def test_PolyRing():
assert srepr(ring("x", ZZ, lex)[0]) == "PolyRing((Symbol('x'),), ZZ, lex)"
assert srepr(
ring("x,y", QQ,
grlex)[0]) == "PolyRing((Symbol('x'), Symbol('y')), QQ, grlex)"
assert srepr(
ring("x,y,z", ZZ["t"], lex)
[0]) == "PolyRing((Symbol('x'), Symbol('y'), Symbol('z')), ZZ[t], lex)"
def test_PolyRing():
assert str(ring("x", ZZ,
lex)[0]) == "Polynomial ring in x over ZZ with lex order"
assert str(
ring("x,y", QQ,
grlex)[0]) == "Polynomial ring in x, y over QQ with grlex order"
assert str(
ring("x,y,z", ZZ["t"],
lex)[0]) == "Polynomial ring in x, y, z over ZZ[t] with lex order"
def test_PolyRing():
sT(ring("x", ZZ, lex)[0], "PolyRing((Symbol('x'),), "
"%s, LexOrder())" % repr(ZZ))
sT(ring("x,y", QQ, grlex)[0], "PolyRing((Symbol('x'), Symbol('y')), "
"%s, GradedLexOrder())" % repr(QQ))
sT(ring("x,y,z", ZZ["t"], lex)[0],
"PolyRing((Symbol('x'), Symbol('y'), Symbol('z')), "
"PolynomialRing(PolyRing((Symbol('t'),), "
"%s, LexOrder())), LexOrder())" % repr(ZZ))
def test_FractionField_from_PolynomialRing():
R, x, y = ring("x,y", QQ)
F, X, Y = field("x,y", ZZ)
f = 3 * x**2 + 5 * y**2
g = x**2 / 3 + y**2 / 5
assert F.convert(f, R) == 3 * X**2 + 5 * Y**2
assert F.convert(g, R) == (5 * X**2 + 3 * Y**2) / 15
RALG, u, v = ring("u,v", ALG)
pytest.raises(CoercionFailed,
lambda: F.convert(3 * u**2 + 5 * sqrt(2) * v**2))
def test_FractionField_from_PolynomialRing():
R, x, y = ring("x,y", QQ)
F, X, Y = field("x,y", ZZ)
f = 3*x**2 + 5*y**2
g = x**2/3 + y**2/5
assert F.convert(f, R) == 3*X**2 + 5*Y**2
assert F.convert(g, R) == (5*X**2 + 3*Y**2)/15
RALG, u, v = ring("u,v", ALG)
pytest.raises(CoercionFailed,
lambda: F.convert(3*u**2 + 5*sqrt(2)*v**2))
def test_PolyElement():
Ruv, u, v = ring("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Ruv)
assert str(x - x) == "0"
assert str(x - 1) == "x - 1"
assert str(x + 1) == "x + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + u + 1) == "(u**2 + 3*u*v + 1)*x**2*y + u + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1"
assert str((-u**2 + 3*u*v - 1)*x**2*y - (u + 1)*x - 1) == "-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1"
assert str(-(v**2 + v + 1)*x + 3*u*v + 1) == "-(v**2 + v + 1)*x + 3*u*v + 1"
assert str(-(v**2 + v + 1)*x - 3*u*v + 1) == "-(v**2 + v + 1)*x - 3*u*v + 1"
def test_PolyElement():
R, x, y = ring("x,y", ZZ)
g = R.domain.dtype
assert srepr(3 * x**2 * y +
1) == ("PolyElement(PolyRing((Symbol('x'), "
"Symbol('y')), ZZ, lex), [((2, 1), %s), "
"((0, 0), %s)])" % (repr(g(3)), repr(g(1))))
def test_PolyElement():
R, x, y = ring("x,y", ZZ)
g = R.domain.dtype
assert repr(3 * x**2 * y +
1) == ("PolyElement(PolynomialRing(%s, (Symbol('x'), "
