def test_scalar_funcs():
assert SetExpr(Interval(0, 1)).set == Interval(0, 1)
a, b = Symbol('a', real=True), Symbol('b', real=True)
a, b = 1, 2
# TODO: add support for more functions in the future:
for f in [exp, log]:
input_se = f(SetExpr(Interval(a, b)))
output = input_se.set
expected = Interval(Min(f(a), f(b)), Max(f(a), f(b)))
assert output == expected
def test_SetExpr_Intersection():
x, y, z, w = symbols("x y z w")
set1 = Interval(x, y)
set2 = Interval(w, z)
inter = Intersection(set1, set2)
se = SetExpr(inter)
assert exp(se).set == Intersection(ImageSet(Lambda(x, exp(x)), set1),
ImageSet(Lambda(x, exp(x)), set2))
assert cos(se).set == ImageSet(Lambda(x, cos(x)), inter)
def doit(self, **kwargs):
from sympy.sets.setexpr import SetExpr
f = self.lamda
sig = f.signature
if len(sig) == 1 and sig[0].is_symbol and isinstance(f.expr, Expr):
base_set = self.base_sets[0]
return SetExpr(base_set)._eval_func(f).set
if all(s.is_FiniteSet for s in self.base_sets):
return FiniteSet(*(f(*a) for a in cartes(*self.base_sets)))
return self
def test_Many_Sets():
assert (SetExpr(Interval(0, 1)) + SetExpr(Interval(2, 3)) +
SetExpr(FiniteSet(10, 11, 12))).set == Interval(12, 16)
def test_Interval_FiniteSet():
assert (SetExpr(FiniteSet(1, 2)) + SetExpr(Interval(0, 10))).set == \
Interval(1, 12)
def test_FiniteSet_FiniteSet():
assert (SetExpr(FiniteSet(1, 2, 3)) + SetExpr(FiniteSet(1, 2))).set ==\
FiniteSet(2, 3, 4, 5)
assert (SetExpr(FiniteSet(1, 2, 3)) * SetExpr(FiniteSet(1, 2))).set ==\
FiniteSet(1, 2, 3, 4, 6)
def test_Interval_Interval():
assert (SetExpr(Interval(1, 2)) + SetExpr(Interval(10, 20))).set == \
Interval(11, 22)
assert (SetExpr(Interval(1, 2)) * SetExpr(Interval(10, 20))).set == \
Interval(10, 40)
def test_compound():
assert (exp(SetExpr(Interval(0, 1)) * 2 + 1)).set == \
Interval(exp(1), exp(3))
def test_Pow():
assert (SetExpr(Interval(0, 2))**2).set == Interval(0, 4)
def test_SetExpr_Integers():
assert SetExpr(S.Integers) + 1 == SetExpr(S.Integers)
assert SetExpr(S.Integers) + I == SetExpr(
ImageSet(Lambda(_d, _d + I), S.Integers))
assert SetExpr(S.Integers) * (-1) == SetExpr(S.Integers)
assert SetExpr(S.Integers) * 2 == SetExpr(
ImageSet(Lambda(_d, 2 * _d), S.Integers))
assert SetExpr(S.Integers) * I == SetExpr(
ImageSet(Lambda(_d, I * _d), S.Integers))
# issue #18050:
assert SetExpr(S.Integers)._eval_func(Lambda(x, I * x + 1)) == SetExpr(
ImageSet(Lambda(_d, I * _d + 1), S.Integers))
# needs improvement:
assert SetExpr(S.Integers) * I + 1 == SetExpr(
ImageSet(Lambda(x, x + 1), ImageSet(Lambda(_d, _d * I), S.Integers)))
def test_SetExpr_Interval_pow():
assert SetExpr(Interval(0, 2))**2 == SetExpr(Interval(0, 4))
assert SetExpr(Interval(-1, 1))**2 == SetExpr(Interval(0, 1))
assert SetExpr(Interval(1, 2))**2 == SetExpr(Interval(1, 4))
assert SetExpr(Interval(-1, 2))**3 == SetExpr(Interval(-1, 8))
assert SetExpr(Interval(-1, 1))**0 == SetExpr(FiniteSet(1))
#assert SetExpr(Interval(1, 2))**Rational(5, 2) == SetExpr(Interval(1, 4*sqrt(2)))
#assert SetExpr(Interval(-1, 2))**Rational(1, 3) == SetExpr(Interval(-1, 2**Rational(1, 3)))
#assert SetExpr(Interval(0, 2))**S.Half == SetExpr(Interval(0, sqrt(2)))
