def test_Domain_get_ring(): assert ZZ.has_assoc_Ring is True assert QQ.has_assoc_Ring is True assert ZZ[x].has_assoc_Ring is True assert QQ[x].has_assoc_Ring is True assert ZZ[x, y].has_assoc_Ring is True assert QQ[x, y].has_assoc_Ring is True assert ZZ.frac_field(x).has_assoc_Ring is True assert QQ.frac_field(x).has_assoc_Ring is True assert ZZ.frac_field(x, y).has_assoc_Ring is True assert QQ.frac_field(x, y).has_assoc_Ring is True assert EX.has_assoc_Ring is False assert RR.has_assoc_Ring is False assert ALG.has_assoc_Ring is False assert ZZ.get_ring() == ZZ assert QQ.get_ring() == ZZ assert ZZ[x].get_ring() == ZZ[x] assert QQ[x].get_ring() == QQ[x] assert ZZ[x, y].get_ring() == ZZ[x, y] assert QQ[x, y].get_ring() == QQ[x, y] assert ZZ.frac_field(x).get_ring() == ZZ[x] assert QQ.frac_field(x).get_ring() == QQ[x] assert ZZ.frac_field(x, y).get_ring() == ZZ[x, y] assert QQ.frac_field(x, y).get_ring() == QQ[x, y] assert EX.get_ring() == EX pytest.raises(DomainError, lambda: RR.get_ring()) pytest.raises(DomainError, lambda: ALG.get_ring())
def test_Domain_preprocess(): assert Domain.preprocess(ZZ) == ZZ assert Domain.preprocess(QQ) == QQ assert Domain.preprocess(EX) == EX assert Domain.preprocess(FF(2)) == FF(2) assert Domain.preprocess(ZZ[x, y]) == ZZ[x, y] assert Domain.preprocess('Z') == ZZ assert Domain.preprocess('Q') == QQ assert Domain.preprocess('ZZ') == ZZ assert Domain.preprocess('QQ') == QQ assert Domain.preprocess('EX') == EX assert Domain.preprocess('FF(23)') == FF(23) assert Domain.preprocess('GF(23)') == GF(23) pytest.raises(OptionError, lambda: Domain.preprocess('Z[]')) assert Domain.preprocess('Z[x]') == ZZ[x] assert Domain.preprocess('Q[x]') == QQ[x] assert Domain.preprocess('ZZ[x]') == ZZ[x] assert Domain.preprocess('QQ[x]') == QQ[x] assert Domain.preprocess('Z[x,y]') == ZZ[x, y] assert Domain.preprocess('Q[x,y]') == QQ[x, y] assert Domain.preprocess('ZZ[x,y]') == ZZ[x, y] assert Domain.preprocess('QQ[x,y]') == QQ[x, y] pytest.raises(OptionError, lambda: Domain.preprocess('Z()')) assert Domain.preprocess('Z(x)') == ZZ.frac_field(x) assert Domain.preprocess('Q(x)') == QQ.frac_field(x) assert Domain.preprocess('ZZ(x)') == ZZ.frac_field(x) assert Domain.preprocess('QQ(x)') == QQ.frac_field(x) assert Domain.preprocess('Z(x,y)') == ZZ.frac_field(x, y) assert Domain.preprocess('Q(x,y)') == QQ.frac_field(x, y) assert Domain.preprocess('ZZ(x,y)') == ZZ.frac_field(x, y) assert Domain.preprocess('QQ(x,y)') == QQ.frac_field(x, y) assert Domain.preprocess('Q<I>') == QQ.algebraic_field(I) assert Domain.preprocess('QQ<I>') == QQ.algebraic_field(I) assert Domain.preprocess('Q<sqrt(2), I>') == QQ.algebraic_field(sqrt(2), I) assert Domain.preprocess('QQ<sqrt(2), I>') == QQ.algebraic_field( sqrt(2), I) pytest.raises(OptionError, lambda: Domain.preprocess('abc'))
def test_Domain___eq__(): assert (ZZ[x, y] == ZZ[x, y]) is True assert (QQ[x, y] == QQ[x, y]) is True assert (ZZ[x, y] == QQ[x, y]) is False assert (QQ[x, y] == ZZ[x, y]) is False assert (ZZ.frac_field(x, y) == ZZ.frac_field(x, y)) is True assert (QQ.frac_field(x, y) == QQ.frac_field(x, y)) is True assert (ZZ.frac_field(x, y) == QQ.frac_field(x, y)) is False assert (QQ.frac_field(x, y) == ZZ.frac_field(x, y)) is False
