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_RR_Float():
f1 = Float("1.01")
f2 = Float("1.0000000000000000000001")
assert f1._prec == 53
assert f2._prec == 80
assert RR(f1)-1 > 1e-50
assert RR(f2)-1 < 1e-50 # RR's precision is lower than f2's
RR2 = RealField(prec=f2._prec)
assert RR2(f1)-1 > 1e-50
assert RR2(f2)-1 > 1e-50 # RR's precision is equal to f2's
def test_RR_double():
assert RR(3.14) > 1e-50
assert RR(1e-13) > 1e-50
assert RR(1e-14) > 1e-50
assert RR(1e-15) > 1e-50
assert RR(1e-20) > 1e-50
assert RR(1e-40) > 1e-50
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_issue_18278():
assert str(RR(2).parent()) == 'RR'
assert str(CC(2).parent()) == 'CC'
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, [(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, [(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, [(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, [(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_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)]
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 = 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(Rational(2, 3)) == (QQ, QQ(2, 3))
assert construct_domain({}) == (ZZ, {})
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_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_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(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)])
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), [])
R, x, y = ring("x,y", ZZ['y'])
assert R.dmp_factor_list(0) == (DMP([], ZZ), [])
assert R.dmp_factor_list(DMP([ZZ(7)], ZZ)) == (DMP([ZZ(7)], ZZ), [])
R, x, y = ring("x,y", QQ['y'])
assert R.dmp_factor_list(0) == (DMP([], QQ), [])
assert R.dmp_factor_list(DMP([QQ(1, 7)], QQ)) == (DMP([QQ(1, 7)], QQ), [])
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)])
R, x, y = ring("x,y", ZZ['t'])
f = DMP([ZZ(4), ZZ(0)], ZZ) * x**2 + DMP([ZZ(4), ZZ(0), ZZ(0)], ZZ) * x
assert R.dmp_factor_list(f) == \
(DMP([ZZ(4)], ZZ), [(DMP([ZZ(1), ZZ(0)], ZZ), 1),
(DMP([ZZ(1)], ZZ)*x, 1),
(DMP([ZZ(1)], ZZ)*x + DMP([ZZ(1), ZZ(0)], ZZ), 1)])
R, x, y = ring("x,y", QQ['t'])
f = DMP([QQ(1, 2), QQ(0)], QQ) * x**2 + DMP(
[QQ(1, 2), QQ(0), QQ(0)], QQ) * x
assert R.dmp_factor_list(f) == \
(DMP([QQ(1, 2)], QQ), [(DMP([QQ(1), QQ(0)], QQ), 1),
(DMP([QQ(1)], QQ)*x, 1),
(DMP([QQ(1)], QQ)*x + DMP([QQ(1), QQ(0)], QQ), 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))))
