert QQ[x].has_assoc_Ring is True
assert ZZ[x, y].has_assoc_Ring is True
assert QQ[x, y].has_assoc_Ring is True
assert ZZ.frac_field(x).has_assoc_Ring is True
assert QQ.frac_field(x).has_assoc_Ring is True
assert ZZ.frac_field(x, y).has_assoc_Ring is True
assert QQ.frac_field(x, y).has_assoc_Ring is True
assert EX.has_assoc_Ring is False
assert RR.has_assoc_Ring is False
assert ALG.has_assoc_Ring is False
assert ZZ.get_ring() == ZZ
assert QQ.get_ring() == ZZ
assert ZZ[x].get_ring() == ZZ[x]
assert QQ[x].get_ring() == QQ[x]
assert ZZ[x, y].get_ring() == ZZ[x, y]
assert QQ[x, y].get_ring() == QQ[x, y]
assert ZZ.frac_field(x).get_ring() == ZZ[x]
assert QQ.frac_field(x).get_ring() == QQ[x]
assert ZZ.frac_field(x, y).get_ring() == ZZ[x, y]
assert QQ.frac_field(x, y).get_ring() == QQ[x, y]
assert EX.get_ring() == EX
raises(DomainError, lambda: RR.get_ring())
raises(DomainError, lambda: ALG.get_ring())
def test_Domain_get_ring():
assert ZZ.has_assoc_Ring is True
assert QQ.has_assoc_Ring is True
assert ZZ[x].has_assoc_Ring is True
assert QQ[x].has_assoc_Ring is True
assert ZZ[x, y].has_assoc_Ring is True
assert QQ[x, y].has_assoc_Ring is True
assert ZZ.frac_field(x).has_assoc_Ring is True
assert QQ.frac_field(x).has_assoc_Ring is True
assert ZZ.frac_field(x, y).has_assoc_Ring is True
assert QQ.frac_field(x, y).has_assoc_Ring is True
assert EX.has_assoc_Ring is False
assert RR.has_assoc_Ring is False
assert ALG.has_assoc_Ring is False
assert ZZ.get_ring() == ZZ
assert QQ.get_ring() == ZZ
assert ZZ[x].get_ring() == ZZ[x]
assert QQ[x].get_ring() == QQ[x]
assert ZZ[x, y].get_ring() == ZZ[x, y]
assert QQ[x, y].get_ring() == QQ[x, y]
assert ZZ.frac_field(x).get_ring() == ZZ[x]
assert QQ.frac_field(x).get_ring() == QQ[x]
assert ZZ.frac_field(x, y).get_ring() == ZZ[x, y]
assert QQ.frac_field(x, y).get_ring() == QQ[x, y]
assert EX.get_ring() == EX
assert RR.get_ring() == RR
# XXX: This should also be like RR
raises(DomainError, lambda: ALG.get_ring())
def from_sympy(self, a):
"""Convert SymPy's Integer to `dtype`. """
if a.is_Rational:
return GMPYRationalType(a.p, a.q)
elif a.is_Float:
from sympy.polys.domains import RR
return GMPYRationalType(*RR.as_integer_ratio(a))
else:
raise CoercionFailed("expected `Rational` object, got %s" % a)
def from_sympy(self, a):
"""Convert SymPy's Rational to `dtype`. """
if a.is_Rational and a.q != 0:
return a
elif a.is_Real:
from sympy.polys.domains import RR
return SymPyRationalType(*RR.as_integer_ratio(a))
else:
raise CoercionFailed("expected `Rational` object, got %s" % a)
def from_sympy(self, a):
"""Convert SymPy's Rational to `dtype`. """
if a.is_Rational:
return PythonRational(a.p, a.q)
elif a.is_Float:
from sympy.polys.domains import RR
p, q = RR.to_rational(a)
return PythonRational(int(p), int(q))
else:
raise CoercionFailed("expected `Rational` object, got %s" % a)
def test_Domain_get_exact():
assert EX.get_exact() == EX
assert ZZ.get_exact() == ZZ
assert QQ.get_exact() == QQ
assert RR.get_exact() == QQ
assert ALG.get_exact() == ALG
assert ZZ[x].get_exact() == ZZ[x]
assert QQ[x].get_exact() == QQ[x]
assert ZZ[x,y].get_exact() == ZZ[x,y]
assert QQ[x,y].get_exact() == QQ[x,y]
assert ZZ.frac_field(x).get_exact() == ZZ.frac_field(x)
assert QQ.frac_field(x).get_exact() == QQ.frac_field(x)
assert ZZ.frac_field(x,y).get_exact() == ZZ.frac_field(x,y)
assert QQ.frac_field(x,y).get_exact() == QQ.frac_field(x,y)
def test_Domain_get_field():
assert EX.has_assoc_Field == True
assert ZZ.has_assoc_Field == True
assert QQ.has_assoc_Field == True
assert RR.has_assoc_Field == False
assert ALG.has_assoc_Field == True
assert ZZ[x].has_assoc_Field == True
assert QQ[x].has_assoc_Field == True
assert ZZ[x,y].has_assoc_Field == True
assert QQ[x,y].has_assoc_Field == True
assert EX.get_field() == EX
assert ZZ.get_field() == QQ
assert QQ.get_field() == QQ
raises(DomainError, lambda: RR.get_field())
assert ALG.get_field() == ALG
assert ZZ[x].get_field() == ZZ.frac_field(x)
assert QQ[x].get_field() == QQ.frac_field(x)
assert ZZ[x,y].get_field() == ZZ.frac_field(x,y)
assert QQ[x,y].get_field() == QQ.frac_field(x,y)
def test_Domain_get_field():
assert EX.has_assoc_Field is True
assert ZZ.has_assoc_Field is True
assert QQ.has_assoc_Field is True
assert RR.has_assoc_Field is True
assert ALG.has_assoc_Field is True
assert ZZ[x].has_assoc_Field is True
assert QQ[x].has_assoc_Field is True
assert ZZ[x, y].has_assoc_Field is True
assert QQ[x, y].has_assoc_Field is True
assert EX.get_field() == EX
assert ZZ.get_field() == QQ
assert QQ.get_field() == QQ
assert RR.get_field() == RR
assert ALG.get_field() == ALG