def test_Domain_get_exact(): assert EX.get_exact() == EX assert ZZ.get_exact() == ZZ assert QQ.get_exact() == QQ assert RR.get_exact() == QQ assert ALG.get_exact() == ALG assert ZZ[x].get_exact() == ZZ[x] assert QQ[x].get_exact() == QQ[x] assert ZZ[x, y].get_exact() == ZZ[x, y] assert QQ[x, y].get_exact() == QQ[x, y] assert ZZ.frac_field(x).get_exact() == ZZ.frac_field(x) assert QQ.frac_field(x).get_exact() == QQ.frac_field(x) assert ZZ.frac_field(x, y).get_exact() == ZZ.frac_field(x, y) assert QQ.frac_field(x, y).get_exact() == QQ.frac_field(x, y)
def test_Domain_get_field(): assert EX.has_assoc_Field is True assert ZZ.has_assoc_Field is True assert QQ.has_assoc_Field is True assert RR.has_assoc_Field is True assert ALG.has_assoc_Field is True assert ZZ[x].has_assoc_Field is True assert QQ[x].has_assoc_Field is True assert ZZ[x, y].has_assoc_Field is True assert QQ[x, y].has_assoc_Field is True assert EX.get_field() == EX assert ZZ.get_field() == QQ assert QQ.get_field() == QQ assert RR.get_field() == RR assert ALG.get_field() == ALG assert ZZ[x].get_field() == ZZ.frac_field(x) assert QQ[x].get_field() == QQ.frac_field(x) assert ZZ[x, y].get_field() == ZZ.frac_field(x, y) assert QQ[x, y].get_field() == QQ.frac_field(x, y)
def test_localring(): Qxy = QQ.frac_field(x, y) R = QQ.poly_ring(x, y, order="ilex") X = R.convert(x) Y = R.convert(y) assert x in R assert 1/x not in R assert Y in R assert X.ring == R.ring assert X + Y == R.convert(x + y) assert X - Y == R.convert(x - y) assert X + 1 == R.convert(x + 1) assert X**2 / X == X assert R.from_PolynomialRing(ZZ.poly_ring(x, y).convert(x), ZZ.poly_ring(x, y)) == X assert R.from_FractionField(Qxy.convert(x), Qxy) == X
def test_globalring(): Qxy = QQ.frac_field(x, y) R = QQ.poly_ring(x, y) X = R.convert(x) Y = R.convert(y) assert x in R assert 1/x not in R assert 1/(1 + x) not in R assert Y in R assert X.ring == R.ring assert X * (Y**2 + 1) == R.convert(x * (y**2 + 1)) assert X * Y == R.convert(x * y) assert X + Y == R.convert(x + y) assert X - Y == R.convert(x - y) assert X + 1 == R.convert(x + 1) assert X**2 / X == X assert R.from_PolynomialRing(ZZ.poly_ring(x, y).convert(x), ZZ.poly_ring(x, y)) == X assert R.from_FractionField(Qxy.convert(x), Qxy) == X
def test___eq__(): assert not QQ[x] == ZZ[x] assert not QQ.frac_field(x) == ZZ.frac_field(x)
def test_Domain_unify(): F3 = GF(3) assert unify(F3, F3) == F3 assert unify(F3, ZZ) == ZZ assert unify(F3, QQ) == QQ assert unify(F3, ALG) == ALG assert unify(F3, RR) == RR assert unify(F3, CC) == CC assert unify(F3, ZZ[x]) == ZZ[x] assert unify(F3, ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(F3, EX) == EX assert unify(ZZ, F3) == ZZ assert unify(ZZ, ZZ) == ZZ assert unify(ZZ, QQ) == QQ assert unify(ZZ, ALG) == ALG assert unify(ZZ, RR) == RR assert unify(ZZ, CC) == CC assert unify(ZZ, ZZ[x]) == ZZ[x] assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ, EX) == EX assert unify(QQ, F3) == QQ assert unify(QQ, ZZ) == QQ assert unify(QQ, QQ) == QQ assert unify(QQ, ALG) == ALG assert unify(QQ, RR) == RR assert unify(QQ, CC) == CC assert unify(QQ, ZZ[x]) == QQ[x] assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ, EX) == EX assert unify(RR, F3) == RR assert unify(RR, ZZ) == RR assert unify(RR, QQ) == RR assert unify(RR, ALG) == RR assert unify(RR, RR) == RR assert unify(RR, CC) == CC assert unify(RR, ZZ[x]) == RR[x] assert unify(RR, ZZ.frac_field(x)) == RR.frac_field(x) assert unify(RR, EX) == EX assert unify(CC, F3) == CC assert unify(CC, ZZ) == CC assert unify(CC, QQ) == CC assert unify(CC, ALG) == CC assert unify(CC, RR) == CC assert unify(CC, CC) == CC assert unify(CC, ZZ[x]) == CC[x] assert unify(CC, ZZ.frac_field(x)) == CC.frac_field(x) assert unify(CC, EX) == EX