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NAGtypes :: NumericalVariety

NumericalVariety -- a numerical variety

Description

This type stores a collection of witness sets representing a complex affine variety.

Note that Basic service routines:
i1 : R = CC[x,y]; I = ideal((x^2+y^2+2)*x,(x^2+y^2+2)*y*(y-1));

o2 : Ideal of R
i3 : w1 := witnessSet(I , ideal(x-y), {point {{0.999*ii,0.999*ii}}, point {{-1.001*ii,-1.001*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 : w0' := witnessSet(I, ideal R, {point {{0.,1.}}})

o5 = [dim=0,deg=1]-*may be reducible*-

o5 : WitnessSet
i6 : V := numericalVariety {w0,w1,w0'}

o6 = a numerical variety with components in
     dim 0:  [dim=0,deg=1]-*may be reducible*- [dim=0,deg=1]-*may be reducible*-
     dim 1:  [dim=1,deg=2]-*may be reducible*-

o6 : NumericalVariety
i7 : dim V

o7 = 1
i8 : degree V

o8 = 2

See also

Functions and methods returning a numerical variety :

Methods that use a numerical variety :

For the programmer

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