def test_construct_domain():
assert construct_domain([1, 2, 3]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([1, 2, 3], field=True) == (QQ, [QQ(1), QQ(2), QQ(3)])
assert construct_domain([S.One, S(2), S(3)]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([S.One, S(2), S(3)], field=True) == (QQ, [QQ(1), QQ(2), QQ(3)])
assert construct_domain([S.Half, S(2)]) == (QQ, [QQ(1, 2), QQ(2)])
result = construct_domain([3.14, 1, S.Half])
assert isinstance(result[0], RealField)
assert result[1] == [RR(3.14), RR(1.0), RR(0.5)]
result = construct_domain([3.14, I, S.Half])
assert isinstance(result[0], ComplexField)
assert result[1] == [CC(3.14), CC(1.0j), CC(0.5)]
assert construct_domain([1, I]) == (ZZ_I, [ZZ_I(1, 0), ZZ_I(0, 1)])
assert construct_domain([1, I/2]) == (QQ_I, [QQ_I(1, 0), QQ_I(0, S.Half)])
assert construct_domain([3.14, sqrt(2)], extension=None) == (EX, [EX(3.14), EX(sqrt(2))])
assert construct_domain([3.14, sqrt(2)], extension=True) == (EX, [EX(3.14), EX(sqrt(2))])
assert construct_domain([1, sqrt(2)], extension=None) == (EX, [EX(1), EX(sqrt(2))])
assert construct_domain([x, sqrt(x)]) == (EX, [EX(x), EX(sqrt(x))])
assert construct_domain([x, sqrt(x), sqrt(y)]) == (EX, [EX(x), EX(sqrt(x)), EX(sqrt(y))])
alg = QQ.algebraic_field(sqrt(2))
assert construct_domain([7, S.Half, sqrt(2)], extension=True) == \
(alg, [alg.convert(7), alg.convert(S.Half), alg.convert(sqrt(2))])
alg = QQ.algebraic_field(sqrt(2) + sqrt(3))
assert construct_domain([7, sqrt(2), sqrt(3)], extension=True) == \
(alg, [alg.convert(7), alg.convert(sqrt(2)), alg.convert(sqrt(3))])
dom = ZZ[x]
assert construct_domain([2*x, 3]) == \
(dom, [dom.convert(2*x), dom.convert(3)])
dom = ZZ[x, y]
assert construct_domain([2*x, 3*y]) == \
(dom, [dom.convert(2*x), dom.convert(3*y)])
dom = QQ[x]
assert construct_domain([x/2, 3]) == \
(dom, [dom.convert(x/2), dom.convert(3)])
dom = QQ[x, y]
assert construct_domain([x/2, 3*y]) == \
(dom, [dom.convert(x/2), dom.convert(3*y)])
dom = ZZ_I[x]
assert construct_domain([2*x, I]) == \
(dom, [dom.convert(2*x), dom.convert(I)])
dom = ZZ_I[x, y]
assert construct_domain([2*x, I*y]) == \
(dom, [dom.convert(2*x), dom.convert(I*y)])
dom = QQ_I[x]
assert construct_domain([x/2, I]) == \
(dom, [dom.convert(x/2), dom.convert(I)])
dom = QQ_I[x, y]
assert construct_domain([x/2, I*y]) == \
(dom, [dom.convert(x/2), dom.convert(I*y)])
dom = RR[x]
assert construct_domain([x/2, 3.5]) == \
(dom, [dom.convert(x/2), dom.convert(3.5)])
dom = RR[x, y]
assert construct_domain([x/2, 3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(3.5*y)])
dom = CC[x]
assert construct_domain([I*x/2, 3.5]) == \
(dom, [dom.convert(I*x/2), dom.convert(3.5)])
dom = CC[x, y]
assert construct_domain([I*x/2, 3.5*y]) == \
(dom, [dom.convert(I*x/2), dom.convert(3.5*y)])
dom = CC[x]
assert construct_domain([x/2, I*3.5]) == \
(dom, [dom.convert(x/2), dom.convert(I*3.5)])
dom = CC[x, y]
assert construct_domain([x/2, I*3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(I*3.5*y)])
