PPVector

• class PPVector
  • Examples
• Fields and main functions
  • Utility functions
  • Mathemetical functions
• Bugs, Shortcomings and other ideas
  • Abstract Class

modernise

class PPVector

WARNING THIS IS STILL A PRELIMINARY IMPLEMENTATION as indicated by the names of the implementation files: TmpPPVector.H and TmpPPVector.C.

This class is for dealing with lists of power-products.

This class has been designed to be used by monomial ideal operations, Hilbert, and Mayer-Vietoris trees.

The key functions interpret the list as generators of a monomial ideal: interreduction, divisibility test (ideal membership), lcms (ideal intersection).

The elements are PPWithMask, to make fast divisibility tests. Constructor requires a PPMonoid and a DivMaskRule (see DivMask), so that the user can choose the best suited implementations (mostly depending on the number of indeterminates and on the size of the exponents).

Examples

• ex-PPVector1.C

Fields and main functions

Member fields are

      PPMonoid myPPM;
      DivMaskRule myDMR;
      std::vector<PPWithMask> myVec;

Utility functions

• PPMonoid PPM(const PPVector& PPs)
• DivMaskRule DMR(const PPVector& PPs)
• std::ostream& operator<<(std::ostream&, PPVector)
• bool IsEmpty(const PPVector& PPs)
• long len(const PPVector& PPs)
• void convert(std::vector<RingElem>& v, ring P, const PPVector& PPs) converts PP's into RingElem's
• void convert(PPVector PPs, const std::vector<RingElem>& v) converts vector<RingElem> (if monomial!) into PPVector
• void PushBack(PPVector& PPs, ConstRefPPMonoidElem pp) if owner(pp) != PPM(PPs) it maps it
• void PushBackPopBack(PPVector& ToPPs, PPVector& FromPPs) move last PP from FromPPs into ToPPs
• void swap(PPVector& PPs1, PPVector& PPs2) swap PPs1 and PPs1

Mathemetical functions

• bool IsDivisible(const PPWithMask& pp, const PPVector& ByL); true is pp is divisible by an element of L
• bool IsDivisible(ConstRefPPMonoidElem pp, const PPVector& ByL); true is pp is divisible by an element of L
• void interreduce(PPVector& PPs); interreduce PPs (NOT exception clean)
• void InterreduceSort(PPVector& PPs); interreduce and sort PPs (NOT exception clean)
• void lcms(PPVector& PPs, const PPVector& PPs1, const PPVector& PPs2); all the lcm between elements of PPs1 and PPs2, effectively the generators of the intersection ideal

Bugs, Shortcomings and other ideas

Abstract Class

There was an attempt to make it an abstract class, PPVectorBase, made of abstract PPVectorElem, with the plan to have concrete classes a vector of PPWithMask, of PPMonoidElem, and of square-free pps (which cannot make a PPMonoid because x*x is not square-free).

But this failed because most operations would need to know the type of the elements in the vector making it more suitable for templates. But

• (1) I much prefer inheritance (mathematically cleaner) and
• (2) probably all this generality is useless.

So it was sadly abandoned.