assert ZZ[x].get_field() == ZZ.frac_field(x)
assert QQ[x].get_field() == QQ.frac_field(x)
assert ZZ[x, y].get_field() == ZZ.frac_field(x, y)
assert QQ[x, y].get_field() == QQ.frac_field(x, y)
def test_construct_domain():
assert construct_domain([1, 2, 3]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain(
[1, 2, 3], field=True) == (QQ, [QQ(1), QQ(2), QQ(3)])
assert construct_domain([S(1), S(2), S(3)]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain(
[S(1), S(2), S(3)], field=True) == (QQ, [QQ(1), QQ(2), QQ(3)])
assert construct_domain([S(1)/2, S(2)]) == (QQ, [QQ(1, 2), QQ(2)])
assert construct_domain(
[3.14, 1, S(1)/2]) == (RR, [RR(3.14), RR(1.0), RR(0.5)])
assert construct_domain(
[3.14, sqrt(2)], extension=None) == (EX, [EX(3.14), EX(sqrt(2))])
assert construct_domain(
[3.14, sqrt(2)], extension=True) == (EX, [EX(3.14), EX(sqrt(2))])
assert construct_domain(
[1, sqrt(2)], extension=None) == (EX, [EX(1), EX(sqrt(2))])
alg = QQ.algebraic_field(sqrt(2))
assert construct_domain([7, S(1)/2, sqrt(2)], extension=True) == \
(alg, [alg.convert(7), alg.convert(S(1)/2), alg.convert(sqrt(2))])
alg = QQ.algebraic_field(sqrt(2) + sqrt(3))
assert construct_domain([7, sqrt(2), sqrt(3)], extension=True) == \
(alg, [alg.convert(7), alg.convert(sqrt(2)), alg.convert(sqrt(3))])
dom = ZZ[x]
assert construct_domain([2*x, 3]) == \
(dom, [dom.convert(2*x), dom.convert(3)])
dom = ZZ[x, y]
assert construct_domain([2*x, 3*y]) == \
(dom, [dom.convert(2*x), dom.convert(3*y)])
dom = QQ[x]
assert construct_domain([x/2, 3]) == \
(dom, [dom.convert(x/2), dom.convert(3)])
dom = QQ[x, y]
assert construct_domain([x/2, 3*y]) == \
(dom, [dom.convert(x/2), dom.convert(3*y)])
dom = RR[x]
assert construct_domain([x/2, 3.5]) == \
(dom, [dom.convert(x/2), dom.convert(3.5)])
dom = RR[x, y]
assert construct_domain([x/2, 3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(3.5*y)])
dom = ZZ.frac_field(x)
assert construct_domain([2/x, 3]) == \
(dom, [dom.convert(2/x), dom.convert(3)])
dom = ZZ.frac_field(x, y)
assert construct_domain([2/x, 3*y]) == \
(dom, [dom.convert(2/x), dom.convert(3*y)])
dom = RR.frac_field(x)
assert construct_domain([2/x, 3.5]) == \
(dom, [dom.convert(2/x), dom.convert(3.5)])
dom = RR.frac_field(x, y)
assert construct_domain([2/x, 3.5*y]) == \
(dom, [dom.convert(2/x), dom.convert(3.5*y)])
assert construct_domain(2) == (ZZ, ZZ(2))
assert construct_domain(S(2)/3) == (QQ, QQ(2, 3))
def test_dmp_gcd():
assert dmp_zz_heu_gcd([[]], [[]], 1, ZZ) == ([[]], [[]], [[]])
assert dmp_rr_prs_gcd([[]], [[]], 1, ZZ) == ([[]], [[]], [[]])
assert dmp_zz_heu_gcd([[2]], [[]], 1, ZZ) == ([[2]], [[1]], [[]])
assert dmp_rr_prs_gcd([[2]], [[]], 1, ZZ) == ([[2]], [[1]], [[]])
assert dmp_zz_heu_gcd([[-2]], [[]], 1, ZZ) == ([[2]], [[-1]], [[]])
assert dmp_rr_prs_gcd([[-2]], [[]], 1, ZZ) == ([[2]], [[-1]], [[]])
assert dmp_zz_heu_gcd([[]], [[-2]], 1, ZZ) == ([[2]], [[]], [[-1]])
assert dmp_rr_prs_gcd([[]], [[-2]], 1, ZZ) == ([[2]], [[]], [[-1]])
assert dmp_zz_heu_gcd([[]], [[2], [4]], 1, ZZ) == ([[2], [4]], [[]], [[1]])
assert dmp_rr_prs_gcd([[]], [[2], [4]], 1, ZZ) == ([[2], [4]], [[]], [[1]])
assert dmp_zz_heu_gcd([[2], [4]], [[]], 1, ZZ) == ([[2], [4]], [[1]], [[]])
assert dmp_rr_prs_gcd([[2], [4]], [[]], 1, ZZ) == ([[2], [4]], [[1]], [[]])
assert dmp_zz_heu_gcd([[2]], [[2]], 1, ZZ) == ([[2]], [[1]], [[1]])
assert dmp_rr_prs_gcd([[2]], [[2]], 1, ZZ) == ([[2]], [[1]], [[1]])
assert dmp_zz_heu_gcd([[-2]], [[2]], 1, ZZ) == ([[2]], [[-1]], [[1]])
assert dmp_rr_prs_gcd([[-2]], [[2]], 1, ZZ) == ([[2]], [[-1]], [[1]])
assert dmp_zz_heu_gcd([[2]], [[-2]], 1, ZZ) == ([[2]], [[1]], [[-1]])
assert dmp_rr_prs_gcd([[2]], [[-2]], 1, ZZ) == ([[2]], [[1]], [[-1]])
assert dmp_zz_heu_gcd([[-2]], [[-2]], 1, ZZ) == ([[2]], [[-1]], [[-1]])
assert dmp_rr_prs_gcd([[-2]], [[-2]], 1, ZZ) == ([[2]], [[-1]], [[-1]])
assert dmp_zz_heu_gcd([[1], [2], [1]], [[1]], 1,
ZZ) == ([[1]], [[1], [2], [1]], [[1]])
assert dmp_rr_prs_gcd([[1], [2], [1]], [[1]], 1,
ZZ) == ([[1]], [[1], [2], [1]], [[1]])
assert dmp_zz_heu_gcd([[1], [2], [1]], [[2]], 1,
ZZ) == ([[1]], [[1], [2], [1]], [[2]])
assert dmp_rr_prs_gcd([[1], [2], [1]], [[2]], 1,
ZZ) == ([[1]], [[1], [2], [1]], [[2]])
assert dmp_zz_heu_gcd([[2], [4], [2]], [[2]], 1,
ZZ) == ([[2]], [[1], [2], [1]], [[1]])
assert dmp_rr_prs_gcd([[2], [4], [2]], [[2]], 1,
ZZ) == ([[2]], [[1], [2], [1]], [[1]])
assert dmp_zz_heu_gcd([[2]], [[2], [4], [2]], 1,
ZZ) == ([[2]], [[1]], [[1], [2], [1]])
assert dmp_rr_prs_gcd([[2]], [[2], [4], [2]], 1,
ZZ) == ([[2]], [[1]], [[1], [2], [1]])
assert dmp_zz_heu_gcd([[2], [4], [2]], [[1], [1]], 1,