dom = ZZ.frac_field(x)
assert construct_domain([2/x, 3]) == \
(dom, [dom.convert(2/x), dom.convert(3)])
dom = ZZ.frac_field(x, y)
assert construct_domain([2/x, 3*y]) == \
(dom, [dom.convert(2/x), dom.convert(3*y)])
dom = RR.frac_field(x)
assert construct_domain([2/x, 3.5]) == \
(dom, [dom.convert(2/x), dom.convert(3.5)])
dom = RR.frac_field(x, y)
assert construct_domain([2/x, 3.5*y]) == \
(dom, [dom.convert(2/x), dom.convert(3.5*y)])
dom = RealField(prec=336)[x]
assert construct_domain([pi.evalf(100)*x]) == \
(dom, [dom.convert(pi.evalf(100)*x)])
assert construct_domain(2) == (ZZ, ZZ(2))
assert construct_domain(S(2)/3) == (QQ, QQ(2, 3))
assert construct_domain(Rational(2, 3)) == (QQ, QQ(2, 3))
assert construct_domain({}) == (ZZ, {})
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 RR[x].unify(ZZ.frac_field(y)) == RR.frac_field(x, y)
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_CC_double():
assert CC(3.14).real > 1e-50
assert CC(1e-13).real > 1e-50
assert CC(1e-14).real > 1e-50
assert CC(1e-15).real > 1e-50
assert CC(1e-20).real > 1e-50
assert CC(1e-40).real > 1e-50
assert CC(3.14j).imag > 1e-50
assert CC(1e-13j).imag > 1e-50
assert CC(1e-14j).imag > 1e-50
assert CC(1e-15j).imag > 1e-50
assert CC(1e-20j).imag > 1e-50
assert CC(1e-40j).imag > 1e-50
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(ZZ_I, F3) == ZZ_I
assert unify(ZZ_I, ZZ) == ZZ_I
assert unify(ZZ_I, ZZ_I) == ZZ_I
assert unify(ZZ_I, QQ) == QQ_I
assert unify(ZZ_I, ALG) == QQ.algebraic_field(I, sqrt(2), sqrt(3))
assert unify(ZZ_I, RR) == CC
assert unify(ZZ_I, CC) == CC
assert unify(ZZ_I, ZZ[x]) == ZZ_I[x]
assert unify(ZZ_I, ZZ_I[x]) == ZZ_I[x]
assert unify(ZZ_I, ZZ.frac_field(x)) == ZZ_I.frac_field(x)
assert unify(ZZ_I, ZZ_I.frac_field(x)) == ZZ_I.frac_field(x)
assert unify(ZZ_I, EX) == EX
assert unify(QQ_I, F3) == QQ_I
assert unify(QQ_I, ZZ) == QQ_I
assert unify(QQ_I, ZZ_I) == QQ_I
assert unify(QQ_I, QQ) == QQ_I
assert unify(QQ_I, ALG) == QQ.algebraic_field(I, sqrt(2), sqrt(3))
assert unify(QQ_I, RR) == CC
assert unify(QQ_I, CC) == CC
assert unify(QQ_I, ZZ[x]) == QQ_I[x]
assert unify(QQ_I, ZZ_I[x]) == QQ_I[x]
assert unify(QQ_I, QQ[x]) == QQ_I[x]
assert unify(QQ_I, QQ_I[x]) == QQ_I[x]
assert unify(QQ_I, ZZ.frac_field(x)) == QQ_I.frac_field(x)
assert unify(QQ_I, ZZ_I.frac_field(x)) == QQ_I.frac_field(x)
assert unify(QQ_I, QQ.frac_field(x)) == QQ_I.frac_field(x)
assert unify(QQ_I, QQ_I.frac_field(x)) == QQ_I.frac_field(x)
assert unify(QQ_I, 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 RR[x].unify(ZZ.frac_field(y)) == RR.frac_field(x, y)
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_is_nonpositive():
I = S.ImaginaryUnit
a, b = [CC.convert(x) for x in (2 + I, 5)]
assert CC.is_nonpositive(a) == False
assert CC.is_nonpositive(b) == False
def test_issue_18278():
assert str(RR(2).parent()) == 'RR'
assert str(CC(2).parent()) == 'CC'
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
