CellPlot - Maple Help

RootFinding[Parametric]

 CellPlot
 plot one or more open cells

 Calling Sequence CellPlot (m, k, options)

Parameters

 m - solution module, as returned by CellDecomposition k - (optional) positive integer or list of positive integers; cell indices options - (optional) equations of the form option=value; see below for details

Description

 • The command CellPlot($m$,$k$) plots the $k$th cell of the cell decomposition given by the solution module $m$. If $k$ is a list, then all cells whose indices are in $k$ are plotted. If $k$ is omitted entirely, then all open cells are plotted.
 • Currently, this command can only be used in the case of exactly $2$ parameters. A corresponding error message is returned otherwise.
 • If more than once cell is plotted, then any two adjacent cells have a different color. These colors can be controlled using the option color=c, where c can be either a single color specification or a list of color specifications; if less than 4 colors are provided, then the default colors are used to complete the list; see plot/color.
 • The following options are recognized by CellPlot.
 – samplepoints=b, where b is either true or false, controls whether the sample point of each cell is plotted (the default is false).
 – pointcolor=p, where p is a color specification (see plot/color), controls in which color the sample points are plotted (the default is black). The options symbol and symbolsize (see plot/options) control the shape of the sample points.
 – thickness=t, where t is a positive integer (the default is $2$), controls the thickness of the boundary of each cell.
 – cellcolor=c, where c can be a color or a list of colors, controls the color of each plotted cell; if the list is shorter than the number of displayed cells, then the colors are completed by repeating the list.
 – The remaining options are the same as those found in plot. For more information, see plot/options.
 • When the solution module m has been computed by CellDecomposition with the option output=cad, the plotting is certified; otherwise, a numerical algorithm is used to render the cells.
 • This command is part of the RootFinding[Parametric] package, so it can be used in the form CellPlot(..) 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][CellPlot](..).

Examples

 > $\mathrm{with}\left(\mathrm{RootFinding}\left[\mathrm{Parametric}\right]\right):$
 > $m≔\mathrm{CellDecomposition}\left(\left[{x}^{3}+a{x}^{2}+bx+a=0\right],\left[x\right],\left[a,b\right]\right):$
 > $\mathrm{CellPlot}\left(m\right)$
 > $\mathrm{CellDescription}\left(m,2\right)$
 $\left[\left[{-}{\mathrm{\infty }}{,}{0}{,}{b}{,}{b}{,}{1}\right]{,}\left[{4}{}{{a}}^{{4}}{-}{{a}}^{{2}}{}{{b}}^{{2}}{-}{18}{}{{a}}^{{2}}{}{b}{+}{4}{}{{b}}^{{3}}{+}{27}{}{{a}}^{{2}}{,}{1}{,}{a}{,}{4}{}{{a}}^{{4}}{-}{{a}}^{{2}}{}{{b}}^{{2}}{-}{18}{}{{a}}^{{2}}{}{b}{+}{4}{}{{b}}^{{3}}{+}{27}{}{{a}}^{{2}}{,}{2}\right]\right]$ (1)
 > $\mathrm{CellPlot}\left(m,2,\mathrm{color}=\mathrm{yellow}\right)$
 > $\mathrm{CellPlot}\left(m,\left[1,2,3,4\right],\mathrm{samplepoints}=\mathrm{true},\mathrm{pointcolor}=\mathrm{magenta},\mathrm{view}=\left[-2..2,-2..2\right]\right)$
 > $m≔\mathrm{CellDecomposition}\left(\left[{x}^{3}+a{x}^{2}+bx+a=0\right],\left[x\right],\left[b,a\right]\right):$
 > $\mathrm{CellPlot}\left(m\right)$
 > $\mathrm{CellPlot}\left(m,\left[2,3\right],\mathrm{cellcolor}=\left[\mathrm{blue},\mathrm{red}\right]\right)$
 > $\mathrm{with}\left(\mathrm{RootFinding}\right):$
 > $\mathrm{EnclosingBox}\left(m\right):$
 > $\mathrm{CellPlot}\left(m,\mathrm{samplepoints}\right)$