Inequality Solvers¶

sympy.solvers.inequalities.
solve_rational_inequalities
(eqs)[source]¶ Solve a system of rational inequalities with rational coefficients.
See also
Examples
>>> from sympy.abc import x >>> from sympy import Poly >>> from sympy.solvers.inequalities import solve_rational_inequalities
>>> solve_rational_inequalities([[ ... ((Poly(x + 1), Poly(1, x)), '>='), ... ((Poly(x + 1), Poly(1, x)), '<=')]]) {1}
>>> solve_rational_inequalities([[ ... ((Poly(x), Poly(1, x)), '!='), ... ((Poly(x + 1), Poly(1, x)), '>=')]]) (oo, 0) U (0, 1]

sympy.solvers.inequalities.
solve_poly_inequality
(poly, rel)[source]¶ Solve a polynomial inequality with rational coefficients.
See also
solve_poly_inequalities
Examples
>>> from sympy import Poly >>> from sympy.abc import x >>> from sympy.solvers.inequalities import solve_poly_inequality
>>> solve_poly_inequality(Poly(x, x, domain='ZZ'), '==') [{0}]
>>> solve_poly_inequality(Poly(x**2  1, x, domain='ZZ'), '!=') [(oo, 1), (1, 1), (1, oo)]
>>> solve_poly_inequality(Poly(x**2  1, x, domain='ZZ'), '==') [{1}, {1}]

sympy.solvers.inequalities.
reduce_rational_inequalities
(exprs, gen, relational=True)[source]¶ Reduce a system of rational inequalities with rational coefficients.
Examples
>>> from sympy import Poly, Symbol >>> from sympy.solvers.inequalities import reduce_rational_inequalities
>>> x = Symbol('x', real=True)
>>> reduce_rational_inequalities([[x**2 <= 0]], x) Eq(x, 0)
>>> reduce_rational_inequalities([[x + 2 > 0]], x) And(2 < x, x < oo) >>> reduce_rational_inequalities([[(x + 2, ">")]], x) And(2 < x, x < oo) >>> reduce_rational_inequalities([[x + 2]], x) Eq(x, 2)

sympy.solvers.inequalities.
reduce_abs_inequality
(expr, rel, gen)[source]¶ Reduce an inequality with nested absolute values.
See also
Examples
>>> from sympy import Abs, Symbol >>> from sympy.solvers.inequalities import reduce_abs_inequality >>> x = Symbol('x', real=True)
>>> reduce_abs_inequality(Abs(x  5)  3, '<', x) And(2 < x, x < 8)
>>> reduce_abs_inequality(Abs(x + 2)*3  13, '<', x) And(19/3 < x, x < 7/3)

sympy.solvers.inequalities.
reduce_abs_inequalities
(exprs, gen)[source]¶ Reduce a system of inequalities with nested absolute values.
See also
Examples
>>> from sympy import Abs, Symbol >>> from sympy.abc import x >>> from sympy.solvers.inequalities import reduce_abs_inequalities >>> x = Symbol('x', real=True)
>>> reduce_abs_inequalities([(Abs(3*x  5)  7, '<'), ... (Abs(x + 25)  13, '>')], x) And(2/3 < x, Or(And(12 < x, x < oo), And(oo < x, x < 38)), x < 4)
>>> reduce_abs_inequalities([(Abs(x  4) + Abs(3*x  5)  7, '<')], x) And(1/2 < x, x < 4)

sympy.solvers.inequalities.
reduce_inequalities
(inequalities, symbols=[])[source]¶ Reduce a system of inequalities with rational coefficients.
Examples
>>> from sympy import sympify as S, Symbol >>> from sympy.abc import x, y >>> from sympy.solvers.inequalities import reduce_inequalities
>>> reduce_inequalities(0 <= x + 3, []) And(3 <= x, x < oo)
>>> reduce_inequalities(0 <= x + y*2  1, [x]) x >= 2*y + 1

sympy.solvers.inequalities.
solve_univariate_inequality
(expr, gen, relational=True)[source]¶ Solves a real univariate inequality.
Examples
>>> from sympy.solvers.inequalities import solve_univariate_inequality >>> from sympy.core.symbol import Symbol >>> x = Symbol('x')
>>> solve_univariate_inequality(x**2 >= 4, x) Or(And(oo < x, x <= 2), And(2 <= x, x < oo))
>>> solve_univariate_inequality(x**2 >= 4, x, relational=False) (oo, 2] U [2, oo)