SemiAlgebraic System Solving - Maple Help
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SemiAlgebraic System Solving

The SolveTools[SemiAlgebraic] command has been integrated directly into the solve command, such that many systems involving non-linear polynomial inequalities that could not be solved previously, are solved.

In Maple 16, no solutions were found for the following system, but in Maple 17 it is easily solved.

> 

sol:=solve⁡0≤x−y2&comma;x2&plus;y2<9&comma;0<−y&plus;3⁢x−2&comma;x&comma;y

sol:=x&equals;1&comma;y<1&comma;−1≤y&comma;x&equals;−12&plus;12⁢37&comma;y<12⁢−2&plus;2⁢37&comma;−12⁢−2&plus;2⁢37<y&comma;x&equals;35&plus;110⁢86&comma;y≤110⁢60&plus;10⁢86&comma;−110⁢60&plus;10⁢86≤y&comma;x<35&plus;110⁢86&comma;1<x&comma;y&equals;x&comma;x<35&plus;110⁢86&comma;1<x&comma;y&equals;−x&comma;x<1&comma;49<x&comma;y&equals;−x&comma;x<−12&plus;12⁢37&comma;35&plus;110⁢86<x&comma;y&equals;x&comma;x<−12&plus;12⁢37&comma;35&plus;110⁢86<x&comma;y&equals;−x&comma;x<35&plus;110⁢86&comma;1<x&comma;y<x&comma;−x<y&comma;x<1&comma;49<x&comma;y<3⁢x−2&comma;−x<y&comma;x<3&comma;−12&plus;12⁢37<x&comma;y<−x2&plus;9&comma;−−x2&plus;9<y&comma;x<−12&plus;12⁢37&comma;35&plus;110⁢86<x&comma;y<x&comma;−x<y

(1)

A solution to such a system of inequalities is a decomposition of the feasible region of the inequalities into bands as can be seen in the inequality plot:

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plots&lsqb;inequal&rsqb;⁡sol&comma;x&equals;0..3&comma;y&equals;−2..2

Additionally, the SemiAlgebraic command now can build case discussions for systems with real-valued parameters.

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SolveTools&lsqb;SemiAlgebraic&rsqb;⁡a⁢x2<b&comma;a<x&comma;x

&lcub;0<xAnd⁡a&equals;0&comma;0<ba<x&comma;x<a⁢baAnd⁡0<a&comma;a3<b0<x&comma;a<x&comma;x<0And⁡a<0&comma;b&equals;0−a<xAnd⁡a<0&comma;b&equals;a3a<xAnd⁡a<0&comma;0<b−a⁢ba<xAnd⁡a<0&comma;b<a3−a⁢ba<x&comma;a<x&comma;x<a⁢baAnd⁡a<0&comma;a3<b&comma;b<0otherwise

(2)

SeeAlso

SolveTools[SemiAlgebraic]