def solve_poly_inequalities(polys):
"""Solve polynomial inequalities with rational coefficients.
Examples
========
>>> from sympy.solvers.inequalities import solve_poly_inequalities
>>> from sympy.polys import Poly
>>> from sympy.abc import x
>>> solve_poly_inequalities(((
... Poly(x**2 - 3), ">"), (
... Poly(-x**2 + 1), ">")))
(-oo, -sqrt(3)) U (-1, 1) U (sqrt(3), oo)
"""
from sympy import Union
return Union(*[solve_poly_inequality(*p) for p in polys])
def solve_univariate_inequality(expr, gen, assume=True, relational=True):
"""Solves a real univariate inequality.
Examples
========
>>> from sympy.solvers.inequalities import solve_univariate_inequality
>>> from sympy.core.symbol import Symbol
>>> x = Symbol('x', real=True)
>>> solve_univariate_inequality(x**2 >= 4, x)
Or(x <= -2, x >= 2)
>>> solve_univariate_inequality(x**2 >= 4, x, relational=False)
(-oo, -2] U [2, oo)
"""
# Implementation for continous functions
from sympy.solvers.solvers import solve
solns = solve(expr.lhs - expr.rhs, gen, assume=assume)
oo = S.Infinity
start = -oo
sol_sets = [S.EmptySet]
for x in sorted(s for s in solns if s.is_real):
end = x
if expr.subs(gen, (start + end) / 2 if start != -oo else end - 1):
sol_sets.append(Interval(start, end, True, True))
if expr.subs(gen, x):
sol_sets.append(FiniteSet(x))
start = end
end = oo
if expr.subs(gen, start + 1):
sol_sets.append(Interval(start, end, True, True))
rv = Union(*sol_sets)
return rv if not relational else rv.as_relational(gen)
def as_set(self):
"""
Rewrite logic operators and relationals in terms of real sets.
Examples
========
>>> from sympy import Or, Symbol
>>> x = Symbol('x', real=True)
>>> Or(x>2, x<-2).as_set()
(-oo, -2) U (2, oo)
"""
from sympy.core.sets import Union
if len(self.free_symbols) == 1:
return Union(*[arg.as_set() for arg in self.args])
else:
raise NotImplementedError("Sorry, Or.as_set has not yet been"
" implemented for multivariate"
" expressions")
def test_sympy__core__sets__Union():
from sympy.core.sets import Union, Interval
assert _test_args(Union(Interval(0, 1), Interval(2, 3)))