# components(NumericalVariety) -- list components of a numerical variety

## Synopsis

• Function: components
• Usage:
components(V)
components(V,a)
components(V,a,b)
• Inputs:
• Outputs:

## Description

Returns a list of components of a numerical variety. If a (an integer) and/or b (an integer or infinity) are specified, then components of dimension a (respectively, components of dimension at least a and at most b) are returned.

 i1 : R = CC[x,y]; I = ideal((x^2+y^2+2)*x,(x^2+y^2+2)*y); o2 : Ideal of R i3 : w1 := witnessSet(I , ideal(x-y), {point {{0.999999*ii,0.999999*ii}}, point {{-1.000001*ii,-1.000001*ii}}} ) o3 = [dim=1,deg=2]-*may be reducible*- o3 : WitnessSet i4 : w0 := witnessSet(I, ideal R, {point {{0.,0.}}}) o4 = [dim=0,deg=1]-*may be reducible*- o4 : WitnessSet i5 : V := numericalVariety {w0,w1} o5 = a "numerical variety" with components in dim 0: [dim=0,deg=1]-*may be reducible*- dim 1: [dim=1,deg=2]-*may be reducible*- o5 : NumericalVariety i6 : components V o6 = {[dim=0,deg=1]-*may be reducible*-, [dim=1,deg=2]-*may be reducible*-} o6 : List

## Ways to use this method:

• components(NumericalVariety) -- list components of a numerical variety
• "components(NumericalVariety,ZZ)"
• "components(NumericalVariety,ZZ,InfiniteNumber)"
• "components(NumericalVariety,ZZ,ZZ)"