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

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.

DualSpace -- a dual functional vector subspace

Description

See also

Methods that use an object of class DualSpace :

For the programmer