NumericalVariety -- a numerical variety

Description

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

Note that

The ambient space is expected to be the same, i.e., dimension (or ProjectionDimension) of witness sets should be the same.
The constructor numericalVariety(List) does not check the sensibility of the input; run check(NumericalVariety) to verify the validity of a numerical variety.

Basic service routines:

dim -- the dimension
codim -- the codimension
deg -- the degree
components(NumericalVariety)

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

Functions and methods returning a numerical variety:

numericalVariety -- see numericalVariety(List) -- construct a numerical variety

Methods that use a numerical variety:

components(NumericalVariety) -- list components of a numerical variety
components(NumericalVariety,ZZ) -- see components(NumericalVariety) -- list components of a numerical variety
components(NumericalVariety,ZZ,InfiniteNumber) -- see components(NumericalVariety) -- list components of a numerical variety
components(NumericalVariety,ZZ,ZZ) -- see components(NumericalVariety) -- list components of a numerical variety
check(NumericalVariety)
degree(NumericalVariety)
dim(NumericalVariety)
net(NumericalVariety)

For the programmer

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

The source of this document is in NAGtypes/doc-NAGtypes.m2:720:0.

NumericalVariety -- a numerical variety

Description

See also

Functions and methods returning a numerical variety:

Methods that use a numerical variety:

For the programmer