find all cells with a given number of real solutions - Maple Help

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RootFinding[Parametric][CellsWithSolutions] - find all cells with a given number of real solutions

 Calling Sequence CellsWithSolutions(m, k) CellsWithSolutions(m, l..r)

Parameters

 m - solution record, as returned by CellDecomposition k,l - non-negative integers r - non-negative integer or $\mathrm{\infty }$

Description

 • The CellsWithSolutions($m,k$) calling sequence returns the indices of all cells where the system

${\left[f=0,g>0\right]}_{f\in m:-\mathrm{Equations},g\in m:-\mathrm{Inequalities}}$

 has exactly $k$ real solutions.
 • The CellsWithSolutions($m,l..r$) calling sequence returns the indices of all cells where the system above has between $l$ and $r$ (inclusive) real solutions.
 • If there are no cells with the requested number of solutions, the empty list is returned.
 • This command is part of the RootFinding[Parametric] package, so it can be used in the form CellsWithSolutions(..) only after executing the command with(RootFinding[Parametric]). However, it can always be accessed through the long form of the command by using RootFinding[Parametric][CellsWithSolutions](..).

Examples

 > $\mathrm{with}\left(\mathrm{RootFinding}[\mathrm{Parametric}]\right):$
 > $m:=\mathrm{CellDecomposition}\left(\left[{x}^{6}+a{y}^{2}-b=0,a{x}^{2}+{y}^{2}-bxy=0\right],\left[x,y\right]\right):$
 > $m:-\mathrm{SamplePoints}$
 $\left[\left[{a}{=}{-}{4}{,}{b}{=}{-}{3}\right]{,}\left[{a}{=}{-}{2}{,}{b}{=}{-}{3}\right]{,}\left[{a}{=}{1}{,}{b}{=}{-}{3}\right]{,}\left[{a}{=}{3}{,}{b}{=}{-}{3}\right]{,}\left[{a}{=}{-}{2}{,}{b}{=}{-}{1}\right]{,}\left[{a}{=}{-}{1}{,}{b}{=}{-}{1}\right]{,}\left[{a}{=}{0}{,}{b}{=}{-}{1}\right]{,}\left[{a}{=}{1}{,}{b}{=}{-}{1}\right]{,}\left[{a}{=}{-}{2}{,}{b}{=}{1}\right]{,}\left[{a}{=}{-}{1}{,}{b}{=}{1}\right]{,}\left[{a}{=}{0}{,}{b}{=}{1}\right]{,}\left[{a}{=}{1}{,}{b}{=}{1}\right]{,}\left[{a}{=}{-}{4}{,}{b}{=}{3}\right]{,}\left[{a}{=}{-}{2}{,}{b}{=}{3}\right]{,}\left[{a}{=}{1}{,}{b}{=}{3}\right]{,}\left[{a}{=}{3}{,}{b}{=}{3}\right]\right]$ (1)
 > $\mathrm{NumberOfSolutions}\left(m\right)$
 $\left[\left[{1}{,}{8}\right]{,}\left[{2}{,}{4}\right]{,}\left[{3}{,}{0}\right]{,}\left[{4}{,}{0}\right]{,}\left[{5}{,}{8}\right]{,}\left[{6}{,}{4}\right]{,}\left[{7}{,}{0}\right]{,}\left[{8}{,}{0}\right]{,}\left[{9}{,}{4}\right]{,}\left[{10}{,}{4}\right]{,}\left[{11}{,}{4}\right]{,}\left[{12}{,}{0}\right]{,}\left[{13}{,}{4}\right]{,}\left[{14}{,}{4}\right]{,}\left[{15}{,}{4}\right]{,}\left[{16}{,}{0}\right]\right]$ (2)
 > $\mathrm{CellsWithSolutions}\left(m,4\right)$
 $\left[{2}{,}{6}{,}{9}{,}{10}{,}{11}{,}{13}{,}{14}{,}{15}\right]$ (3)
 > $\mathrm{CellsWithSolutions}\left(m,0..3\right)$
 $\left[{3}{,}{4}{,}{7}{,}{8}{,}{12}{,}{16}\right]$ (4)
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