Macaulay2 » Documentation
Packages » NAGtypes :: DualSpace
next | previous | forward | backward | up | index | toc

DualSpace -- a dual functional vector subspace

Description

This type stores a finite dimensional subspace of the local dual of a polynomial ring at a point. In practice, the subspace is stored as a PolySpace with functionals represented by the corresponding polynomial, along with a AbstractPoint. The following methods can be used to access a DualSpace:

  • gens -- a one-row matrix of the generators
  • dim -- the number of generators
  • ring -- the ring of the generators
  • point -- the base point of the dual space

See also

Methods that use an object of class DualSpace:

  • areEqual(DualSpace,DualSpace) -- approximate equality of dual spaces
  • dim(DualSpace)
  • generators(DualSpace)
  • net(DualSpace)
  • point(DualSpace)
  • ring(DualSpace)
  • dualSpace(DualSpace) -- see dualSpace -- construct a DualSpace
  • isContained(DualSpace,DualSpace) -- see isContained -- Is one space contained in the other
  • random(DualSpace) -- see random(PolySpace) -- random element of a subspace
  • random(ZZ,DualSpace) -- see random(PolySpace) -- random element of a subspace
  • reduceSpace(DualSpace) -- see reduceSpace -- reduce the generators of a space

For the programmer

The object DualSpace is a type, with ancestor classes MutableHashTable < HashTable < Thing.

The source of this document is in NAGtypes/doc-NAGtypes.m2:910:0.