"Symbol('y')), LexOrder()), [((2, 1), "
"%s), ((0, 0), %s)])" %
(repr(ZZ), repr(g(3)), repr(g(1))))
def test_PolyElement():
R, x, y = ring("x,y", ZZ)
g = R.domain.dtype
assert repr(3*x**2*y + 1) == ("PolyElement(PolynomialRing(%s, (Symbol('x'), "
"Symbol('y')), LexOrder()), [((2, 1), "
"%s), ((0, 0), %s)])" % (repr(ZZ),
repr(g(3)),
repr(g(1))))
def test_PolyElement():
Ruv, u, v = ring("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Ruv)
assert str(x - x) == "0"
assert str(x - 1) == "x - 1"
assert str(x + 1) == "x + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + u + 1) == "(u**2 + 3*u*v + 1)*x**2*y + u + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1"
assert str((-u**2 + 3*u*v - 1)*x**2*y - (u + 1)*x - 1) == "-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1"
assert str(-(v**2 + v + 1)*x + 3*u*v + 1) == "-(v**2 + v + 1)*x + 3*u*v + 1"
assert str(-(v**2 + v + 1)*x - 3*u*v + 1) == "-(v**2 + v + 1)*x - 3*u*v + 1"
K, t = field('t', ZZ)
R, x = ring('x', K)
assert str(x/t) == '1/t*x'
def test_PolynomialRing_from_FractionField():
F, x, y = field("x,y", ZZ)
R, X, Y = ring("x,y", ZZ)
f = (x**2 + y**2) / (x + 1)
g = (x**2 + y**2) / 4
h = x**2 + y**2
pytest.raises(CoercionFailed, lambda: R.convert(f, F))
pytest.raises(CoercionFailed, lambda: R.convert(g, F))
assert R.convert(h, F) == X**2 + Y**2
F, x, y = field("x,y", QQ)
R, X, Y = ring("x,y", QQ)
f = (x**2 + y**2) / (x + 1)
g = (x**2 + y**2) / 4
h = x**2 + y**2
pytest.raises(CoercionFailed, lambda: R.convert(f, F))
assert R.convert(g, F) == X**2 / 4 + Y**2 / 4
assert R.convert(h, F) == X**2 + Y**2
def test_PolynomialRing_from_FractionField():
F, x, y = field("x,y", ZZ)
R, X, Y = ring("x,y", ZZ)
f = (x**2 + y**2)/(x + 1)
g = (x**2 + y**2)/4
h = x**2 + y**2
pytest.raises(CoercionFailed, lambda: R.convert(f, F))
assert R.convert(g, F) == X**2/4 + Y**2/4
assert R.convert(h, F) == X**2 + Y**2
F, x, y = field("x,y", QQ)
R, X, Y = ring("x,y", QQ)
f = (x**2 + y**2)/(x + 1)
g = (x**2 + y**2)/4
h = x**2 + y**2
pytest.raises(CoercionFailed, lambda: R.convert(f, F))
assert R.convert(g, F) == X**2/4 + Y**2/4
assert R.convert(h, F) == X**2 + Y**2
def test_Domain_convert():
assert QQ.convert(10e-52) == QQ(
1684996666696915,
1684996666696914987166688442938726917102321526408785780068975640576)
R, x = ring("x", ZZ)
assert ZZ.convert(x - x) == 0
assert ZZ.convert(x - x, R) == 0
F3 = FF(3)
assert F3.convert(Float(2.0)) == F3.dtype(2)
assert F3.convert(PythonRational(2, 1)) == F3.dtype(2)
pytest.raises(CoercionFailed, lambda: F3.convert(PythonRational(1, 2)))
assert F3.convert(2.0) == F3.dtype(2)
pytest.raises(CoercionFailed, lambda: F3.convert(2.1))
assert RR.convert(CC(1)) == RR(1)
