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:

cells : list(CADCell); list of CAD cells for the CAD.

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).

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.

$\mathrm{ex}≔':-\mathrm{exists}'\left(\left[y\&comma;x\right]\&comma;':-\mathrm{And}'\left(3x^2-2y<0\&comma;0<x-y\&comma;0<y+2\right)\right)$

$\mathrm{ex}≔\exists \left(\left[y\&comma;x\right]\&comma;3x^2-2y<0\wedge 0<x-y\wedge 0<y+2\right)$

$\mathrm{cad}≔\mathrm{QuantifierElimination}:-\mathrm{PartialCylindricalAlgebraicDecompose}\left(\mathrm{ex}\&comma;\mathrm{output}=\left['\mathrm{data}'\right]\right)$

$\mathrm{cad}≔\left[\begin{array}{lll}\mathrm{Variables}& \&equals;& \left[x\&comma;y\right]\\ \mathrm{Input\; Formula}& \&equals;& \exists \left(\left[x\&comma;y\right]\&comma;3x^2-2y<0\wedge -x+y<0\wedge -y<2\right)\\ \mathrm{\#\; Cells}& \&equals;& 29\\ \mathrm{Projection\; polynomials\; for\; level\; 1}& \&equals;& \left[\begin{array}{cccc}x& 2+x& 3x-2& 3x^2+4\end{array}\right]\\ \mathrm{Projection\; polynomials\; for\; level\; 2}& \&equals;& \left[\begin{array}{ccc}x-y& y+2& 3x^2-2y\end{array}\right]\end{array}\right.$

$\mathrm{cells}≔\mathrm{GetCells}\left(\mathrm{cad}\right)\&colon;$

$\mathrm{cells}\left[1..5\right]$

$\left[\left[\begin{array}{lll}\mathrm{Description}& \&equals;& x<\mathrm{-2}\wedge y<x\\ \mathrm{Sample\; Point}& \&equals;& \left[x=\mathrm{-3}\&comma;y=\mathrm{-4}\right]\\ \mathrm{Index}& \&equals;& \left[1\&comma;1\right]\end{array}\right.\&comma;\left[\begin{array}{lll}\mathrm{Description}& \&equals;& x<\mathrm{-2}\wedge y=x\\ \mathrm{Sample\; Point}& \&equals;& \left[x=\mathrm{-3}\&comma;y=\mathrm{-3}\right]\\ \mathrm{Index}& \&equals;& \left[1\&comma;2\right]\end{array}\right.\&comma;\left[\begin{array}{lll}\mathrm{Description}& \&equals;& x<\mathrm{-2}\wedge x<y\wedge y<\mathrm{-2}\\ \mathrm{Sample\; Point}& \&equals;& \left[x=\mathrm{-3}\&comma;y=-\frac{5}{2}\right]\\ \mathrm{Index}& \&equals;& \left[1\&comma;3\right]\end{array}\right.\&comma;\left[\begin{array}{lll}\mathrm{Description}& \&equals;& x<\mathrm{-2}\wedge y=\mathrm{-2}\\ \mathrm{Sample\; Point}& \&equals;& \left[x=\mathrm{-3}\&comma;y=\mathrm{-2}\right]\\ \mathrm{Index}& \&equals;& \left[1\&comma;4\right]\end{array}\right.\&comma;\left[\begin{array}{lll}\mathrm{Description}& \&equals;& x<\mathrm{-2}\wedge \mathrm{-2}<y\wedge y<\frac{3x^2}{2}\\ \mathrm{Sample\; Point}& \&equals;& \left[x=\mathrm{-3}\&comma;y=0\right]\\ \mathrm{Index}& \&equals;& \left[1\&comma;5\right]\end{array}\right.\right]$

$\mathrm{trueSamplePoints}≔\mathrm{GetCells}\left(\mathrm{cad}\&comma;'\mathrm{truthvalue}'=\mathrm{true}\&comma;'\mathrm{output}'=\left['\mathrm{samplepoints}'\right]\right)$

$\mathrm{trueSamplePoints}≔\left[\left[x=\frac{1}{2}\&comma;y=\frac{2}{5}\right]\right]$

$\mathrm{GetCells}\left(\mathrm{cad}\&comma;'\mathrm{truthvalue}'=\mathrm{true}\&comma;'\mathrm{output}'=\left['\mathrm{descriptions}'\right]\right)$

$\left[0<x\wedge x<\frac{2}{3}\wedge \frac{3x^2}{2}<y\wedge y<x\right]$

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

For more information on Maple 2023 changes, see Updates in Maple 2023.

The output option was introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.