PolyhedralSets[ZPolyhedralSets]
PlotIntegerPoints3d
plot the integer points of a 3-D polyhedron
Calling Sequence
Parameters
Description
Examples
Compatibility
PlotIntegerPoints3d(zpoly)
zpoly
-
ZPolyhedralSet
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.
withPolyhedralSets:
withZPolyhedralSets:
Plot a three-dimensional Z-Polyhedral set.
ineqs≔0≤−16+2y+z,0≤−72+4x+4y+3z,0≤2y−z,0≤−24+4x+4y−3z,0≤−4x+4y+3z,0≤48−4x+4y−3z,0≤48−4x−4y+3z,0≤8−2y+z,0≤−24+4x−4y+3z,0≤24−2y−z,0≤24+4x−4y−3z,0≤96−4x−4y−3z
ps≔PolyhedralSetineqs;PolyhedralSets:-Plotps
ps≔{Coordinates:x,y,zRelations:−y−z2≤−8,−y+z2≤0,y−z2≤4,y+z2≤12,−x−y−3z4≤−18,−x−y+3z4≤−6,−x+y−3z4≤−6,−x+y+3z4≤6,x−y−3z4≤0,x−y+3z4≤12, and 2 more constraints
L≔LatticeMatrix1,0,2,0,−1,1,0,0,2,Vector0,0,1
L≔Lattice1020−11002,001
vars≔x,y,z
zp≔ZPolyhedralSetineqs,vars,:-lattice=L
zp≔Relations:0≤2y−z0≤−16+2y+z0≤8−2y+z0≤24−2y−z0≤−4x+4y+3z0≤−72+4x+4y+3z0≤−24+4x−4y+3z0≤−24+4x+4y−3z0≤24+4x−4y−3z0≤48−4x−4y+3z0≤48−4x+4y−3z0≤96−4x−4y−3zVariables:x,y,zParameters:ParameterConstraints:Lattice:ZSpan1020−11002,,,001
PlotIntegerPoints3dzp
Trying to plot a Z-Polyhedral set which is not three-dimensional.
ineqs≔x+2y3≤4,−x+y≤1,111x+2411≤y
ineqs≔x+2y3≤4,−x+y≤1,x11+2411≤y
zp≔ZPolyhedralSetineqs,x,y
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.
See Also
ZPolyhedralSets:-IsEmpty
ZPolyhedralSets:-IsIntegerPointOf
ZPolyhedralSets:-SamplePoint
ZPolyhedralSets:-IntegerPointDecomposition
ZPolyhedralSets:-IsContained
ZPolyhedralSets:-ZPolyhedralSet
ZPolyhedralSets
PolyhedralSets
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