IsEmpty - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


PolyhedralSets[ZPolyhedralSets]

  

IsEmpty

  

check whether a given ZPolyhedralSet is empty or not

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

IsEmpty(zpoly)

Parameters

zpoly

-

ZPolyhedralSet

Description

• 

IsEmpty(zpoly) returns true if zpoly is empty, and otherwise returns false.

Examples

withPolyhedralSets:

withZPolyhedralSets:

Create a Z-polyhedron in the two-dimensional space with a system of three linear inequalities.

ineqsx+2y34,x+y78,1x11+2411y

ineqsx+2y34,x+y78,x11+2411y

(1)

zpZPolyhedralSetineqs,x,y

Check whether it is empty.

ZPolyhedralSets:-IsEmptyzp

true

(2)

Double-check that latter answer.

EnumerateIntegerPointszp

(3)

Create another Z-polyhedron in the three-dimensional space with a system of linear inequalities.

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

(4)

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

LLattice1020−11002,001

(5)

varsx,y,z

varsx,y,z

(6)

zpZPolyhedralSetineqs,vars,':-lattice'=L

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

(7)

Check whether it is empty.

ZPolyhedralSets:-IsEmptyzp

false

(8)

Double-check that latter answer.

Point_from_pzpSamplePointzp

Point_from_pzpx=10,y=7,z=9

(9)

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:-IsEmpty command was introduced in Maple 2023.

• 

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

See Also

ZPolyhedralSets:-IsIntegerPointOf

ZPolyhedralSets:-IsContained

ZPolyhedralSets:-SamplePoint

ZPolyhedralSets:-IntegerPointDecomposition

ZPolyhedralSets:-EnumerateIntegerPoints

ZPolyhedralSets:-ZPolyhedralSet

ZPolyhedralSets

PolyhedralSets