assert unify(ZZ[x], F3) == ZZ[x] assert unify(ZZ[x], ZZ) == ZZ[x] assert unify(ZZ[x], QQ) == QQ[x] assert unify(ZZ[x], ALG) == ALG[x] assert unify(ZZ[x], RR) == RR[x] assert unify(ZZ[x], CC) == CC[x] assert unify(ZZ[x], ZZ[x]) == ZZ[x] assert unify(ZZ[x], ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ[x], EX) == EX assert unify(ZZ.frac_field(x), F3) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x) assert unify(ZZ.frac_field(x), ALG) == ALG.frac_field(x) assert unify(ZZ.frac_field(x), RR) == RR.frac_field(x) assert unify(ZZ.frac_field(x), CC) == CC.frac_field(x) assert unify(ZZ.frac_field(x), ZZ[x]) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), EX) == EX assert unify(EX, F3) == EX assert unify(EX, ZZ) == EX assert unify(EX, QQ) == EX assert unify(EX, ALG) == EX assert unify(EX, RR) == EX assert unify(EX, CC) == EX assert unify(EX, ZZ[x]) == EX assert unify(EX, ZZ.frac_field(x)) == EX assert unify(EX, EX) == EX
def test_Domain_unify_composite(): assert unify(ZZ.poly_ring(x), ZZ) == ZZ.poly_ring(x) assert unify(ZZ.poly_ring(x), QQ) == QQ.poly_ring(x) assert unify(QQ.poly_ring(x), ZZ) == QQ.poly_ring(x) assert unify(QQ.poly_ring(x), QQ) == QQ.poly_ring(x) assert unify(ZZ, ZZ.poly_ring(x)) == ZZ.poly_ring(x) assert unify(QQ, ZZ.poly_ring(x)) == QQ.poly_ring(x) assert unify(ZZ, QQ.poly_ring(x)) == QQ.poly_ring(x) assert unify(QQ, QQ.poly_ring(x)) == QQ.poly_ring(x) assert unify(ZZ.poly_ring(x, y), ZZ) == ZZ.poly_ring(x, y) assert unify(ZZ.poly_ring(x, y), QQ) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x, y), ZZ) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x, y), QQ) == QQ.poly_ring(x, y) assert unify(ZZ, ZZ.poly_ring(x, y)) == ZZ.poly_ring(x, y) assert unify(QQ, ZZ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(ZZ, QQ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(QQ, QQ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x) assert unify(QQ.frac_field(x), ZZ) == QQ.frac_field(x) assert unify(QQ.frac_field(x), QQ) == QQ.frac_field(x) assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x) assert unify(ZZ, QQ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ, QQ.frac_field(x)) == QQ.frac_field(x) assert unify(ZZ.frac_field(x, y), ZZ) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), QQ) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x, y), ZZ) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x, y), QQ) == QQ.frac_field(x, y) assert unify(ZZ, ZZ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(QQ, ZZ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(ZZ, QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(QQ, QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x)) == ZZ.poly_ring(x) assert unify(ZZ.poly_ring(x), QQ.poly_ring(x)) == QQ.poly_ring(x) assert unify(QQ.poly_ring(x), ZZ.poly_ring(x)) == QQ.poly_ring(x) assert unify(QQ.poly_ring(x), QQ.poly_ring(x)) == QQ.poly_ring(x) assert unify(ZZ.poly_ring(x, y), ZZ.poly_ring(x)) == ZZ.poly_ring(x, y) assert unify(ZZ.poly_ring(x, y), QQ.poly_ring(x)) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x, y), ZZ.poly_ring(x)) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x, y), QQ.poly_ring(x)) == QQ.poly_ring(x, y) assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x, y)) == ZZ.poly_ring(x, y) assert unify(ZZ.poly_ring(x), QQ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x), ZZ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x), QQ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(ZZ.poly_ring(x, y), ZZ.poly_ring(x, z)) == ZZ.poly_ring(x, y, z) assert