PlotIntegerPoints3d(zpoly) plots the integer points of zpoly.

This requires zpoly to be non-parametric, three-dimensional, and bounded. If one of these assumptions does not hold, then an error is raised.

$\mathrm{with}\left(\mathrm{PolyhedralSets}\right)\:$

$\mathrm{with}\left(\mathrm{ZPolyhedralSets}\right)\:$

$\mathrm{ineqs}≔\left[0\le -16+2y+z\,0\le -72+4x+4y+3z\,0\le 2y-z\,0\le -24+4x+4y-3z\,0\le -4x+4y+3z\,0\le 48-4x+4y-3z\,0\le 48-4x-4y+3z\,0\le 8-2y+z\,0\le -24+4x-4y+3z\,0\le 24-2y-z\,0\le 24+4x-4y-3z\,0\le 96-4x-4y-3z\right]$

$\mathrm{ineqs}≔\left[0\le -16+2y+z\,0\le -72+4x+4y+3z\,0\le 2y-z\,0\le -24+4x+4y-3z\,0\le -4x+4y+3z\,0\le 48-4x+4y-3z\,0\le 48-4x-4y+3z\,0\le 8-2y+z\,0\le -24+4x-4y+3z\,0\le 24-2y-z\,0\le 24+4x-4y-3z\,0\le 96-4x-4y-3z\right]$

$\mathrm{ps}≔\mathrm{PolyhedralSet}\left(\mathrm{ineqs}\right)\;$$\mathrm{PolyhedralSets}:-\mathrm{Plot}\left(\mathrm{ps}\right)$

$\mathrm{ps}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x\,y\,z\right]\\ \mathrm{Relations}& \:& \left[-y-\frac{z}{2}\le \mathrm{-8}\,-y+\frac{z}{2}\le 0\,y-\frac{z}{2}\le 4\,y+\frac{z}{2}\le 12\,-x-y-\frac{3z}{4}\le \mathrm{-18}\,-x-y+\frac{3z}{4}\le \mathrm{-6}\,-x+y-\frac{3z}{4}\le \mathrm{-6}\,-x+y+\frac{3z}{4}\le 6\,x-y-\frac{3z}{4}\le 0\,x-y+\frac{3z}{4}\le 12\,\mathrm{and\; 2\; more\; constraints}\right]\end{array}$

$L≔\mathrm{Lattice}\left(\mathrm{Matrix}\left(\left[\left[1\,0\,2\right]\,\left[0\,-1\,1\right]\,\left[0\,0\,2\right]\right]\right)\,\mathrm{Vector}\left(\left[0\,0\,1\right]\right)\right)$

$L≔\mathrm{Lattice}\left(\left[\begin{array}{ccc}1& 0& 2\\ 0& \mathrm{-1}& 1\\ 0& 0& 2\end{array}\right]\,\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\right)$

$\mathrm{vars}≔\left[x\,y\,z\right]$

$\mathrm{vars}≔\left[x\,y\,z\right]$

$\mathrm{zp}≔\mathrm{ZPolyhedralSet}\left(\mathrm{ineqs}\,\mathrm{vars}\,':-\mathrm{lattice}'=L\right)$

$\mathrm{zp}≔\left\{\begin{array}{lll}\text{Relations}& \:& \left\{\begin{array}{:}0\le 2y-z\\ 0\le -16+2y+z\\ 0\le 8-2y+z\\ 0\le 24-2y-z\\ 0\le -4x+4y+3z\\ 0\le -72+4x+4y+3z\\ 0\le -24+4x-4y+3z\\ 0\le -24+4x+4y-3z\\ 0\le 24+4x-4y-3z\\ 0\le 48-4x-4y+3z\\ 0\le 48-4x+4y-3z\\ 0\le 96-4x-4y-3z\end{array}\right.\\ \text{Variables}& \:& \left[x\,y\,z\right]\\ \text{Parameters}& \:& \left[\right]\\ \text{ParameterConstraints}& \:& \left\{\begin{array}{}\end{array}\right.\\ \text{Lattice}& \:& \text{ZSpan}\left(\left[\begin{array}{ccc}1& 0& 2\\ 0& \mathrm{-1}& 1\\ 0& 0& 2\end{array}\right]\,\,\,\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\right)\end{array}\right.$

$\mathrm{PlotIntegerPoints3d}\left(\mathrm{zp}\right)$

$\mathrm{ineqs}≔\left[x+\frac{2y}{3}\le 4\,-x+y\le 1\,\frac{1}{11}x+\frac{24}{11}\le y\right]$

$\mathrm{ineqs}≔\left[x+\frac{2y}{3}\le 4\,-x+y\le 1\,\frac{x}{11}+\frac{24}{11}\le y\right]$

$\mathrm{zp}≔\mathrm{ZPolyhedralSet}\left(\mathrm{ineqs}\,\left[x\,y\right]\right)$

$\mathrm{zp}≔\left\{\begin{array}{lll}\text{Relations}& \:& \left\{\begin{array}{:}-x+y\le 1\\ x+\frac{2y}{3}\le 4\\ \frac{x}{11}+\frac{24}{11}\le y\end{array}\right.\\ \text{Variables}& \:& \left[x\,y\right]\\ \text{Parameters}& \:& \left[\right]\\ \text{ParameterConstraints}& \:& \left\{\begin{array}{}\end{array}\right.\\ \text{Lattice}& \:& \text{ZSpan}\left(\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\,\,\,\left[\begin{array}{c}0\\ 0\end{array}\right]\right)\end{array}\right.$

$\mathrm{PlotIntegerPoints3d}\left(\mathrm{zp}\right)$

Error, (in PolyhedralSets:-ZPolyhedralSets:-PlotIntegerPoints3d) cannot handle this ZPolyhedralSet: its dimension is 2 instead of 3

The PolyhedralSets:-ZPolyhedralSets:-PlotIntegerPoints3d command was introduced in Maple 2023.

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