Inequality Solvers¶

sympy.solvers.inequalities.
solve_rational_inequalities
(eqs)[source]¶ Solve a system of rational inequalities with rational coefficients.
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)), '<=')]]) FiniteSet(1)
>>> solve_rational_inequalities([[ ... ((Poly(x), Poly(1, x)), '!='), ... ((Poly(x + 1), Poly(1, x)), '>=')]]) Union(Interval.open(oo, 0), Interval.Lopen(0, 1))
See also

sympy.solvers.inequalities.
solve_poly_inequality
(poly, rel)[source]¶ Solve a polynomial inequality with rational coefficients.
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'), '==') [FiniteSet(0)]
>>> solve_poly_inequality(Poly(x**2  1, x, domain='ZZ'), '!=') [Interval.open(oo, 1), Interval.open(1, 1), Interval.open(1, oo)]
>>> solve_poly_inequality(Poly(x**2  1, x, domain='ZZ'), '==') [FiniteSet(1), FiniteSet(1)]
See also

sympy.solvers.inequalities.
solve_poly_inequalities
(polys)[source]¶ 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), ">"))) Union(Interval.open(oo, sqrt(3)), Interval.open(1, 1), Interval.open(sqrt(3), oo))

sympy.solvers.inequalities.
reduce_rational_inequalities
(exprs, gen, relational=True)[source]¶ Reduce a system of rational inequalities with rational coefficients.
Examples
>>> from sympy import 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) 2 < x >>> reduce_rational_inequalities([[(x + 2, ">")]], x) 2 < x >>> reduce_rational_inequalities([[x + 2]], x) Eq(x, 2)
This function find the noninfinite solution set so if the unknown symbol is declared as extended real rather than real then the result may include finiteness conditions:
>>> y = Symbol('y', extended_real=True) >>> reduce_rational_inequalities([[y + 2 > 0]], y) (2 < y) & (y < oo)

sympy.solvers.inequalities.
reduce_abs_inequality
(expr, rel, gen)[source]¶ Reduce an inequality with nested absolute values.
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) (2 < x) & (x < 8)
>>> reduce_abs_inequality(Abs(x + 2)*3  13, '<', x) (19/3 < x) & (x < 7/3)
See also

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

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

sympy.solvers.inequalities.
solve_univariate_inequality
(expr, gen, relational=True, domain=Reals, continuous=False)[source]¶ Solves a real univariate inequality.
 Parameters
expr : Relational
The target inequality
gen : Symbol
The variable for which the inequality is solved
relational : bool
A Relational type output is expected or not
domain : Set
The domain over which the equation is solved
continuous: bool
True if expr is known to be continuous over the given domain (and so continuous_domain() doesn’t need to be called on it)
 Raises
NotImplementedError
The solution of the inequality cannot be determined due to limitation in
sympy.solvers.solveset.solvify()
.
Notes
Currently, we cannot solve all the inequalities due to limitations in
sympy.solvers.solveset.solvify()
. Also, the solution returned for trigonometric inequalities are restricted in its periodic interval.Examples
>>> from sympy.solvers.inequalities import solve_univariate_inequality >>> from sympy import Symbol, sin, Interval, S >>> x = Symbol('x')
>>> solve_univariate_inequality(x**2 >= 4, x) ((2 <= x) & (x < oo))  ((x <= 2) & (oo < x))
>>> solve_univariate_inequality(x**2 >= 4, x, relational=False) Union(Interval(oo, 2), Interval(2, oo))
>>> domain = Interval(0, S.Infinity) >>> solve_univariate_inequality(x**2 >= 4, x, False, domain) Interval(2, oo)
>>> solve_univariate_inequality(sin(x) > 0, x, relational=False) Interval.open(0, pi)
See also
sympy.solvers.solveset.solvify
solver returning solveset solutions with solve’s output API