def test_FracElement(): Fuv, u, v = field("u,v", ZZ) Fxyzt, x, y, z, t = field("x,y,z,t", Fuv) assert str(x - x) == "0" assert str(x - 1) == "x - 1" assert str(x + 1) == "x + 1" assert str(x / 3) == "x/3" assert str(x / z) == "x/z" assert str(x * y / z) == "x*y/z" assert str(x / (z * t)) == "x/(z*t)" assert str(x * y / (z * t)) == "x*y/(z*t)" assert str((x - 1) / y) == "(x - 1)/y" assert str((x + 1) / y) == "(x + 1)/y" assert str((-x - 1) / y) == "(-x - 1)/y" assert str((x + 1) / (y * z)) == "(x + 1)/(y*z)" assert str(-y / (x + 1)) == "-y/(x + 1)" assert str(y * z / (x + 1)) == "y*z/(x + 1)" assert str(((u + 1) * x * y + 1) / ((v - 1) * z - 1)) == "((u + 1)*x*y + 1)/((v - 1)*z - 1)" assert str(((u + 1) * x * y + 1) / ((v - 1) * z - t * u * v - 1)) == "((u + 1)*x*y + 1)/((v - 1)*z - u*v*t - 1)"
def test_FracField(): sT(field("x", ZZ, lex)[0], "FracField((Symbol('x'),), " "%s, LexOrder())" % repr(ZZ)) sT(field("x,y", QQ, grlex)[0], "FracField((Symbol('x'), Symbol('y')), " "%s, GradedLexOrder())" % repr(QQ)) sT(field("x,y,z", ZZ["t"], lex)[0], "FracField((Symbol('x'), Symbol('y'), Symbol('z')), " "PolynomialRing(PolyRing((Symbol('t'),), %s, " "LexOrder())), LexOrder())" % repr(ZZ))
def test_FracField(): assert srepr(field("x", ZZ, lex)[0]) == "FracField((Symbol('x'),), ZZ, lex)" assert srepr( field("x,y", QQ, grlex)[0]) == "FracField((Symbol('x'), Symbol('y')), QQ, grlex)" assert srepr( field("x,y,z", ZZ["t"], lex)[0] ) == "FracField((Symbol('x'), Symbol('y'), Symbol('z')), ZZ[t], lex)"
def test_FracField(): assert str( field("x", ZZ, lex)[0]) == "Rational function field in x over ZZ with lex order" assert str( field("x,y", QQ, grlex) [0]) == "Rational function field in x, y over QQ with grlex order" assert str( field("x,y,z", ZZ["t"], lex) [0]) == "Rational function field in x, y, z over ZZ[t] with lex order"
def test_FracElement(): F, x, y = field("x,y", ZZ) g = F.domain.dtype assert repr((3 * x**2 * y + 1) / (x - y**2)) == ( "FracElement(FractionField(%s, (Symbol('x'), " "Symbol('y')), LexOrder()), [((2, 1), %s), " "((0, 0), %s)], [((1, 0), %s), " "((0, 2), %s)])" % (repr(ZZ), repr(g(3)), repr(g(1)), repr(g(1)), repr(g(-1))))
def test_FracElement(): F, x, y = field("x,y", ZZ) g = F.domain.dtype assert srepr( (3 * x**2 * y + 1) / (x - y**2)) == ("FracElement(FracField((Symbol('x'), " "Symbol('y')), ZZ, lex), [((2, 1), %s), " "((0, 0), %s)], [((1, 0), %s), " "((0, 2), %s)])" % (repr(g(3)), repr(g(1)), repr(g(1)), repr(g(-1))))
def test_FracElement(): F, x, y = field("x,y", ZZ) g = F.domain.dtype assert repr((3*x**2*y + 1)/(x - y**2)) == ("FracElement(FractionField(%s, (Symbol('x'), " "Symbol('y')), LexOrder()), [((2, 1), %s), " "((0, 0), %s)], [((1, 0), %s), " "((0, 2), %s)])" % (repr(ZZ), repr(g(3)), repr(g(1)), repr(g(1)), repr(g(-1))))
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_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_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_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_FracElement(): Fuv, u, v = field("u,v", ZZ) Fxyzt, x, y, z, t = field("x,y,z,t", Fuv) assert str(x - x) == "0" assert str(x - 1) == "x - 1" assert str(x + 1) == "x + 1" assert str(x/3) == "x/3" assert str(x/z) == "x/z" assert str(x*y/z) == "x*y/z" assert str(x/(z*t)) == "x/(z*t)" assert str(x*y/(z*t)) == "x*y/(z*t)" assert str((x - 1)/y) == "(x - 1)/y" assert str((x + 1)/y) == "(x + 1)/y" assert str((-x - 1)/y) == "(-x - 1)/y" assert str((x + 1)/(y*z)) == "(x + 1)/(y*z)" assert str(-y/(x + 1)) == "-y/(x + 1)" assert str(y*z/(x + 1)) == "y*z/(x + 1)" assert str(((u + 1)*x*y + 1)/((v - 1)*z - 1)) == "((u + 1)*x*y + 1)/((v - 1)*z - 1)" assert str(((u + 1)*x*y + 1)/((v - 1)*z - t*u*v - 1)) == "((u + 1)*x*y + 1)/((v - 1)*z - u*v*t - 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_FractionField_convert(): F, X, Y = field("x,y", QQ) F.convert(QQ_python(1, 3)) == F.one / 3
def test_FractionField_convert(): F, X, Y = field("x,y", QQ) F.convert(QQ_python(1, 3)) == F.one/3