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))