#assert SetExpr(Interval(-4, 2))**Rational(2, 3) == SetExpr(Interval(0, 2*2**Rational(1, 3)))
#assert SetExpr(Interval(-1, 5))**S.Half == SetExpr(Interval(0, sqrt(5)))
#assert SetExpr(Interval(-oo, 2))**S.Half == SetExpr(Interval(0, sqrt(2)))
#assert SetExpr(Interval(-2, 3))**(Rational(-1, 4)) == SetExpr(Interval(0, oo))
assert SetExpr(Interval(1,
5))**(-2) == SetExpr(Interval(Rational(1, 25), 1))
assert SetExpr(Interval(-1, 3))**(-2) == SetExpr(Interval(0, oo))
assert SetExpr(Interval(0,
2))**(-2) == SetExpr(Interval(Rational(1, 4), oo))
assert SetExpr(Interval(-1, 2))**(-3) == SetExpr(
Union(Interval(-oo, -1), Interval(Rational(1, 8), oo)))
assert SetExpr(Interval(-3, -2))**(-3) == SetExpr(
Interval(Rational(-1, 8), Rational(-1, 27)))
assert SetExpr(Interval(-3, -2))**(-2) == SetExpr(
Interval(Rational(1, 9), Rational(1, 4)))
#assert SetExpr(Interval(0, oo))**S.Half == SetExpr(Interval(0, oo))
#assert SetExpr(Interval(-oo, -1))**Rational(1, 3) == SetExpr(Interval(-oo, -1))
#assert SetExpr(Interval(-2, 3))**(Rational(-1, 3)) == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-oo, 0))**(-2) == SetExpr(Interval.open(0, oo))
assert SetExpr(Interval(-2,
0))**(-2) == SetExpr(Interval(Rational(1, 4), oo))
assert SetExpr(Interval(Rational(1, 3),
S.Half))**oo == SetExpr(FiniteSet(0))
assert SetExpr(Interval(0, S.Half))**oo == SetExpr(FiniteSet(0))
assert SetExpr(Interval(S.Half, 1))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(0, 1))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(2, 3))**oo == SetExpr(FiniteSet(oo))
assert SetExpr(Interval(1, 2))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(S.Half, 3))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(Rational(-1, 3),
Rational(-1, 4)))**oo == SetExpr(FiniteSet(0))
assert SetExpr(Interval(-1, Rational(-1,
2)))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-3, -2))**oo == SetExpr(FiniteSet(-oo, oo))
assert SetExpr(Interval(-2, -1))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-2, Rational(-1,
2)))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(Rational(-1, 2),
S.Half))**oo == SetExpr(FiniteSet(0))
assert SetExpr(Interval(Rational(-1, 2),
1))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(Rational(-2, 3),
2))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(-1, 1))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-1, S.Half))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-1, 2))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-2, S.Half))**oo == SetExpr(Interval(-oo, oo))
assert (SetExpr(Interval(1, 2))**x).dummy_eq(
SetExpr(ImageSet(Lambda(_d, _d**x), Interval(1, 2))))
assert SetExpr(Interval(2, 3))**(-oo) == SetExpr(FiniteSet(0))
assert SetExpr(Interval(0, 2))**(-oo) == SetExpr(Interval(0, oo))
assert (SetExpr(Interval(-1, 2))**(-oo)).dummy_eq(
SetExpr(ImageSet(Lambda(_d, _d**(-oo)), Interval(-1, 2))))
def test_SetExpr_Interval_div():
# TODO: some expressions cannot be calculated due to bugs (currently
# commented):
assert SetExpr(Interval(-3, -2)) / SetExpr(Interval(-2, 1)) == SetExpr(
Interval(-oo, oo))
assert SetExpr(Interval(2, 3)) / SetExpr(Interval(-2, 2)) == SetExpr(
Interval(-oo, oo))
assert SetExpr(Interval(-3, -2)) / SetExpr(Interval(0, 4)) == SetExpr(
