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:=solve0xy2&comma;x2&plus;y2<9&comma;0<y&plus;3x2&comma;x&comma;y

sol:=x&equals;1&comma;y<1&comma;1y&comma;x&equals;12&plus;1237&comma;y<122&plus;237&comma;122&plus;237<y&comma;x&equals;35&plus;11086&comma;y11060&plus;1086&comma;11060&plus;1086y&comma;x<35&plus;11086&comma;1<x&comma;y&equals;x&comma;x<35&plus;11086&comma;1<x&comma;y&equals;x&comma;x<1&comma;49<x&comma;y&equals;x&comma;x<12&plus;1237&comma;35&plus;11086<x&comma;y&equals;x&comma;x<12&plus;1237&comma;35&plus;11086<x&comma;y&equals;x&comma;x<35&plus;11086&comma;1<x&comma;y<x&comma;x<y&comma;x<1&comma;49<x&comma;y<3x2&comma;x<y&comma;x<3&comma;12&plus;1237<x&comma;y<x2&plus;9&comma;x2&plus;9<y&comma;x<12&plus;1237&comma;35&plus;11086<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:

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.

SolveTools&lsqb;SemiAlgebraic&rsqb;ax2<b&comma;a<x&comma;x

&lcub;0<xAnda&equals;0&comma;0<ba<x&comma;x<abaAnd0<a&comma;a3<b0<x&comma;a<x&comma;x<0Anda<0&comma;b&equals;0a<xAnda<0&comma;b&equals;a3a<xAnda<0&comma;0<baba<xAnda<0&comma;b<a3aba<x&comma;a<x&comma;x<abaAnda<0&comma;a3<b&comma;b<0otherwise

(2)

SeeAlso

SolveTools[SemiAlgebraic]