pytest.raises(CoercionFailed, lambda: RR.convert(CC(1, 2)))
assert QQ.convert(ALG(1), ALG) == QQ(1)
pytest.raises(CoercionFailed, lambda: QQ.convert(ALG([1, 1]), ALG))
assert ZZ.convert(ALG(1), ALG) == ZZ(1)
pytest.raises(CoercionFailed, lambda: ZZ.convert(ALG([1, 1]), ALG))
assert EX.convert(ALG([1, 1]), ALG) == sqrt(2) + sqrt(3) + 1
ALG2 = QQ.algebraic_field(sqrt(2))
a2 = ALG2.convert(sqrt(2))
a = ALG.convert(a2, ALG2)
assert a.rep.to_dense() == [QQ(1, 2), 0, -QQ(9, 2), 0]
assert RR.convert(a) == RR(1.4142135623730951)
assert CC.convert(a) == CC(1.4142135623730951)
assert ZZ_python.convert(3.0) == ZZ_python.dtype(3)
pytest.raises(CoercionFailed, lambda: ZZ_python.convert(3.2))
assert CC.convert(QQ_python(1, 2)) == CC(0.5)
CC01 = ComplexField(tol=0.1)
assert CC.convert(CC01(0.3)) == CC(0.3)
assert RR.convert(complex(2 + 0j)) == RR(2)
pytest.raises(CoercionFailed, lambda: RR.convert(complex(2 + 3j)))
assert ALG.convert(EX(sqrt(2)), EX) == ALG.from_expr(sqrt(2))
pytest.raises(CoercionFailed, lambda: ALG.convert(EX(sqrt(5)), EX))
pytest.raises(CoercionFailed, lambda: ALG2.convert(ALG.unit))
def test_Domain_convert():
assert QQ.convert(10e-52) == QQ(1684996666696915, 1684996666696914987166688442938726917102321526408785780068975640576)
R, x = ring("x", ZZ)
assert ZZ.convert(x - x) == 0
assert ZZ.convert(x - x, R) == 0
F3 = FF(3)
assert F3.convert(Float(2.0)) == F3.dtype(2)
assert F3.convert(PythonRational(2, 1)) == F3.dtype(2)
pytest.raises(CoercionFailed, lambda: F3.convert(PythonRational(1, 2)))
assert F3.convert(2.0) == F3.dtype(2)
pytest.raises(CoercionFailed, lambda: F3.convert(2.1))
assert RR.convert(CC(1)) == RR(1)
pytest.raises(CoercionFailed, lambda: RR.convert(CC(1, 2)))
assert QQ.convert(ALG.new(1), ALG) == QQ(1)
pytest.raises(CoercionFailed, lambda: QQ.convert(ALG.new([1, 1]), ALG))
assert ZZ.convert(ALG.new(1), ALG) == ZZ(1)
pytest.raises(CoercionFailed, lambda: ZZ.convert(ALG.new([1, 1]), ALG))
assert EX.convert(ALG.new([1, 1]), ALG) == sqrt(2) + sqrt(3) + 1
ALG2 = QQ.algebraic_field(sqrt(2))
a2 = ALG2.convert(sqrt(2))
a = ALG.convert(a2, ALG2)
assert a.rep.to_dense() == [QQ(1, 2), 0, -QQ(9, 2), 0]
assert ZZ_python.convert(3.0) == ZZ_python.dtype(3)
pytest.raises(CoercionFailed, lambda: ZZ_python.convert(3.2))
assert CC.convert(QQ_python(1, 2)) == CC(0.5)
CC01 = ComplexField(tol=0.1)
assert CC.convert(CC01(0.3)) == CC(0.3)
assert RR.convert(complex(2 + 0j)) == RR(2)
pytest.raises(CoercionFailed, lambda: RR.convert(complex(2 + 3j)))
assert ALG.convert(EX(sqrt(2)), EX) == ALG.from_expr(sqrt(2))
pytest.raises(CoercionFailed, lambda: ALG.convert(EX(sqrt(5)), EX))
pytest.raises(CoercionFailed, lambda: ALG2.convert(ALG.unit))