ZZ) == ([[1], [1]], [[2], [2]], [[1]])
assert dmp_rr_prs_gcd([[2], [4], [2]], [[1], [1]], 1,
ZZ) == ([[1], [1]], [[2], [2]], [[1]])
assert dmp_zz_heu_gcd([[1], [1]], [[2], [4], [2]], 1,
ZZ) == ([[1], [1]], [[1]], [[2], [2]])
assert dmp_rr_prs_gcd([[1], [1]], [[2], [4], [2]], 1,
ZZ) == ([[1], [1]], [[1]], [[2], [2]])
assert dmp_zz_heu_gcd([[[[1, 2, 1]]]], [[[[2, 2]]]], 3,
ZZ) == ([[[[1, 1]]]], [[[[1, 1]]]], [[[[2]]]])
assert dmp_rr_prs_gcd([[[[1, 2, 1]]]], [[[[2, 2]]]], 3,
ZZ) == ([[[[1, 1]]]], [[[[1, 1]]]], [[[[2]]]])
f, g = [[[[1, 2, 1], [1, 1], []]]], [[[[1, 2, 1]]]]
h, cff, cfg = [[[[1, 1]]]], [[[[1, 1], [1], []]]], [[[[1, 1]]]]
assert dmp_zz_heu_gcd(f, g, 3, ZZ) == (h, cff, cfg)
assert dmp_rr_prs_gcd(f, g, 3, ZZ) == (h, cff, cfg)
assert dmp_zz_heu_gcd(g, f, 3, ZZ) == (h, cfg, cff)
assert dmp_rr_prs_gcd(g, f, 3, ZZ) == (h, cfg, cff)
f, g, h = dmp_fateman_poly_F_1(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(4, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 4, ZZ)
assert H == h and dmp_mul(H, cff, 4, ZZ) == f \
and dmp_mul(H, cfg, 4, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(6, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 6, ZZ)
assert H == h and dmp_mul(H, cff, 6, ZZ) == f \
and dmp_mul(H, cfg, 6, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(8, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 8, ZZ)
assert H == h and dmp_mul(H, cff, 8, ZZ) == f \
and dmp_mul(H, cfg, 8, ZZ) == g
f, g, h = dmp_fateman_poly_F_2(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_3(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_3(4, ZZ)
H, cff, cfg = dmp_inner_gcd(f, g, 4, ZZ)
assert H == h and dmp_mul(H, cff, 4, ZZ) == f \
and dmp_mul(H, cfg, 4, ZZ) == g
f = [[QQ(1, 2)], [QQ(1)], [QQ(1, 2)]]
g = [[QQ(1, 2)], [QQ(1, 2)]]
h = [[QQ(1)], [QQ(1)]]
assert dmp_qq_heu_gcd(f, g, 1, QQ) == (h, g, [[QQ(1, 2)]])
assert dmp_ff_prs_gcd(f, g, 1, QQ) == (h, g, [[QQ(1, 2)]])
f = [[RR(2.1), RR(-2.2), RR(2.1)], []]
g = [[RR(1.0)], [], [], []]
assert dmp_ff_prs_gcd(f, g, 1, RR) == \
([[RR(1.0)], []], [[RR(2.1), RR(-2.2), RR(2.1)]], [[RR(1.0)], [], []])
def test_dmp_factor_list():
assert dmp_factor_list([[]], 1, ZZ) == (ZZ(0), [])
assert dmp_factor_list([[]], 1, QQ) == (QQ(0), [])
assert dmp_factor_list([[]], 1, ZZ['y']) == (DMP([], ZZ), [])
assert dmp_factor_list([[]], 1, QQ['y']) == (DMP([], QQ), [])
assert dmp_factor_list_include([[]], 1, ZZ) == [([[]], 1)]
assert dmp_factor_list([[ZZ(7)]], 1, ZZ) == (ZZ(7), [])
assert dmp_factor_list([[QQ(1, 7)]], 1, QQ) == (QQ(1, 7), [])
assert dmp_factor_list([[DMP([ZZ(7)], ZZ)]], 1, ZZ['y']) == (DMP([ZZ(7)],
ZZ), [])
assert dmp_factor_list([[DMP([QQ(1, 7)], QQ)]], 1,
QQ['y']) == (DMP([QQ(1, 7)], QQ), [])
assert dmp_factor_list_include([[ZZ(7)]], 1, ZZ) == [([[ZZ(7)]], 1)]
f, g = [ZZ(1), ZZ(2), ZZ(1)], [ZZ(1), ZZ(1)]
assert dmp_factor_list(dmp_nest(f, 200, ZZ), 200, ZZ) == \
(ZZ(1), [(dmp_nest(g, 200, ZZ), 2)])
assert dmp_factor_list(dmp_raise(f, 200, 0, ZZ), 200, ZZ) == \
(ZZ(1), [(dmp_raise(g, 200, 0, ZZ), 2)])
assert dmp_factor_list([ZZ(1),ZZ(2),ZZ(1)], 0, ZZ) == \
(ZZ(1), [([ZZ(1), ZZ(1)], 2)])
assert dmp_factor_list([QQ(1,2),QQ(1),QQ(1,2)], 0, QQ) == \
(QQ(1,2), [([QQ(1),QQ(1)], 2)])
assert dmp_factor_list([[ZZ(1)],[ZZ(2)],[ZZ(1)]], 1, ZZ) == \
(ZZ(1), [([[ZZ(1)], [ZZ(1)]], 2)])
assert dmp_factor_list([[QQ(1,2)],[QQ(1)],[QQ(1,2)]], 1, QQ) == \
(QQ(1,2), [([[QQ(1)],[QQ(1)]], 2)])
f = [[ZZ(4), ZZ(0)], [ZZ(4), ZZ(0), ZZ(0)], []]
assert dmp_factor_list(f, 1, ZZ) == \
(ZZ(4), [([[ZZ(1),ZZ(0)]], 1),
([[ZZ(1)],[]], 1),
([[ZZ(1)],[ZZ(1),ZZ(0)]], 1)])
assert dmp_factor_list_include(f, 1, ZZ) == \
[([[ZZ(4),ZZ(0)]], 1),
([[ZZ(1)],[]], 1),
([[ZZ(1)],[ZZ(1),ZZ(0)]], 1)]
f = [[QQ(1, 2), QQ(0)], [QQ(1, 2), QQ(0), QQ(0)], []]
assert dmp_factor_list(f, 1, QQ) == \
(QQ(1,2), [([[QQ(1),QQ(0)]], 1),
([[QQ(1)],[]], 1),
([[QQ(1)],[QQ(1),QQ(0)]], 1)])
f = [[RR(2.0)], [], [-RR(8.0), RR(0.0), RR(0.0)]]
assert dmp_factor_list(f, 1, RR) == \
(RR(2.0), [([[RR(1.0)],[-RR(2.0),RR(0.0)]], 1),
([[RR(1.0)],[ RR(2.0),RR(0.0)]], 1)])
f = [[DMP([ZZ(4), ZZ(0)], ZZ)], [DMP([ZZ(4), ZZ(0), ZZ(0)], ZZ)],
[DMP([], ZZ)]]
assert dmp_factor_list(f, 1, ZZ['y']) == \
(DMP([ZZ(4)],ZZ), [([[DMP([ZZ(1),ZZ(0)],ZZ)]], 1),
([[DMP([ZZ(1)],ZZ)],[]], 1),
([[DMP([ZZ(1)],ZZ)],[DMP([ZZ(1),ZZ(0)],ZZ)]], 1)])
f = [[DMP([QQ(1, 2), QQ(0)], ZZ)],
[DMP([QQ(1, 2), QQ(0), QQ(0)], ZZ)], [DMP([], ZZ)]]
assert dmp_factor_list(f, 1, QQ['y']) == \
(DMP([QQ(1,2)],QQ), [([[DMP([QQ(1),QQ(0)],QQ)]], 1),
([[DMP([QQ(1)],QQ)],[]], 1),
([[DMP([QQ(1)],QQ)],[DMP([QQ(1),QQ(0)],QQ)]], 1)])
K = FF(2)