Interval(-oo, Rational(-1, 2)))
assert SetExpr(Interval(2, 4)) / SetExpr(Interval(-3, 0)) == SetExpr(
Interval(-oo, Rational(-2, 3)))
assert SetExpr(Interval(2, 4)) / SetExpr(Interval(0, 3)) == SetExpr(
Interval(Rational(2, 3), oo))
#assert SetExpr(Interval(0, 1))/SetExpr(Interval(0, 1)) == SetExpr(Interval(0, oo))
#assert SetExpr(Interval(-1, 0))/SetExpr(Interval(0, 1)) == SetExpr(Interval(-oo, 0))
assert SetExpr(Interval(-1, 2)) / SetExpr(Interval(-2, 2)) == SetExpr(
Interval(-oo, oo))
assert 1 / SetExpr(Interval(-1, 2)) == SetExpr(
Union(Interval(-oo, -1), Interval(S.Half, oo)))
assert 1 / SetExpr(Interval(0, 2)) == SetExpr(Interval(S.Half, oo))
assert (-1) / SetExpr(Interval(0, 2)) == SetExpr(
Interval(-oo, Rational(-1, 2)))
#assert 1/SetExpr(Interval(-oo, 0)) == SetExpr(Interval.open(-oo, 0))
assert 1 / SetExpr(Interval(-1, 0)) == SetExpr(Interval(-oo, -1))
def test_setexpr():
se = SetExpr(Interval(0, 1))
assert isinstance(se.set, Set)
assert isinstance(se, Expr)
def test_SetExpr_Interval_pow():
assert SetExpr(Interval(0, 2))**2 == SetExpr(Interval(0, 4))
assert SetExpr(Interval(-1, 1))**2 == SetExpr(Interval(0, 1))
assert SetExpr(Interval(1, 2))**2 == SetExpr(Interval(1, 4))
assert SetExpr(Interval(-1, 2))**3 == SetExpr(Interval(-1, 8))
assert SetExpr(Interval(-1, 1))**0 == SetExpr(FiniteSet(1))
#assert SetExpr(Interval(1, 2))**(S(5)/2) == SetExpr(Interval(1, 4*sqrt(2)))
#assert SetExpr(Interval(-1, 2))**(S.One/3) == SetExpr(Interval(-1, 2**(S.One/3)))
#assert SetExpr(Interval(0, 2))**(S.One/2) == SetExpr(Interval(0, sqrt(2)))
#assert SetExpr(Interval(-4, 2))**(S(2)/3) == SetExpr(Interval(0, 2*2**(S.One/3)))
#assert SetExpr(Interval(-1, 5))**(S.One/2) == SetExpr(Interval(0, sqrt(5)))
#assert SetExpr(Interval(-oo, 2))**(S.One/2) == SetExpr(Interval(0, sqrt(2)))
#assert SetExpr(Interval(-2, 3))**(S(-1)/4) == SetExpr(Interval(0, oo))
assert SetExpr(Interval(1, 5))**(-2) == SetExpr(Interval(S.One / 25, 1))
assert SetExpr(Interval(-1, 3))**(-2) == SetExpr(Interval(0, oo))
assert SetExpr(Interval(0, 2))**(-2) == SetExpr(Interval(S.One / 4, oo))
assert SetExpr(Interval(-1, 2))**(-3) == SetExpr(
Union(Interval(-oo, -1), Interval(S(1) / 8, oo)))
assert SetExpr(Interval(-3, -2))**(-3) == SetExpr(
Interval(S(-1) / 8, -S.One / 27))
assert SetExpr(Interval(-3, -2))**(-2) == SetExpr(
Interval(S.One / 9, S.One / 4))
#assert SetExpr(Interval(0, oo))**(S.One/2) == SetExpr(Interval(0, oo))
#assert SetExpr(Interval(-oo, -1))**(S.One/3) == SetExpr(Interval(-oo, -1))
#assert SetExpr(Interval(-2, 3))**(-S.One/3) == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-oo, 0))**(-2) == SetExpr(Interval.open(0, oo))
assert SetExpr(Interval(-2, 0))**(-2) == SetExpr(Interval(S.One / 4, oo))
assert SetExpr(Interval(S.One / 3, S.One / 2))**oo == SetExpr(FiniteSet(0))
assert SetExpr(Interval(0, S.One / 2))**oo == SetExpr(FiniteSet(0))
assert SetExpr(Interval(S.One / 2, 1))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(0, 1))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(2, 3))**oo == SetExpr(FiniteSet(oo))
assert SetExpr(Interval(1, 2))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(S.One / 2, 3))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(-S.One / 3,
