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# PolySpace -- a polynomial vector subspace

## Description

This type stores a finite dimensional vector subspace of a polynomial ring, given by a spanning set. The spanning set is generally assumed to be a basis although this is not enforced. The following methods can be used to access a PolySpace:

- gens -- a one-row matrix of the generators
- dim -- the number of generators
- ring -- the ring of the generators

## See also

- polySpace -- construct a PolySpace
- DualSpace -- a dual functional vector subspace

## Functions and methods returning an object of class PolySpace:

- addition -- Union of polynomial spaces
- intersect(PolySpace,PolySpace) -- Intersection of polynomial spaces

## Methods that use an object of class PolySpace:

- `addition(PolySpace,PolySpace)` -- see addition -- Union of polynomial spaces
- areEqual(PolySpace,PolySpace) -- approximate equality of subspaces spanned by polynomials
- `dualSpace(PolySpace,AbstractPoint)` -- see dualSpace -- construct a DualSpace
- `isContained(PolySpace,PolySpace)` -- see isContained -- Is one space contained in the other
- `dim(PolySpace)`
- `generators(PolySpace)`
- `net(PolySpace)`
- `ring(PolySpace)`
- `polySpace(PolySpace)` -- see polySpace -- construct a PolySpace
- random(PolySpace) -- random element of a subspace
- `random(ZZ,PolySpace)` -- see random(PolySpace) -- random element of a subspace
- `reduceSpace(PolySpace)` -- see reduceSpace -- reduce the generators of a space

## For the programmer

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NAGtypes/doc-NAGtypes.m2:857:0.