raises(DomainError, "dmp_factor_list([[K(1)],[],[K(1),K(0),K(0)]], 1, K)")
raises(DomainError, "dmp_factor_list([[EX(sin(1))]], 1, EX)")
def test_Domain_unify():
F3 = GF(3)
assert unify(F3, F3) == F3
assert unify(F3, ZZ) == ZZ
assert unify(F3, QQ) == QQ
assert unify(F3, ALG) == ALG
assert unify(F3, RR) == RR
assert unify(F3, CC) == CC
assert unify(F3, ZZ[x]) == ZZ[x]
assert unify(F3, ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(F3, EX) == EX
assert unify(ZZ, F3) == ZZ
assert unify(ZZ, ZZ) == ZZ
assert unify(ZZ, QQ) == QQ
assert unify(ZZ, ALG) == ALG
assert unify(ZZ, RR) == RR
assert unify(ZZ, CC) == CC
assert unify(ZZ, ZZ[x]) == ZZ[x]
assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ, EX) == EX
assert unify(QQ, F3) == QQ
assert unify(QQ, ZZ) == QQ
assert unify(QQ, QQ) == QQ
assert unify(QQ, ALG) == ALG
assert unify(QQ, RR) == RR
assert unify(QQ, CC) == CC
assert unify(QQ, ZZ[x]) == QQ[x]
assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x)
assert unify(QQ, EX) == EX
assert unify(RR, F3) == RR
assert unify(RR, ZZ) == RR
assert unify(RR, QQ) == RR
assert unify(RR, ALG) == RR
assert unify(RR, RR) == RR
assert unify(RR, CC) == CC
assert unify(RR, ZZ[x]) == RR[x]
assert unify(RR, ZZ.frac_field(x)) == RR.frac_field(x)
assert unify(RR, EX) == EX
assert RR[x].unify(ZZ.frac_field(y)) == RR.frac_field(x, y)
assert unify(CC, F3) == CC
assert unify(CC, ZZ) == CC
assert unify(CC, QQ) == CC
assert unify(CC, ALG) == CC
assert unify(CC, RR) == CC
assert unify(CC, CC) == CC
assert unify(CC, ZZ[x]) == CC[x]
assert unify(CC, ZZ.frac_field(x)) == CC.frac_field(x)
assert unify(CC, EX) == EX
assert unify(ZZ[x], F3) == ZZ[x]
assert unify(ZZ[x], ZZ) == ZZ[x]
assert unify(ZZ[x], QQ) == QQ[x]
assert unify(ZZ[x], ALG) == ALG[x]
assert unify(ZZ[x], RR) == RR[x]
assert unify(ZZ[x], CC) == CC[x]
assert unify(ZZ[x], ZZ[x]) == ZZ[x]
assert unify(ZZ[x], ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ[x], EX) == EX
assert unify(ZZ.frac_field(x), F3) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x)
assert unify(ZZ.frac_field(x), ALG) == ALG.frac_field(x)
assert unify(ZZ.frac_field(x), RR) == RR.frac_field(x)
assert unify(ZZ.frac_field(x), CC) == CC.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ[x]) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), EX) == EX
assert unify(EX, F3) == EX
assert unify(EX, ZZ) == EX
assert unify(EX, QQ) == EX
assert unify(EX, ALG) == EX
assert unify(EX, RR) == EX
assert unify(EX, CC) == EX
assert unify(EX, ZZ[x]) == EX
assert unify(EX, ZZ.frac_field(x)) == EX
assert unify(EX, EX) == EX
def test_dmp_factor_list():
R, x, y = ring("x,y", ZZ)
assert R.dmp_factor_list(0) == (ZZ(0), [])
assert R.dmp_factor_list(7) == (7, [])
R, x, y = ring("x,y", QQ)
assert R.dmp_factor_list(0) == (QQ(0), [])
assert R.dmp_factor_list(QQ(1, 7)) == (QQ(1, 7), [])
Rt, t = ring("t", ZZ)
R, x, y = ring("x,y", Rt)
assert R.dmp_factor_list(0) == (0, [])
assert R.dmp_factor_list(7) == (ZZ(7), [])
Rt, t = ring("t", QQ)
R, x, y = ring("x,y", Rt)
assert R.dmp_factor_list(0) == (0, [])
assert R.dmp_factor_list(QQ(1, 7)) == (QQ(1, 7), [])
R, x, y = ring("x,y", ZZ)
assert R.dmp_factor_list_include(0) == [(0, 1)]
assert R.dmp_factor_list_include(7) == [(7, 1)]
R, X = xring("x:200", ZZ)
f, g = X[0]**2 + 2 * X[0] + 1, X[0] + 1
assert R.dmp_factor_list(f) == (1, [(g, 2)])
f, g = X[-1]**2 + 2 * X[-1] + 1, X[-1] + 1
assert R.dmp_factor_list(f) == (1, [(g, 2)])
R, x = ring("x", ZZ)
assert R.dmp_factor_list(x**2 + 2 * x + 1) == (1, [(x + 1, 2)])
R, x = ring("x", QQ)
assert R.dmp_factor_list(QQ(1, 2) * x**2 + x + QQ(1, 2)) == (QQ(1, 2),
[(x + 1, 2)])
R, x, y = ring("x,y", ZZ)
assert R.dmp_factor_list(x**2 + 2 * x + 1) == (1, [(x + 1, 2)])
R, x, y = ring("x,y", QQ)
assert R.dmp_factor_list(QQ(1, 2) * x**2 + x + QQ(1, 2)) == (QQ(1, 2),
[(x + 1, 2)])
R, x, y = ring("x,y", ZZ)
f = 4 * x**2 * y + 4 * x * y**2
assert R.dmp_factor_list(f) == \
(4, [(y, 1),
(x, 1),
(x + y, 1)])
assert R.dmp_factor_list_include(f) == \
[(4*y, 1),
(x, 1),
(x + y, 1)]
R, x, y = ring("x,y", QQ)
f = QQ(1, 2) * x**2 * y + QQ(1, 2) * x * y**2
assert R.dmp_factor_list(f) == \
(QQ(1,2), [(y, 1),
(x, 1),
(x + y, 1)])
R, x, y = ring("x,y", RR)
f = 2.0 * x**2 - 8.0 * y**2
assert R.dmp_factor_list(f) == \
(RR(2.0), [(1.0*x - 2.0*y, 1),
(1.0*x + 2.0*y, 1)])
f = 6.7225336055071 * x**2 * y**2 - 10.6463972754741 * x * y - 0.33469524022264
coeff, factors = R.dmp_factor_list(f)
assert coeff == RR(1.0) and len(factors) == 1 and factors[0][0].almosteq(
f, 1e-10) and factors[0][1] == 1
Rt, t = ring("t", ZZ)
R, x, y = ring("x,y", Rt)
f = 4 * t * x**2 + 4 * t**2 * x
