Python ZZ.old_poly_ring Examples

Example #1

File: test_repr.py Project: KonstantinTogoi/sympy

def test_PolynomialRingBase():
    assert srepr(ZZ.old_poly_ring(x)) == \
        "GlobalPolynomialRing(ZZ, Symbol('x'))"
    assert srepr(ZZ[x].old_poly_ring(y)) == \
        "GlobalPolynomialRing(ZZ[x], Symbol('y'))"
    assert srepr(QQ.frac_field(x).old_poly_ring(y)) == \
        "GlobalPolynomialRing(FractionField(FracField((Symbol('x'),), QQ, lex)), Symbol('y'))"

Example #2

def test_PolynomialRingBase():
    assert srepr(ZZ.old_poly_ring(x)) == \
        "GlobalPolynomialRing(ZZ, Symbol('x'))"
    assert srepr(ZZ[x].old_poly_ring(y)) == \
        "GlobalPolynomialRing(ZZ[x], Symbol('y'))"
    assert srepr(QQ.frac_field(x).old_poly_ring(y)) == \
        "GlobalPolynomialRing(FractionField(FracField((Symbol('x'),), QQ, lex)), Symbol('y'))"

Example #3

def test_FreeModule():
    M1 = FreeModule(QQ.old_poly_ring(x), 2)
    assert M1 == FreeModule(QQ.old_poly_ring(x), 2)
    assert M1 != FreeModule(QQ.old_poly_ring(y), 2)
    assert M1 != FreeModule(QQ.old_poly_ring(x), 3)
    M2 = FreeModule(QQ.old_poly_ring(x, order="ilex"), 2)

    assert [x, 1] in M1
    assert [x] not in M1
    assert [2, y] not in M1
    assert [1 / (x + 1), 2] not in M1

    e = M1.convert([x, x**2 + 1])
    X = QQ.old_poly_ring(x).convert(x)
    assert e == [X, X**2 + 1]
    assert e == [x, x**2 + 1]
    assert 2 * e == [2 * x, 2 * x**2 + 2]
    assert e * 2 == [2 * x, 2 * x**2 + 2]
    assert e / 2 == [x / 2, (x**2 + 1) / 2]
    assert x * e == [x**2, x**3 + x]
    assert e * x == [x**2, x**3 + x]
    assert X * e == [x**2, x**3 + x]
    assert e * X == [x**2, x**3 + x]

    assert [x, 1] in M2
    assert [x] not in M2
    assert [2, y] not in M2
    assert [1 / (x + 1), 2] in M2

    e = M2.convert([x, x**2 + 1])
    X = QQ.old_poly_ring(x, order="ilex").convert(x)
    assert e == [X, X**2 + 1]
    assert e == [x, x**2 + 1]
    assert 2 * e == [2 * x, 2 * x**2 + 2]
    assert e * 2 == [2 * x, 2 * x**2 + 2]
    assert e / 2 == [x / 2, (x**2 + 1) / 2]
    assert x * e == [x**2, x**3 + x]
    assert e * x == [x**2, x**3 + x]
    assert e / (1 + x) == [x / (1 + x), (x**2 + 1) / (1 + x)]
    assert X * e == [x**2, x**3 + x]
    assert e * X == [x**2, x**3 + x]

    M3 = FreeModule(QQ.old_poly_ring(x, y), 2)
    assert M3.convert(e) == M3.convert([x, x**2 + 1])

    assert not M3.is_submodule(0)
    assert not M3.is_zero()

    raises(NotImplementedError, lambda: ZZ.old_poly_ring(x).free_module(2))
    raises(NotImplementedError, lambda: FreeModulePolyRing(ZZ, 2))
    raises(
        CoercionFailed,
        lambda: M1.convert(
            QQ.old_poly_ring(x).free_module(3).convert([1, 2, 3])),
    )
    raises(CoercionFailed, lambda: M3.convert(1))

Example #4

File: test_modules.py Project: A-turing-machine/sympy

def test_FreeModule():
    M1 = FreeModule(QQ.old_poly_ring(x), 2)
    assert M1 == FreeModule(QQ.old_poly_ring(x), 2)
    assert M1 != FreeModule(QQ.old_poly_ring(y), 2)
    assert M1 != FreeModule(QQ.old_poly_ring(x), 3)
    M2 = FreeModule(QQ.old_poly_ring(x, order="ilex"), 2)

    assert [x, 1] in M1
    assert [x] not in M1
    assert [2, y] not in M1
    assert [1/(x + 1), 2] not in M1

    e = M1.convert([x, x**2 + 1])
    X = QQ.old_poly_ring(x).convert(x)
    assert e == [X, X**2 + 1]
    assert e == [x, x**2 + 1]
    assert 2*e == [2*x, 2*x**2 + 2]
    assert e*2 == [2*x, 2*x**2 + 2]
    assert e/2 == [x/2, (x**2 + 1)/2]
    assert x*e == [x**2, x**3 + x]
    assert e*x == [x**2, x**3 + x]
    assert X*e == [x**2, x**3 + x]
    assert e*X == [x**2, x**3 + x]

    assert [x, 1] in M2
    assert [x] not in M2
    assert [2, y] not in M2
    assert [1/(x + 1), 2] in M2

    e = M2.convert([x, x**2 + 1])
    X = QQ.old_poly_ring(x, order="ilex").convert(x)
    assert e == [X, X**2 + 1]
    assert e == [x, x**2 + 1]
    assert 2*e == [2*x, 2*x**2 + 2]
    assert e*2 == [2*x, 2*x**2 + 2]
    assert e/2 == [x/2, (x**2 + 1)/2]
    assert x*e == [x**2, x**3 + x]
    assert e*x == [x**2, x**3 + x]
    assert e/(1 + x) == [x/(1 + x), (x**2 + 1)/(1 + x)]
    assert X*e == [x**2, x**3 + x]
    assert e*X == [x**2, x**3 + x]

    M3 = FreeModule(QQ.old_poly_ring(x, y), 2)
    assert M3.convert(e) == M3.convert([x, x**2 + 1])

    assert not M3.is_submodule(0)
    assert not M3.is_zero()

    raises(NotImplementedError, lambda: ZZ.old_poly_ring(x).free_module(2))
    raises(NotImplementedError, lambda: FreeModulePolyRing(ZZ, 2))
    raises(CoercionFailed, lambda: M1.convert(QQ.old_poly_ring(x).free_module(3)
           .convert([1, 2, 3])))
    raises(CoercionFailed, lambda: M3.convert(1))

Example #5

File: test_repr.py Project: KonstantinTogoi/sympy

def test_DMP():
    assert srepr(DMP([1, 2], ZZ)) == 'DMP([1, 2], ZZ)'
    assert srepr(ZZ.old_poly_ring(x)([1, 2])) == \
        "DMP([1, 2], ZZ, ring=GlobalPolynomialRing(ZZ, Symbol('x')))"

Example #6

def test_DMP():
    assert srepr(DMP([1, 2], ZZ)) == 'DMP([1, 2], ZZ)'
    assert srepr(ZZ.old_poly_ring(x)([1, 2])) == \
        "DMP([1, 2], ZZ, ring=GlobalPolynomialRing(ZZ, Symbol('x')))"