Python QQ.poly_ring示例

示例#1

文件： test_homomorphisms.py 项目： StefenYin/sympy

def test_properties():
    R = QQ[x, y]
    F = R.free_module(2)
    h = homomorphism(F, F, [[x, 0], [y, 0]])
    assert h.kernel() == F.submodule([-y, x])
    assert h.image() == F.submodule([x, 0], [y, 0])
    assert not h.is_injective()
    assert not h.is_surjective()
    assert h.restrict_codomain(h.image()).is_surjective()
    assert h.restrict_domain(F.submodule([1, 0])).is_injective()
    assert h.quotient_domain(h.kernel()).restrict_codomain(h.image()).is_isomorphism()

    R2 = QQ.poly_ring(x, y, order=(("lex", x), ("ilex", y))) / [x**2 + 1]
    F = R2.free_module(2)
    h = homomorphism(F, F, [[x, 0], [y, y + 1]])
    assert h.is_isomorphism()

示例#2

def test_properties():
    R = QQ[x, y]
    F = R.free_module(2)
    h = homomorphism(F, F, [[x, 0], [y, 0]])
    assert h.kernel() == F.submodule([-y, x])
    assert h.image() == F.submodule([x, 0], [y, 0])
    assert not h.is_injective()
    assert not h.is_surjective()
    assert h.restrict_codomain(h.image()).is_surjective()
    assert h.restrict_domain(F.submodule([1, 0])).is_injective()
    assert h.quotient_domain(h.kernel()).restrict_codomain(
        h.image()).is_isomorphism()

    R2 = QQ.poly_ring(x, y, order=(("lex", x), ("ilex", y))) / [x**2 + 1]
    F = R2.free_module(2)
    h = homomorphism(F, F, [[x, 0], [y, y + 1]])
    assert h.is_isomorphism()

示例#3

文件： test_quotientring.py 项目： vperic/sympy

def test_QuotientRing():
    I = QQ[x].ideal(x**2 + 1)
    R = QQ[x] / I

    assert R == QQ[x] / [x**2 + 1]
    assert R == QQ[x] / QQ[x].ideal(x**2 + 1)
    assert R != QQ[x]

    assert R.convert(1) / x == -x + I
    assert -1 + I == x**2 + I
    assert R.convert(1, ZZ) == 1 + I
    assert R.convert(R.convert(x), R) == R.convert(x)

    X = R.convert(x)
    Y = QQ[x].convert(x)
    assert -1 + I == X**2 + I
    assert -1 + I == Y**2 + I
    assert R.to_sympy(X) == x

    raises(ValueError, lambda: QQ[x] / QQ[x, y].ideal(x))

    R = QQ.poly_ring(x, order="ilex")
    I = R.ideal(x)
    assert R.convert(1) + I == (R / I).convert(1)

示例#4

文件： test_quotientring.py 项目： StefenYin/sympy

def test_QuotientRing():
    I = QQ[x].ideal(x**2 + 1)
    R = QQ[x]/I

    assert R == QQ[x]/[x**2 + 1]
    assert R == QQ[x]/QQ[x].ideal(x**2 + 1)
    assert R != QQ[x]

    assert R.convert(1)/x == -x + I
    assert -1 + I == x**2 + I
    assert R.convert(1, ZZ) == 1 + I
    assert R.convert(R.convert(x), R) == R.convert(x)

    X = R.convert(x)
    Y = QQ[x].convert(x)
    assert -1 + I == X**2 + I
    assert -1 + I == Y**2 + I
    assert R.to_sympy(X) == x

    raises(ValueError, lambda: QQ[x]/QQ[x, y].ideal(x))

    R = QQ.poly_ring(x, order="ilex")
    I = R.ideal(x)
    assert R.convert(1) + I == (R/I).convert(1)