assert R.dmp_factor_list(f) == \
(4, [(t, 1),
(x, 1),
(x + t, 1)])
Rt, t = ring("t", QQ)
R, x, y = ring("x,y", Rt)
f = QQ(1, 2) * t * x**2 + QQ(1, 2) * t**2 * x
assert R.dmp_factor_list(f) == \
(QQ(1, 2), [(t, 1),
(x, 1),
(x + t, 1)])
R, x, y = ring("x,y", FF(2))
raises(NotImplementedError, lambda: R.dmp_factor_list(x**2 + y**2))
R, x, y = ring("x,y", EX)
raises(DomainError, lambda: R.dmp_factor_list(EX(sin(1))))
def test_dup_factor_list():
R, x = ring("x", ZZ)
assert R.dup_factor_list(0) == (0, [])
assert R.dup_factor_list(7) == (7, [])
R, x = ring("x", QQ)
assert R.dup_factor_list(0) == (0, [])
assert R.dup_factor_list(QQ(1, 7)) == (QQ(1, 7), [])
R, x = ring("x", ZZ['t'])
assert R.dup_factor_list(0) == (0, [])
assert R.dup_factor_list(7) == (7, [])
R, x = ring("x", QQ['t'])
assert R.dup_factor_list(0) == (0, [])
assert R.dup_factor_list(QQ(1, 7)) == (QQ(1, 7), [])
R, x = ring("x", ZZ)
assert R.dup_factor_list_include(0) == [(0, 1)]
assert R.dup_factor_list_include(7) == [(7, 1)]
assert R.dup_factor_list(x**2 + 2 * x + 1) == (1, [(x + 1, 2)])
assert R.dup_factor_list_include(x**2 + 2 * x + 1) == [(x + 1, 2)]
R, x = ring("x", QQ)
assert R.dup_factor_list(QQ(1, 2) * x**2 + x + QQ(1, 2)) == (QQ(1, 2),
[(x + 1, 2)])
R, x = ring("x", FF(2))
assert R.dup_factor_list(x**2 + 1) == (1, [(x + 1, 2)])
R, x = ring("x", RR)
assert R.dup_factor_list(1.0 * x**2 + 2.0 * x + 1.0) == (1.0, [
(1.0 * x + 1.0, 2)
])
assert R.dup_factor_list(2.0 * x**2 + 4.0 * x + 2.0) == (2.0, [
(1.0 * x + 1.0, 2)
])
f = 6.7225336055071 * x**2 - 10.6463972754741 * x - 0.33469524022264
coeff, factors = R.dup_factor_list(f)
assert coeff == RR(1.0) and len(factors) == 1 and factors[0][0].almosteq(
f, 1e-10) and factors[0][1] == 1
Rt, t = ring("t", ZZ)
R, x = ring("x", Rt)
f = 4 * t * x**2 + 4 * t**2 * x
assert R.dup_factor_list(f) == \
(4, [(t, 1),
(x, 1),
(x + t, 1)])
Rt, t = ring("t", QQ)
R, x = ring("x", Rt)
f = QQ(1, 2) * t * x**2 + QQ(1, 2) * t**2 * x
assert R.dup_factor_list(f) == \
(QQ(1, 2), [(t, 1),
(x, 1),
(x + t, 1)])
R, x = ring("x", QQ.algebraic_field(I))
def anp(element):
return ANP(element, [QQ(1), QQ(0), QQ(1)], QQ)
f = anp([QQ(1, 1)]) * x**4 + anp([QQ(2, 1)]) * x**2
assert R.dup_factor_list(f) == \
(anp([QQ(1, 1)]), [(anp([QQ(1, 1)])*x, 2),
(anp([QQ(1, 1)])*x**2 + anp([])*x + anp([QQ(2, 1)]), 1)])
R, x = ring("x", EX)
raises(DomainError, lambda: R.dup_factor_list(EX(sin(1))))
def test_RealField_from_sympy():
assert RR.convert(S.Zero) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S.One) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
def test_issue_18278():
assert str(RR(2).parent()) == 'RR'
assert str(CC(2).parent()) == 'CC'
def test_construct_domain():
assert construct_domain([1, 2, 3]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([1, 2, 3],
field=True) == (QQ, [QQ(1), QQ(2),
QQ(3)])
assert construct_domain([S.One, S(2), S(3)]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([S.One, S(2), S(3)],
field=True) == (QQ, [QQ(1), QQ(2),
QQ(3)])
assert construct_domain([S.Half, S(2)]) == (QQ, [QQ(1, 2), QQ(2)])
result = construct_domain([3.14, 1, S.Half])
assert isinstance(result[0], RealField)
assert result[1] == [RR(3.14), RR(1.0), RR(0.5)]
result = construct_domain([3.14, I, S.Half])
assert isinstance(result[0], ComplexField)
assert result[1] == [CC(3.14), CC(1.0j), CC(0.5)]
assert construct_domain([1.0 + I]) == (CC, [CC(1.0, 1.0)])
assert construct_domain([2.0 + 3.0 * I]) == (CC, [CC(2.0, 3.0)])
assert construct_domain([1, I]) == (ZZ_I, [ZZ_I(1, 0), ZZ_I(0, 1)])
assert construct_domain([1,
I / 2]) == (QQ_I, [QQ_I(1, 0),
QQ_I(0, S.Half)])
assert construct_domain([3.14, sqrt(2)],
extension=None) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([3.14, sqrt(2)],
extension=True) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([1, sqrt(2)],
extension=None) == (EX, [EX(1), EX(sqrt(2))])
assert construct_domain([x, sqrt(x)]) == (EX, [EX(x), EX(sqrt(x))])
assert construct_domain([x, sqrt(x), sqrt(y)
]) == (EX, [EX(x),
EX(sqrt(x)),
EX(sqrt(y))])
alg = QQ.algebraic_field(sqrt(2))
assert construct_domain([7, S.Half, sqrt(2)], extension=True) == \
(alg, [alg.convert(7), alg.convert(S.Half), alg.convert(sqrt(2))])
alg = QQ.algebraic_field(sqrt(2) + sqrt(3))
assert construct_domain([7, sqrt(2), sqrt(3)], extension=True) == \
(alg, [alg.convert(7), alg.convert(sqrt(2)), alg.convert(sqrt(3))])
dom = ZZ[x]
assert construct_domain([2*x, 3]) == \
(dom, [dom.convert(2*x), dom.convert(3)])
dom = ZZ[x, y]
assert construct_domain([2*x, 3*y]) == \
(dom, [dom.convert(2*x), dom.convert(3*y)])
dom = QQ[x]
