RootFinding[Parametric] - Maple Help

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RootFinding[Parametric]

 CellLocation
 find the cell index of a given point

 Calling Sequence CellLocation(m, s) CellLocation(m, p)

Parameters

 m - solution record, as returned by CellDecomposition s - list of equations of the form parameter=rational number representing a point in parameter space p - list of rational numbers representing a point in parameter space

Description

 • The CellLocation command returns a non-negative integer, the index of the open cell in which the point lies, or $0$ if the point does not lie in any of the open cells of $m$.
 • The CellLocation command determines the cell of $m$ in which the given point lies.
 • The point can be specified in two different formats:
 – as a list s of equations of the form parameter=rational number, or
 – as a list p of rational numbers, in which case the $i$th parameter in m:-Parameters gets replaced by ${p}_{i}$, for all $i$.
 • This command is part of the RootFinding[Parametric] package, so it can be used in the form CellLocation(..) 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][CellLocation](..).

Examples

 > $\mathrm{with}\left(\mathrm{RootFinding}[\mathrm{Parametric}]\right):$
 > $m≔\mathrm{CellDecomposition}\left(\left[{x}^{2}+{y}^{2}=a,x-y=b,0
 ${m}{:=}\left[\begin{array}{lll}{\mathrm{Equations}}& {=}& {}\left[{{x}}^{{2}}{+}{{y}}^{{2}}{-}{a}{,}{x}{-}{y}{-}{b}\right]\\ {\mathrm{Inequalities}}& {=}& {}\left[{a}\right]\\ {\mathrm{Filter}}& {=}& {}{0}{\ne }{1}\\ {\mathrm{Variables}}& {=}& {}\left[{x}{,}{y}\right]\\ {\mathrm{Parameters}}& {=}& {}\left[{a}{,}{b}\right]\\ {\mathrm{DiscriminantVariety}}& {=}& {}\left[\left[{a}\right]{,}\left[{-}{{b}}^{{2}}{+}{2}{}{a}\right]\right]\\ {\mathrm{ProjectionPolynomials}}& {=}& {}\left[\left[{b}\right]{,}\left[{a}{,}{-}{{b}}^{{2}}{+}{2}{}{a}\right]\right]\\ {\mathrm{SamplePoints}}& {=}& {}\left[\left[{a}{=}\frac{{1}}{{4}}{,}{b}{=}{-1}\right]{,}\left[{a}{=}{1}{,}{b}{=}{-1}\right]{,}\left[{a}{=}\frac{{1}}{{4}}{,}{b}{=}{1}\right]{,}\left[{a}{=}{1}{,}{b}{=}{1}\right]\right]\end{array}\right$ (1)
 > $\mathrm{CellPlot}\left(m,'\mathrm{samplepoints}'\right)$
 > $\mathrm{CellLocation}\left(m,\left[a=\frac{1}{2},b=3\right]\right)$
 ${3}$ (2)
 > $\mathrm{CellLocation}\left(m,\left[1,-1\right]\right)$
 ${2}$ (3)

The point $\left[\frac{1}{2},1\right]$ lies on the discriminant variety and therefore not in any open cell.

 > $\mathrm{CellLocation}\left(m,\left[a=\frac{1}{2},b=1\right]\right)$
 ${0}$ (4)

The point $\left[-1,1\right]$ violates the inequality $0, and $m$ does not contain any cells in the negative half plane for $a$.

 > $\mathrm{CellLocation}\left(m,\left[-1,1\right]\right)$
 ${0}$ (5)