def test_contains(): assert Interval(0, 2).contains(1) is S.true assert Interval(0, 2).contains(3) is S.false assert Interval(0, 2, True, False).contains(0) is S.false assert Interval(0, 2, True, False).contains(2) is S.true assert Interval(0, 2, False, True).contains(0) is S.true assert Interval(0, 2, False, True).contains(2) is S.false assert Interval(0, 2, True, True).contains(0) is S.false assert Interval(0, 2, True, True).contains(2) is S.false assert (Interval(0, 2) in Interval(0, 2)) is False assert FiniteSet(1, 2, 3).contains(2) is S.true assert FiniteSet(1, 2, Symbol('x')).contains(Symbol('x')) is S.true assert FiniteSet(y)._contains(x) is None raises(TypeError, lambda: x in FiniteSet(y)) assert FiniteSet({x, y})._contains({x}) is None assert FiniteSet({x, y}).subs(y, x)._contains({x}) is True assert FiniteSet({x, y}).subs(y, x + 1)._contains({x}) is False # issue 8197 from sympy.abc import a, b assert isinstance(FiniteSet(b).contains(-a), Contains) assert isinstance(FiniteSet(b).contains(a), Contains) assert isinstance(FiniteSet(a).contains(1), Contains) raises(TypeError, lambda: 1 in FiniteSet(a)) # issue 8209 rad1 = Pow(Pow(2, S(1) / 3) - 1, S(1) / 3) rad2 = Pow(S(1) / 9, S(1) / 3) - Pow(S(2) / 9, S(1) / 3) + Pow(S(4) / 9, S(1) / 3) s1 = FiniteSet(rad1) s2 = FiniteSet(rad2) assert s1 - s2 == S.EmptySet items = [1, 2, S.Infinity, S('ham'), -1.1] fset = FiniteSet(*items) assert all(item in fset for item in items) assert all(fset.contains(item) is S.true for item in items) assert Union(Interval(0, 1), Interval(2, 5)).contains(3) is S.true assert Union(Interval(0, 1), Interval(2, 5)).contains(6) is S.false assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) is S.false assert S.EmptySet.contains(1) is S.false assert FiniteSet(rootof(x**3 + x - 1, 0)).contains(S.Infinity) is S.false assert rootof(x**5 + x**3 + 1, 0) in S.Reals assert not rootof(x**5 + x**3 + 1, 1) in S.Reals # non-bool results assert Union(Interval(1, 2), Interval(3, 4)).contains(x) == \ Or(And(S(1) <= x, x <= 2), And(S(3) <= x, x <= 4)) assert Intersection(Interval(1, x), Interval(2, 3)).contains(y) == \ And(y <= 3, y <= x, S(1) <= y, S(2) <= y) assert (S.Complexes).contains(S.ComplexInfinity) == S.false
def test_contains(): assert Interval(0, 2).contains(1) is S.true assert Interval(0, 2).contains(3) is S.false assert Interval(0, 2, True, False).contains(0) is S.false assert Interval(0, 2, True, False).contains(2) is S.true assert Interval(0, 2, False, True).contains(0) is S.true assert Interval(0, 2, False, True).contains(2) is S.false assert Interval(0, 2, True, True).contains(0) is S.false assert Interval(0, 2, True, True).contains(2) is S.false assert (Interval(0, 2) in Interval(0, 2)) is False assert FiniteSet(1, 2, 3).contains(2) is S.true assert FiniteSet(1, 2, Symbol('x')).contains(Symbol('x')) is S.true # issue 8197 from sympy.abc import a, b assert isinstance(FiniteSet(b).contains(-a), Contains) assert isinstance(FiniteSet(b).contains(a), Contains) assert isinstance(FiniteSet(a).contains(1), Contains) raises(TypeError, lambda: 1 in FiniteSet(a)) # issue 8209 rad1 = Pow(Pow(2, S(1)/3) - 1, S(1)/3) rad2 = Pow(S(1)/9, S(1)/3) - Pow(S(2)/9, S(1)/3) + Pow(S(4)/9, S(1)/3) s1 = FiniteSet(rad1) s2 = FiniteSet(rad2) assert s1 - s2 == S.EmptySet items = [1, 2, S.Infinity, S('ham'), -1.1] fset = FiniteSet(*items) assert all(item in fset for item in items) assert all(fset.contains(item) is S.true for item in items) assert Union(Interval(0, 1), Interval(2, 5)).contains(3) is S.true assert Union(Interval(0, 1), Interval(2, 5)).contains(6) is S.false assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) is S.false assert S.EmptySet.contains(1) is S.false assert FiniteSet(rootof(x**3 + x - 1, 0)).contains(S.Infinity) is S.false assert rootof(x**5 + x**3 + 1, 0) in S.Reals assert not rootof(x**5 + x**3 + 1, 1) in S.Reals # non-bool results assert Union(Interval(1, 2), Interval(3, 4)).contains(x) == \ Or(And(x <= 2, x >= 1), And(x <= 4, x >= 3)) assert Intersection(Interval(1, x), Interval(2, 3)).contains(y) == \ And(y <= 3, y <= x, y >= 1, y >= 2) assert (S.Complexes).contains(S.ComplexInfinity) == S.false
from sympy.polys.subresultants_qq_zz import * x = var('x') ############### f = x**3 - 7 * x + 7 g = f * (x - 3) ############### print('derivative of f is : ', f.as_poly().diff()) print('integral of f is : ', f.as_poly().integrate()) print('gcd(f, diff(f)) is : ', f.as_poly().gcd(f.as_poly().diff())) print('gcd(f, g) is : ', f.as_poly().gcd(g.as_poly())) print('real root isolating intervals of f are : ', f.as_poly().intervals(), '\n') print('sturm sequence of f is = ', f.as_poly().sturm()) print('real roots of f are = ', f.as_poly().real_roots()) ############### f1 = x**2 + 4 pprint(f1) ############### print('complex roots of f1 are = ', solve((f1), x)) print('complex roots of f1 are = ', rootof((f1), x, 0)) print('complex roots of f1 are = ', CRootOf((f1), x, 0)) print('complex roots of f1 are = ', RootOf((f1), x, 0)) f2 = x**2 + 1 print('*****complex roots of f2 are = ', CRootOf((f2), x, 1)) print('complex roots of f1 are = ', solve((f2), x)) print('roots of f1 are = ', rootof((f2), x, 0)) print('complex roots of f1 are = ', RootOf((f2), x, 1))