assert construct_domain([x/2, 3]) == \
(dom, [dom.convert(x/2), dom.convert(3)])
dom = QQ[x, y]
assert construct_domain([x/2, 3*y]) == \
(dom, [dom.convert(x/2), dom.convert(3*y)])
dom = ZZ_I[x]
assert construct_domain([2*x, I]) == \
(dom, [dom.convert(2*x), dom.convert(I)])
dom = ZZ_I[x, y]
assert construct_domain([2*x, I*y]) == \
(dom, [dom.convert(2*x), dom.convert(I*y)])
dom = QQ_I[x]
assert construct_domain([x/2, I]) == \
(dom, [dom.convert(x/2), dom.convert(I)])
dom = QQ_I[x, y]
assert construct_domain([x/2, I*y]) == \
(dom, [dom.convert(x/2), dom.convert(I*y)])
dom = RR[x]
assert construct_domain([x/2, 3.5]) == \
(dom, [dom.convert(x/2), dom.convert(3.5)])
dom = RR[x, y]
assert construct_domain([x/2, 3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(3.5*y)])
dom = CC[x]
assert construct_domain([I*x/2, 3.5]) == \
(dom, [dom.convert(I*x/2), dom.convert(3.5)])
dom = CC[x, y]
assert construct_domain([I*x/2, 3.5*y]) == \
(dom, [dom.convert(I*x/2), dom.convert(3.5*y)])
dom = CC[x]
assert construct_domain([x/2, I*3.5]) == \
(dom, [dom.convert(x/2), dom.convert(I*3.5)])
dom = CC[x, y]
assert construct_domain([x/2, I*3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(I*3.5*y)])
dom = ZZ.frac_field(x)
assert construct_domain([2/x, 3]) == \
(dom, [dom.convert(2/x), dom.convert(3)])
dom = ZZ.frac_field(x, y)
assert construct_domain([2/x, 3*y]) == \
(dom, [dom.convert(2/x), dom.convert(3*y)])
dom = RR.frac_field(x)
assert construct_domain([2/x, 3.5]) == \
(dom, [dom.convert(2/x), dom.convert(3.5)])
dom = RR.frac_field(x, y)
assert construct_domain([2/x, 3.5*y]) == \
(dom, [dom.convert(2/x), dom.convert(3.5*y)])
dom = RealField(prec=336)[x]
assert construct_domain([pi.evalf(100)*x]) == \
(dom, [dom.convert(pi.evalf(100)*x)])
assert construct_domain(2) == (ZZ, ZZ(2))
assert construct_domain(S(2) / 3) == (QQ, QQ(2, 3))
assert construct_domain(Rational(2, 3)) == (QQ, QQ(2, 3))
assert construct_domain({}) == (ZZ, {})
def test_construct_domain():
assert construct_domain([1, 2, 3]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([1, 2, 3],
field=True) == (QQ, [QQ(1), QQ(2),
QQ(3)])
assert construct_domain([S(1), S(2), S(3)]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([S(1), S(2), S(3)],
field=True) == (QQ, [QQ(1), QQ(2),
QQ(3)])
assert construct_domain([S(1) / 2, S(2)]) == (QQ, [QQ(1, 2), QQ(2)])
assert construct_domain([3.14, 1,
S(1) / 2]) == (RR, [RR(3.14),
RR(1.0),
RR(0.5)])
assert construct_domain([3.14, sqrt(2)],
extension=None) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([3.14, sqrt(2)],
extension=True) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([1, sqrt(2)],
extension=None) == (EX, [EX(1), EX(sqrt(2))])
alg = QQ.algebraic_field(sqrt(2))
assert construct_domain([7, S(1)/2, sqrt(2)], extension=True) == \
(alg, [alg.convert(7), alg.convert(S(1)/2), alg.convert(sqrt(2))])
alg = QQ.algebraic_field(sqrt(2) + sqrt(3))
assert construct_domain([7, sqrt(2), sqrt(3)], extension=True) == \
(alg, [alg.convert(7), alg.convert(sqrt(2)), alg.convert(sqrt(3))])
dom = ZZ[x]
assert construct_domain([2*x, 3]) == \
(dom, [dom.convert(2*x), dom.convert(3)])
dom = ZZ[x, y]
assert construct_domain([2*x, 3*y]) == \
(dom, [dom.convert(2*x), dom.convert(3*y)])
dom = QQ[x]
assert construct_domain([x/2, 3]) == \
(dom, [dom.convert(x/2), dom.convert(3)])
dom = QQ[x, y]
assert construct_domain([x/2, 3*y]) == \
(dom, [dom.convert(x/2), dom.convert(3*y)])
dom = RR[x]
assert construct_domain([x/2, 3.5]) == \
(dom, [dom.convert(x/2), dom.convert(3.5)])
dom = RR[x, y]
assert construct_domain([x/2, 3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(3.5*y)])
dom = ZZ.frac_field(x)
assert construct_domain([2/x, 3]) == \
(dom, [dom.convert(2/x), dom.convert(3)])
dom = ZZ.frac_field(x, y)
assert construct_domain([2/x, 3*y]) == \
(dom, [dom.convert(2/x), dom.convert(3*y)])
dom = RR.frac_field(x)
assert construct_domain([2/x, 3.5]) == \
(dom, [dom.convert(2/x), dom.convert(3.5)])
dom = RR.frac_field(x, y)
assert construct_domain([2/x, 3.5*y]) == \
(dom, [dom.convert(2/x), dom.convert(3.5*y)])
assert construct_domain(2) == (ZZ, ZZ(2))
assert construct_domain(S(2) / 3) == (QQ, QQ(2, 3))
assert construct_domain({}) == (ZZ, {})
def test_Domain_unify():
F3 = GF(3)
assert unify(F3, F3) == F3
assert unify(F3, ZZ) == ZZ
assert unify(F3, QQ) == QQ
assert unify(F3, ALG) == ALG
assert unify(F3, RR) == RR
assert unify(F3, CC) == CC
assert unify(F3, ZZ[x]) == ZZ[x]
assert unify(F3, ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(F3, EX) == EX
assert unify(ZZ, F3) == ZZ
assert unify(ZZ, ZZ) == ZZ
assert unify(ZZ, QQ) == QQ
