def test_Domain_convert(): def check_element(e1, e2, K1, K2, K3): assert type(e1) is type(e2), '%s, %s: %s %s -> %s' % (e1, e2, K1, K2, K3) assert e1 == e2, '%s, %s: %s %s -> %s' % (e1, e2, K1, K2, K3) def check_domains(K1, K2): K3 = K1.unify(K2) check_element(K3.convert_from(K1.one, K1), K3.one , K1, K2, K3) check_element(K3.convert_from(K2.one, K2), K3.one , K1, K2, K3) check_element(K3.convert_from(K1.zero, K1), K3.zero, K1, K2, K3) check_element(K3.convert_from(K2.zero, K2), K3.zero, K1, K2, K3) def composite_domains(K): return [K, K[y], K[z], K[y, z], K.frac_field(y), K.frac_field(z), K.frac_field(y, z)] QQ2 = QQ.algebraic_field(sqrt(2)) QQ3 = QQ.algebraic_field(sqrt(3)) doms = [ZZ, QQ, QQ2, QQ3, QQ_I, ZZ_I, RR, CC] for i, K1 in enumerate(doms): for K2 in doms[i:]: for K3 in composite_domains(K1): for K4 in composite_domains(K2): check_domains(K3, K4) 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.to_domain()) == 0 assert CC.convert(ZZ_I(1, 2)) == CC(1, 2) assert CC.convert(QQ_I(1, 2)) == CC(1, 2)
def test_Domain_convert(): def check_element(e1, e2, K1, K2, K3): assert type(e1) is type(e2), '%s, %s: %s %s -> %s' % (e1, e2, K1, K2, K3) assert e1 == e2, '%s, %s: %s %s -> %s' % (e1, e2, K1, K2, K3) def check_domains(K1, K2): K3 = K1.unify(K2) check_element(K3.convert_from(K1.one, K1), K3.one, K1, K2, K3) check_element(K3.convert_from(K2.one, K2), K3.one, K1, K2, K3) check_element(K3.convert_from(K1.zero, K1), K3.zero, K1, K2, K3) check_element(K3.convert_from(K2.zero, K2), K3.zero, K1, K2, K3) def composite_domains(K): domains = [ K, K[y], K[z], K[y, z], K.frac_field(y), K.frac_field(z), K.frac_field(y, z), # XXX: These should be tested and made to work... # K.old_poly_ring(y), K.old_frac_field(y), ] return domains QQ2 = QQ.algebraic_field(sqrt(2)) QQ3 = QQ.algebraic_field(sqrt(3)) doms = [ZZ, QQ, QQ2, QQ3, QQ_I, ZZ_I, RR, CC] for i, K1 in enumerate(doms): for K2 in doms[i:]: for K3 in composite_domains(K1): for K4 in composite_domains(K2): check_domains(K3, K4) assert QQ.convert(10e-52) == QQ( 1684996666696915, 1684996666696914987166688442938726917102321526408785780068975640576) R, xr = ring("x", ZZ) assert ZZ.convert(xr - xr) == 0 assert ZZ.convert(xr - xr, R.to_domain()) == 0 assert CC.convert(ZZ_I(1, 2)) == CC(1, 2) assert CC.convert(QQ_I(1, 2)) == CC(1, 2) K1 = QQ.frac_field(x) K2 = ZZ.frac_field(x) K3 = QQ[x] K4 = ZZ[x] Ks = [K1, K2, K3, K4] for Ka, Kb in product(Ks, Ks): assert Ka.convert_from(Kb.from_sympy(x), Kb) == Ka.from_sympy(x) assert K2.convert_from(QQ(1, 2), QQ) == K2(QQ(1, 2))
def test_issue_18278(): assert str(RR(2).parent()) == 'RR' assert str(CC(2).parent()) == 'CC'
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_issue_18278(): assert str(RR(2).parent()) == "RR" assert str(CC(2).parent()) == "CC"
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, {})