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PolyhedralSets[ZPolyhedralSets]

  

SamplePoint

  

return a sample point of a ZPolyhedralSet

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

SamplePoint(zpoly)

Parameters

zpoly

-

ZPolyhedralSet

Description

• 

SamplePoint(zpoly) returns a sample point of zpoly. If zpoly is empty, then an error is raised.

Examples

withPolyhedralSets:

withZPolyhedralSets:

Create a Z-polyhedron in three-dimensional space.

ineqs016+2y+z,072+4x+4y+3z,02yz,024+4x+4y3z,04x+4y+3z,0484x+4y3z,0484x4y+3z,082y+z,024+4x4y+3z,0242yz,024+4x4y3z,0964x4y3z

ineqs016+2y+z,072+4x+4y+3z,02yz,024+4x+4y3z,04x+4y+3z,0484x+4y3z,0484x4y+3z,082y+z,024+4x4y+3z,0242yz,024+4x4y3z,0964x4y3z

(1)

LLatticeMatrix1,0,2,0,1,1,0,0,2,Vector0,0,1

LLattice1020−11002,001

(2)

varsz,x,y

varsz,x,y

(3)

zpZPolyhedralSetineqs,vars,lattice=L

zpRelations:02yz016+2y+z082y+z0242yz04x+4y+3z072+4x+4y+3z024+4x4y+3z024+4x+4y3z024+4x4y3z0484x4y+3z0484x+4y3z0964x4y3zVariables:z,x,yParameters:ParameterConstraints:Lattice:ZSpan1020−11002,,,001

(4)

Get a sample point from zp.

SamplePointzp

z=10,x=9,y=7

(5)

Double-check that latter answer by enumerating the points of zp.

EnumerateIntegerPointszp

x=9,y=5,z=6,x=9,y=7,z=6,x=8,y=5,z=7,x=9,y=5,z=7,x=10,y=5,z=7,x=8,y=7,z=7,x=9,y=7,z=7,x=10,y=7,z=7,x=7,y=5,z=8,x=8,y=5,z=8,x=9,y=5,z=8,x=10,y=5,z=8,x=11,y=5,z=8,x=7,y=7,z=8,x=8,y=7,z=8,x=9,y=7,z=8,x=10,y=7,z=8,x=11,y=7,z=8,x=8,y=5,z=9,x=9,y=5,z=9,x=10,y=5,z=9,x=8,y=7,z=9,x=9,y=7,z=9,x=10,y=7,z=9,x=9,y=5,z=10,x=9,y=7,z=10

(6)

References

  

Rachid Seghir, Vincent Loechner, and Benoı̂t Meister. "Integer affine transformations of parametric Z-polytopes and applications to loop nest optimization." Proceedings of TACO, Vol. 9(2):8:1–8:27, 2012.

  

Rui-Juan Jing and Marc Moreno Maza. "Computing the Integer Points of a Polyhedron, I: Algorithm." Proceedings of CASC 2017: 225-241, Springer.

  

Rui-Juan Jing and Marc Moreno Maza. "Computing the Integer Points of a Polyhedron, II: Complexity Estimates." Proceedings of CASC 2017: 242-256, Springer.

Compatibility

• 

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

• 

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

See Also

ZPolyhedralSets[IsEmpty]

ZPolyhedralSets[IsContained]

ZPolyhedralSets[IsIntegerPointOf]

ZPolyhedralSets[IntegerPointDecomposition]

ZPolyhedralSets[EnumerateIntegerPoints]

ZPolyhedralSets

PolyhedralSets