assert unify(ZZ, ALG) == ALG
assert unify(ZZ, RR) == RR
assert unify(ZZ, CC) == CC
assert unify(ZZ, ZZ[x]) == ZZ[x]
assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ, EX) == EX
assert unify(QQ, F3) == QQ
assert unify(QQ, ZZ) == QQ
assert unify(QQ, QQ) == QQ
assert unify(QQ, ALG) == ALG
assert unify(QQ, RR) == RR
assert unify(QQ, CC) == CC
assert unify(QQ, ZZ[x]) == QQ[x]
assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x)
assert unify(QQ, EX) == EX
assert unify(RR, F3) == RR
assert unify(RR, ZZ) == RR
assert unify(RR, QQ) == RR
assert unify(RR, ALG) == RR
assert unify(RR, RR) == RR
assert unify(RR, CC) == CC
assert unify(RR, ZZ[x]) == RR[x]
assert unify(RR, ZZ.frac_field(x)) == RR.frac_field(x)
assert unify(RR, EX) == EX
assert RR[x].unify(ZZ.frac_field(y)) == RR.frac_field(x, y)
assert unify(CC, F3) == CC
assert unify(CC, ZZ) == CC
assert unify(CC, QQ) == CC
assert unify(CC, ALG) == CC
assert unify(CC, RR) == CC
assert unify(CC, CC) == CC
assert unify(CC, ZZ[x]) == CC[x]
assert unify(CC, ZZ.frac_field(x)) == CC.frac_field(x)
assert unify(CC, EX) == EX
assert unify(ZZ[x], F3) == ZZ[x]
assert unify(ZZ[x], ZZ) == ZZ[x]
assert unify(ZZ[x], QQ) == QQ[x]
assert unify(ZZ[x], ALG) == ALG[x]
assert unify(ZZ[x], RR) == RR[x]
assert unify(ZZ[x], CC) == CC[x]
assert unify(ZZ[x], ZZ[x]) == ZZ[x]
assert unify(ZZ[x], ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ[x], EX) == EX
assert unify(ZZ.frac_field(x), F3) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x)
assert unify(ZZ.frac_field(x), ALG) == ALG.frac_field(x)
assert unify(ZZ.frac_field(x), RR) == RR.frac_field(x)
assert unify(ZZ.frac_field(x), CC) == CC.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ[x]) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), EX) == EX
assert unify(EX, F3) == EX
assert unify(EX, ZZ) == EX
assert unify(EX, QQ) == EX
assert unify(EX, ALG) == EX
assert unify(EX, RR) == EX
assert unify(EX, CC) == EX
assert unify(EX, ZZ[x]) == EX
assert unify(EX, ZZ.frac_field(x)) == EX
assert unify(EX, EX) == EX
def test_dup_factor_list():
assert dup_factor_list([], ZZ) == (ZZ(0), [])
assert dup_factor_list([], QQ) == (QQ(0), [])
assert dup_factor_list([], ZZ['y']) == (DMP([], ZZ), [])
assert dup_factor_list([], QQ['y']) == (DMP([], QQ), [])
assert dup_factor_list_include([], ZZ) == [([], 1)]
assert dup_factor_list([ZZ(7)], ZZ) == (ZZ(7), [])
assert dup_factor_list([QQ(1, 7)], QQ) == (QQ(1, 7), [])
assert dup_factor_list([DMP([ZZ(7)], ZZ)], ZZ['y']) == (DMP([ZZ(7)],
ZZ), [])
assert dup_factor_list([DMP([QQ(1, 7)], QQ)], QQ['y']) == (DMP([QQ(1, 7)],
QQ), [])
assert dup_factor_list_include([ZZ(7)], ZZ) == [([ZZ(7)], 1)]
assert dup_factor_list([ZZ(1),ZZ(2),ZZ(1)], ZZ) == \
(ZZ(1), [([ZZ(1), ZZ(1)], 2)])
assert dup_factor_list([QQ(1,2),QQ(1),QQ(1,2)], QQ) == \
(QQ(1,2), [([QQ(1),QQ(1)], 2)])
assert dup_factor_list_include([ZZ(1),ZZ(2),ZZ(1)], ZZ) == \
[([ZZ(1), ZZ(1)], 2)]
K = FF(2)
assert dup_factor_list([K(1),K(0),K(1)], K) == \
(K(1), [([K(1), K(1)], 2)])
assert dup_factor_list([RR(1.0),RR(2.0),RR(1.0)], RR) == \
(RR(1.0), [([RR(1.0),RR(1.0)], 2)])
assert dup_factor_list([RR(2.0),RR(4.0),RR(2.0)], RR) == \
(RR(2.0), [([RR(1.0),RR(1.0)], 2)])
f = [DMP([ZZ(4), ZZ(0)], ZZ), DMP([ZZ(4), ZZ(0), ZZ(0)], ZZ), DMP([], ZZ)]
assert dup_factor_list(f, ZZ['y']) == \
(DMP([ZZ(4)],ZZ), [([DMP([ZZ(1),ZZ(0)],ZZ)], 1),
([DMP([ZZ(1)],ZZ),DMP([],ZZ)], 1),
([DMP([ZZ(1)],ZZ),DMP([ZZ(1),ZZ(0)],ZZ)], 1)])
f = [
DMP([QQ(1, 2), QQ(0)], ZZ),
DMP([QQ(1, 2), QQ(0), QQ(0)], ZZ),
DMP([], ZZ)
]
assert dup_factor_list(f, QQ['y']) == \
(DMP([QQ(1,2)],QQ), [([DMP([QQ(1),QQ(0)],QQ)], 1),
([DMP([QQ(1)],QQ),DMP([],QQ)], 1),
([DMP([QQ(1)],QQ),DMP([QQ(1),QQ(0)],QQ)], 1)])
K = QQ.algebraic_field(I)
h = [QQ(1, 1), QQ(0, 1), QQ(1, 1)]
f = [
ANP([QQ(1, 1)], h, QQ),
ANP([], h, QQ),
ANP([QQ(2, 1)], h, QQ),
ANP([], h, QQ),
ANP([], h, QQ)
]
assert dup_factor_list(f, K) == \
(ANP([QQ(1,1)], h, QQ), [([ANP([QQ(1,1)], h, QQ), ANP([], h, QQ)], 2),
([ANP([QQ(1,1)], h, QQ), ANP([], h, QQ), ANP([QQ(2,1)], h, QQ)], 1)])
raises(DomainError, "dup_factor_list([EX(sin(1))], EX)")
def test_RealField_from_sympy():
assert RR.convert(S(0)) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S(1)) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
assert RR.convert(oo) == RR("+inf")
assert RR.convert(-oo) == RR("-inf")
raises(CoercionFailed, lambda: RR.convert(x))
def test_construct_domain():
assert construct_domain([1, 2, 3]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([1, 2, 3], field=True) == (QQ, [QQ(1), QQ(2), QQ(3)])