unify(ZZ.poly_ring(x, y), QQ.poly_ring(x, z)) == QQ.poly_ring(x, y, z) assert unify(QQ.poly_ring(x, y), ZZ.poly_ring(x, z)) == QQ.poly_ring(x, y, z) assert unify(QQ.poly_ring(x, y), QQ.poly_ring(x, z)) == QQ.poly_ring(x, y, z) assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ.frac_field(x), ZZ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ.frac_field(x), QQ.frac_field(x)) == QQ.frac_field(x) assert unify(ZZ.frac_field(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x, y), ZZ.frac_field(x)) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y) assert unify(ZZ.frac_field(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x), ZZ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z) assert unify(ZZ.frac_field(x, y), QQ.frac_field(x, z)) == QQ.frac_field(x, y, z) assert unify(QQ.frac_field(x, y), ZZ.frac_field(x, z)) == QQ.frac_field(x, y, z) assert unify(QQ.frac_field(x, y), QQ.frac_field(x, z)) == QQ.frac_field(x, y, z) assert unify(ZZ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.poly_ring(x), QQ.frac_field(x)) == ZZ.frac_field(x) assert unify(QQ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(QQ.poly_ring(x), QQ.frac_field(x)) == QQ.frac_field(x) assert unify(ZZ.poly_ring(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y) assert unify(ZZ.poly_ring(x, y), QQ.frac_field(x)) == ZZ.frac_field(x, y) assert unify(QQ.poly_ring(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y) assert unify(QQ.poly_ring(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y) assert unify(ZZ.poly_ring(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(ZZ.poly_ring(x), QQ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(QQ.poly_ring(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(QQ.poly_ring(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(ZZ.poly_ring(x, y), ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z) assert unify(ZZ.poly_ring(x, y), QQ.frac_field(x, z)) == ZZ.frac_field(x, y, z) assert unify(QQ.poly_ring(x, y), ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z) assert unify(QQ.poly_ring(x, y), QQ.frac_field(x, z)) == QQ.frac_field(x, y, z) assert unify(ZZ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ.poly_ring(x)) == ZZ.frac_field(x) assert unify(QQ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x) assert unify(QQ.frac_field(x), QQ.poly_ring(x)) == QQ.frac_field(x) assert unify(ZZ.frac_field(x, y), ZZ.poly_ring(x)) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), QQ.poly_ring(x)) == ZZ.frac_field(x, y) assert unify(QQ.frac_field(x, y), ZZ.poly_ring(x)) == ZZ.frac_field(x, y) assert unify(QQ.frac_field(x, y), QQ.poly_ring(x)) == QQ.frac_field(x, y) assert unify(ZZ.frac_field(x), ZZ.poly_ring(x, y)) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x), QQ.poly_ring(x, y)) == ZZ.frac_field(x, y) assert unify(QQ.frac_field(x), ZZ.poly_ring(x, y)) == ZZ.frac_field(x, y) assert unify(QQ.frac_field(x), QQ.poly_ring(x, y)) == QQ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), ZZ.poly_ring(x, z)) == ZZ.frac_field(x, y, z) assert unify(ZZ.frac_field(x, y), QQ.poly_ring(x, z)) == ZZ.frac_field(x, y, z) assert unify(QQ.frac_field(x, y), ZZ.poly_ring(x, z)) == ZZ.frac_field(x, y, z) assert unify(QQ.frac_field(x, y), QQ.poly_ring(x, z)) == QQ.frac_field(x, y, z)
def test_poly_frac(): pytest.raises(GeneratorsNeeded, lambda: QQ.poly_ring()) pytest.raises(GeneratorsNeeded, lambda: QQ.frac_field())