-S.One / 4))**oo == SetExpr(FiniteSet(0))
assert SetExpr(Interval(-1, -S.One / 2))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-3, -2))**oo == SetExpr(FiniteSet(-oo, oo))
assert SetExpr(Interval(-2, -1))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-2, -S.One / 2))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-S.One / 2,
S.One / 2))**oo == SetExpr(FiniteSet(0))
assert SetExpr(Interval(-S.One / 2, 1))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(-S(2) / 3, 2))**oo == SetExpr(Interval(0, oo))
assert SetExpr(Interval(-1, 1))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-1, S.One / 2))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-1, 2))**oo == SetExpr(Interval(-oo, oo))
assert SetExpr(Interval(-2, S.One / 2))**oo == SetExpr(Interval(-oo, oo))
assert (SetExpr(Interval(1, 2))**x).dummy_eq(
SetExpr(ImageSet(Lambda(_d, _d**x), Interval(1, 2))))
assert SetExpr(Interval(2, 3))**(-oo) == SetExpr(FiniteSet(0))
assert SetExpr(Interval(0, 2))**(-oo) == SetExpr(Interval(0, oo))
assert (SetExpr(Interval(-1, 2))**(-oo)).dummy_eq(
SetExpr(ImageSet(Lambda(_d, _d**(-oo)), Interval(-1, 2))))
def test_same_setexprs_are_not_identical():
a = SetExpr(FiniteSet(0, 1))
b = SetExpr(FiniteSet(0, 1))
assert (a + b).set == FiniteSet(0, 1, 2)
def test_Add_Mul():
assert (SetExpr(Interval(0, 1)) + 1).set == Interval(1, 2)
assert (SetExpr(Interval(0, 1)) * 2).set == Interval(0, 2)
def test_Interval_arithmetic():
i12cc = SetExpr(Interval(1, 2))
i12lo = SetExpr(Interval.Lopen(1, 2))
i12ro = SetExpr(Interval.Ropen(1, 2))
i12o = SetExpr(Interval.open(1, 2))
n23cc = SetExpr(Interval(-2, 3))
n23lo = SetExpr(Interval.Lopen(-2, 3))
n23ro = SetExpr(Interval.Ropen(-2, 3))
n23o = SetExpr(Interval.open(-2, 3))
n3n2cc = SetExpr(Interval(-3, -2))
assert i12cc + i12cc == SetExpr(Interval(2, 4))
assert i12cc - i12cc == SetExpr(Interval(-1, 1))
assert i12cc * i12cc == SetExpr(Interval(1, 4))
assert i12cc / i12cc == SetExpr(Interval(S.Half, 2))
assert i12cc**2 == SetExpr(Interval(1, 4))
assert i12cc**3 == SetExpr(Interval(1, 8))
assert i12lo + i12ro == SetExpr(Interval.open(2, 4))
assert i12lo - i12ro == SetExpr(Interval.Lopen(-1, 1))
assert i12lo * i12ro == SetExpr(Interval.open(1, 4))
assert i12lo / i12ro == SetExpr(Interval.Lopen(S.Half, 2))
assert i12lo + i12lo == SetExpr(Interval.Lopen(2, 4))
assert i12lo - i12lo == SetExpr(Interval.open(-1, 1))
assert i12lo * i12lo == SetExpr(Interval.Lopen(1, 4))
assert i12lo / i12lo == SetExpr(Interval.open(S.Half, 2))
assert i12lo + i12cc == SetExpr(Interval.Lopen(2, 4))
assert i12lo - i12cc == SetExpr(Interval.Lopen(-1, 1))
assert i12lo * i12cc == SetExpr(Interval.Lopen(1, 4))
assert i12lo / i12cc == SetExpr(Interval.Lopen(S.Half, 2))
assert i12lo + i12o == SetExpr(Interval.open(2, 4))
assert i12lo - i12o == SetExpr(Interval.open(-1, 1))
assert i12lo * i12o == SetExpr(Interval.open(1, 4))
assert i12lo / i12o == SetExpr(Interval.open(S.Half, 2))
assert i12lo**2 == SetExpr(Interval.Lopen(1, 4))
assert i12lo**3 == SetExpr(Interval.Lopen(1, 8))
assert i12ro + i12ro == SetExpr(Interval.Ropen(2, 4))
assert i12ro - i12ro == SetExpr(Interval.open(-1, 1))
assert i12ro * i12ro == SetExpr(Interval.Ropen(1, 4))
