GetCells - Maple Help

 GetCells

 Calling Sequence GetCells( cad, truthvalue = t, output = o )

Parameters

 cad - CADData object from a QE or CAD computation. t - (optional) truefalse; defines a filter such that only cells with the truth value t are returned. (default $\mathrm{FAIL}$ which defines no filtering) o - (optional) a list of symbols including cells, samplepoints and descriptions. This customizes the output of this method as described in the description. (default $\mathrm{FAIL}$, with return value as described below)

Returns

 • By default, i.e. without specification of the keyword option o, a list of cells for the CAD is returned.
 • Otherwise, returns a list of outputs (list of lists) corresponding to the elements specified in the list passed as value for output:
 – samplepoints : list of lists; each inner list is a sample point for the corresponding cell, of the form name = realalgnum.
 – descriptions : list of quantifier free formulae; a relation or conjunction of relations describing the boundaries of the cell in n-space (where the CAD is in n variables).

Description

 • The $\mathrm{GetCells}\left(\mathrm{cad}\right)$ calling sequence produces a list of all leaf CADCells for the CAD $\mathrm{cad}$. By leaf CAD cell we mean one which either could not or did not need to be subdivided into further cells.
 • Usage of the o keyword option customizes the output such that the most interesting properties of CADCells may be accessed more directly without intermediate calls to e.g. map that would be needed in usage of the default calling sequence when intending to access said properties such as sample points as the end goal.

Examples

 > $\mathrm{ex}≔':-\mathrm{exists}'\left(\left[y,x\right],':-\mathrm{And}'\left(3{x}^{2}-2y<0,0
 ${\mathrm{ex}}{≔}{\exists }{}\left(\left[{y}{,}{x}\right]{,}{3}{}{{x}}^{{2}}{-}{2}{}{y}{<}{0}{\wedge }{0}{<}{x}{-}{y}{\wedge }{0}{<}{y}{+}{2}\right)$ (1)
 > $\mathrm{cad}≔\mathrm{QuantifierElimination}:-\mathrm{PartialCylindricalAlgebraicDecompose}\left(\mathrm{ex},\mathrm{output}=\left['\mathrm{data}'\right]\right)$
 ${\mathrm{cad}}{≔}\left[\begin{array}{lll}{\mathrm{Variables}}& {=}& {}\left[{x}{,}{y}\right]\\ {\mathrm{Input Formula}}& {=}& {}{\exists }{}\left(\left[{x}{,}{y}\right]{,}{3}{}{{x}}^{{2}}{-}{2}{}{y}{<}{0}{\wedge }{-}{x}{+}{y}{<}{0}{\wedge }{-}{y}{<}{2}\right)\\ {\mathrm{# Cells}}& {=}& {}{29}\\ {\mathrm{Projection polynomials for level 1}}& {=}& {}\left[\begin{array}{cccc}{x}& {2}{+}{x}& {3}{}{x}{-}{2}& {3}{}{{x}}^{{2}}{+}{4}\end{array}\right]\\ {\mathrm{Projection polynomials for level 2}}& {=}& {}\left[\begin{array}{ccc}{x}{-}{y}& {y}{+}{2}& {3}{}{{x}}^{{2}}{-}{2}{}{y}\end{array}\right]\end{array}\right$ (2)
 > $\mathrm{cells}≔\mathrm{GetCells}\left(\mathrm{cad}\right):$
 > $\mathrm{cells}\left[1..5\right]$
 $\left[\left[\begin{array}{lll}{\mathrm{Description}}& {=}& {}{x}{<}{-2}{\wedge }{y}{<}{x}\\ {\mathrm{Sample Point}}& {=}& {}\left[{x}{=}{-3}{,}{y}{=}{-4}\right]\\ {\mathrm{Index}}& {=}& {}\left[{1}{,}{1}\right]\end{array}\right{,}\left[\begin{array}{lll}{\mathrm{Description}}& {=}& {}{x}{<}{-2}{\wedge }{y}{=}{x}\\ {\mathrm{Sample Point}}& {=}& {}\left[{x}{=}{-3}{,}{y}{=}{-3}\right]\\ {\mathrm{Index}}& {=}& {}\left[{1}{,}{2}\right]\end{array}\right{,}\left[\begin{array}{lll}{\mathrm{Description}}& {=}& {}{x}{<}{-2}{\wedge }{x}{<}{y}{\wedge }{y}{<}{-2}\\ {\mathrm{Sample Point}}& {=}& {}\left[{x}{=}{-3}{,}{y}{=}{-}\frac{{5}}{{2}}\right]\\ {\mathrm{Index}}& {=}& {}\left[{1}{,}{3}\right]\end{array}\right{,}\left[\begin{array}{lll}{\mathrm{Description}}& {=}& {}{x}{<}{-2}{\wedge }{y}{=}{-2}\\ {\mathrm{Sample Point}}& {=}& {}\left[{x}{=}{-3}{,}{y}{=}{-2}\right]\\ {\mathrm{Index}}& {=}& {}\left[{1}{,}{4}\right]\end{array}\right{,}\left[\begin{array}{lll}{\mathrm{Description}}& {=}& {}{x}{<}{-2}{\wedge }{-2}{<}{y}{\wedge }{y}{<}\frac{{3}{}{{x}}^{{2}}}{{2}}\\ {\mathrm{Sample Point}}& {=}& {}\left[{x}{=}{-3}{,}{y}{=}{0}\right]\\ {\mathrm{Index}}& {=}& {}\left[{1}{,}{5}\right]\end{array}\right\right]$ (3)
 > $\mathrm{trueSamplePoints}≔\mathrm{GetCells}\left(\mathrm{cad},'\mathrm{truthvalue}'=\mathrm{true},'\mathrm{output}'=\left['\mathrm{samplepoints}'\right]\right)$
 ${\mathrm{trueSamplePoints}}{≔}\left[\left[{x}{=}\frac{{1}}{{2}}{,}{y}{=}\frac{{2}}{{5}}\right]\right]$ (4)
 > $\mathrm{GetCells}\left(\mathrm{cad},'\mathrm{truthvalue}'=\mathrm{true},'\mathrm{output}'=\left['\mathrm{descriptions}'\right]\right)$
 $\left[{0}{<}{x}{\wedge }{x}{<}\frac{{2}}{{3}}{\wedge }\frac{{3}{}{{x}}^{{2}}}{{2}}{<}{y}{\wedge }{y}{<}{x}\right]$ (5)

Compatibility

 • The QuantifierElimination:-CADData:-GetCells command was introduced in Maple 2023.