next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
NumericalAlgebraicGeometry :: numericalVariety(Ideal)

numericalVariety(Ideal) -- constructs a numerical variety defined by the given ideal

Synopsis

Description

The witness sets of V are in one-to-one correspondence with irreducible components of the variety defined by I.
i1 : R = CC[x,y,z]

o1 = R

o1 : PolynomialRing
i2 : sph = (x^2+y^2+z^2-1); 
i3 : I = ideal {sph*(x-1)*(y-x^2), sph*(y-1)*(z-x^3)};

o3 : Ideal of R
i4 : setRandomSeed 7

o4 = 7
i5 : V = numericalVariety I 

o5 = A variety of dimension 2 with components in
     dim 1:  (dim=1,deg=1) (dim=1,deg=1) (dim=1,deg=1) (dim=1,deg=3)
     dim 2:  (dim=2,deg=2)

o5 : NumericalVariety
i6 : peek V

o6 = NumericalVariety{1 => {(dim=1,deg=1), (dim=1,deg=1), (dim=1,deg=1),
                      2 => {(dim=2,deg=2)}
     ------------------------------------------------------------------------
     (dim=1,deg=3)}}

Caveat

This function is under development. It may not work well if the input represents a nonreduced scheme.

See also