assert i12ro / i12ro == SetExpr(Interval.open(S.Half, 2))
assert i12ro + i12cc == SetExpr(Interval.Ropen(2, 4))
assert i12ro - i12cc == SetExpr(Interval.Ropen(-1, 1))
assert i12ro * i12cc == SetExpr(Interval.Ropen(1, 4))
assert i12ro / i12cc == SetExpr(Interval.Ropen(S.Half, 2))
assert i12ro + i12o == SetExpr(Interval.open(2, 4))
assert i12ro - i12o == SetExpr(Interval.open(-1, 1))
assert i12ro * i12o == SetExpr(Interval.open(1, 4))
assert i12ro / i12o == SetExpr(Interval.open(S.Half, 2))
assert i12ro**2 == SetExpr(Interval.Ropen(1, 4))
assert i12ro**3 == SetExpr(Interval.Ropen(1, 8))
assert i12o + i12lo == SetExpr(Interval.open(2, 4))
assert i12o - i12lo == SetExpr(Interval.open(-1, 1))
assert i12o * i12lo == SetExpr(Interval.open(1, 4))
assert i12o / i12lo == SetExpr(Interval.open(S.Half, 2))
assert i12o + i12ro == SetExpr(Interval.open(2, 4))
assert i12o - i12ro == SetExpr(Interval.open(-1, 1))
assert i12o * i12ro == SetExpr(Interval.open(1, 4))
assert i12o / i12ro == SetExpr(Interval.open(S.Half, 2))
assert i12o + i12cc == SetExpr(Interval.open(2, 4))
assert i12o - i12cc == SetExpr(Interval.open(-1, 1))
assert i12o * i12cc == SetExpr(Interval.open(1, 4))
assert i12o / i12cc == SetExpr(Interval.open(S.Half, 2))
assert i12o**2 == SetExpr(Interval.open(1, 4))
assert i12o**3 == SetExpr(Interval.open(1, 8))
assert n23cc + n23cc == SetExpr(Interval(-4, 6))
assert n23cc - n23cc == SetExpr(Interval(-5, 5))
assert n23cc * n23cc == SetExpr(Interval(-6, 9))
assert n23cc / n23cc == SetExpr(Interval.open(-oo, oo))
assert n23cc + n23ro == SetExpr(Interval.Ropen(-4, 6))
assert n23cc - n23ro == SetExpr(Interval.Lopen(-5, 5))
assert n23cc * n23ro == SetExpr(Interval.Ropen(-6, 9))
assert n23cc / n23ro == SetExpr(Interval.Lopen(-oo, oo))
assert n23cc + n23lo == SetExpr(Interval.Lopen(-4, 6))
assert n23cc - n23lo == SetExpr(Interval.Ropen(-5, 5))
assert n23cc * n23lo == SetExpr(Interval(-6, 9))
assert n23cc / n23lo == SetExpr(Interval.open(-oo, oo))
assert n23cc + n23o == SetExpr(Interval.open(-4, 6))
assert n23cc - n23o == SetExpr(Interval.open(-5, 5))
assert n23cc * n23o == SetExpr(Interval.open(-6, 9))
assert n23cc / n23o == SetExpr(Interval.open(-oo, oo))
assert n23cc**2 == SetExpr(Interval(0, 9))
assert n23cc**3 == SetExpr(Interval(-8, 27))
n32cc = SetExpr(Interval(-3, 2))
n32lo = SetExpr(Interval.Lopen(-3, 2))
n32ro = SetExpr(Interval.Ropen(-3, 2))
assert n32cc * n32lo == SetExpr(Interval.Ropen(-6, 9))
assert n32cc * n32cc == SetExpr(Interval(-6, 9))
assert n32lo * n32cc == SetExpr(Interval.Ropen(-6, 9))
assert n32cc * n32ro == SetExpr(Interval(-6, 9))
assert n32lo * n32ro == SetExpr(Interval.Ropen(-6, 9))
assert n32cc / n32lo == SetExpr(Interval.Ropen(-oo, oo))
assert i12cc / n32lo == SetExpr(Interval.Ropen(-oo, oo))
assert n3n2cc**2 == SetExpr(Interval(4, 9))
assert n3n2cc**3 == SetExpr(Interval(-27, -8))
assert n23cc + i12cc == SetExpr(Interval(-1, 5))
assert n23cc - i12cc == SetExpr(Interval(-4, 2))
assert n23cc * i12cc == SetExpr(Interval(-4, 6))
assert n23cc / i12cc == SetExpr(Interval(-2, 3))
def doit(self, **kwargs):
from sympy.sets.setexpr import SetExpr
f = self.lamda
base_set = self.base_set
return SetExpr(base_set)._eval_func(f).set
