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

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

See also

Ways to use this method:

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

The source of this document is in NAGtypes/doc-NAGtypes.m2:769:0.