There is an undocumented user-contributed feature of Maxima for rational inequalities: **solve_rat_ineq()**.

Here are few examples of its capabilities and limitations:

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# Solving Rational Inequalities in Maxima: solve_rat_ineq()

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There is an undocumented user-contributed feature of Maxima for rational inequalities: **solve_rat_ineq()**.

Here are few examples of its capabilities and limitations:

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For *systems* of inequalities, you can use **fourier_elim** in the **to_poly_solve** package:

(%i1) load(to_poly_solve)$

WARNING: redefining MAXIMA::OPAPPLY in DEFMACRO

WARNING: redefining MAXIMA::OPCONS in DEFMACRO

(%i2) fourier_elim( [ a+b > 0, a*b < 0 ], [a,b] );

(%o2) [- b < a, a < 0, 0 < b] or [- b < a, b 0, a*b < 0, a = 2 ], [a,b] );

(%o3) [a = 2, – 2 < b, b < 0]

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