assert construct_domain([S(1), S(2), S(3)]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([S(1), S(2), S(3)], field=True) == (QQ, [QQ(1), QQ(2), QQ(3)])
assert construct_domain([S(1)/2, S(2)]) == (QQ, [QQ(1, 2), QQ(2)])
result = construct_domain([3.14, 1, S(1)/2])
assert isinstance(result[0], RealField)
assert result[1] == [RR(3.14), RR(1.0), RR(0.5)]
assert construct_domain([3.14, sqrt(2)], extension=None) == (EX, [EX(3.14), EX(sqrt(2))])
assert construct_domain([3.14, sqrt(2)], extension=True) == (EX, [EX(3.14), EX(sqrt(2))])
assert construct_domain([1, sqrt(2)], extension=None) == (EX, [EX(1), EX(sqrt(2))])
assert construct_domain([x, sqrt(x)]) == (EX, [EX(x), EX(sqrt(x))])
assert construct_domain([x, sqrt(x), sqrt(y)]) == (EX, [EX(x), EX(sqrt(x)), EX(sqrt(y))])
alg = QQ.algebraic_field(sqrt(2))
assert construct_domain([7, S(1)/2, sqrt(2)], extension=True) == \
(alg, [alg.convert(7), alg.convert(S(1)/2), alg.convert(sqrt(2))])
alg = QQ.algebraic_field(sqrt(2) + sqrt(3))
assert construct_domain([7, sqrt(2), sqrt(3)], extension=True) == \
(alg, [alg.convert(7), alg.convert(sqrt(2)), alg.convert(sqrt(3))])
dom = ZZ[x]
assert construct_domain([2*x, 3]) == \
(dom, [dom.convert(2*x), dom.convert(3)])
dom = ZZ[x, y]
assert construct_domain([2*x, 3*y]) == \
(dom, [dom.convert(2*x), dom.convert(3*y)])
dom = QQ[x]
assert construct_domain([x/2, 3]) == \
(dom, [dom.convert(x/2), dom.convert(3)])
dom = QQ[x, y]
assert construct_domain([x/2, 3*y]) == \
(dom, [dom.convert(x/2), dom.convert(3*y)])
dom = RR[x]
assert construct_domain([x/2, 3.5]) == \
(dom, [dom.convert(x/2), dom.convert(3.5)])
dom = RR[x, y]
assert construct_domain([x/2, 3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(3.5*y)])
dom = ZZ.frac_field(x)
assert construct_domain([2/x, 3]) == \
(dom, [dom.convert(2/x), dom.convert(3)])
dom = ZZ.frac_field(x, y)
assert construct_domain([2/x, 3*y]) == \
(dom, [dom.convert(2/x), dom.convert(3*y)])
dom = RR.frac_field(x)
assert construct_domain([2/x, 3.5]) == \
(dom, [dom.convert(2/x), dom.convert(3.5)])
dom = RR.frac_field(x, y)
assert construct_domain([2/x, 3.5*y]) == \
(dom, [dom.convert(2/x), dom.convert(3.5*y)])
dom = RealField(prec=336)[x]
assert construct_domain([pi.evalf(100)*x]) == \
(dom, [dom.convert(pi.evalf(100)*x)])
assert construct_domain(2) == (ZZ, ZZ(2))
assert construct_domain(S(2)/3) == (QQ, QQ(2, 3))
assert construct_domain({}) == (ZZ, {})
def test_RealField_from_sympy():
assert RR.convert(S(0)) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S(1)) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
assert RR.convert(oo) == RR("+inf")
assert RR.convert(-oo) == RR("-inf")
raises(CoercionFailed, lambda: RR.convert(x))
def test_RealDomain_from_sympy():
RR = RR_mpmath()
assert RR.convert(S(0)) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S(1)) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
raises(CoercionFailed, lambda: RR.convert(x))
raises(CoercionFailed, lambda: RR.convert(oo))
raises(CoercionFailed, lambda: RR.convert(-oo))
RR = RR_sympy()
assert RR.convert(S(0)) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S(1)) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
assert RR.n(3, 2) == RR.evalf(3, 2) == Rational(3).n(2)
raises(CoercionFailed, lambda: RR.convert(x))
raises(CoercionFailed, lambda: RR.convert(oo))
raises(CoercionFailed, lambda: RR.convert(-oo))
def test_RealDomain_from_sympy():
RR = RR_mpmath()
assert RR.convert(S(0)) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S(1)) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
raises(CoercionFailed, "RR.convert(x)")
raises(CoercionFailed, "RR.convert(oo)")
raises(CoercionFailed, "RR.convert(-oo)")
RR = RR_sympy()
assert RR.convert(S(0)) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S(1)) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
raises(CoercionFailed, "RR.convert(x)")
raises(CoercionFailed, "RR.convert(oo)")
raises(CoercionFailed, "RR.convert(-oo)")
def test_RealDomain_from_sympy():
RR = RR_mpmath()
assert RR.convert(S(0)) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S(1)) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
raises(CoercionFailed, "RR.convert(x)")
raises(CoercionFailed, "RR.convert(oo)")
raises(CoercionFailed, "RR.convert(-oo)")
RR = RR_sympy()
assert RR.convert(S(0)) == RR.dtype(0)
assert RR.convert(S(0.0)) == RR.dtype(0.0)
assert RR.convert(S(1)) == RR.dtype(1)
assert RR.convert(S(1.0)) == RR.dtype(1.0)
assert RR.convert(sin(1)) == RR.dtype(sin(1).evalf())
raises(CoercionFailed, "RR.convert(x)")
raises(CoercionFailed, "RR.convert(oo)")
raises(CoercionFailed, "RR.convert(-oo)")