decompose(WitnessSet) -- decompose a witness set into irreducibles

Function: decompose
Usage:

Ws = decompose W
Inputs:
- W, a witness set, represents an equidimensional component of a variety
Outputs:
- Ws, contains irreducible witness sets witness sets, the union of which is W

Description

Monodromy driven decomposition is followed by the linear trace test.

i1 : R = CC[x,y]

o1 = R

o1 : PolynomialRing

i2 : F = {x^2+y^2-1, x*y};

i3 : W = first components regeneration F 

o3 = W

o3 : WitnessSet

i4 : decompose W

o4 = {(dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1)}

o4 : List

i5 : R = CC[x,y,z]

o5 = R

o5 : PolynomialRing

i6 : sph = (x^2+y^2+z^2-1);

i7 : decompose \ components regeneration {sph*(x-1)*(y-x^2), sph*(y-2)*(z-x^3)}

o7 = {{(dim=1,deg=1), (dim=1,deg=1), (dim=1,deg=1), (dim=1,deg=1),
     ------------------------------------------------------------------------
     (dim=1,deg=3)}, {(dim=2,deg=2)}}

o7 : List

Caveat

This function is under development. It can not decompose nonreduced components at the moment. If monodromy breakup algorithm fails to classify some points, the unnclassified points appear as one witness set (that is not marked as irreducible).

Ways to use this method:

decompose(WitnessSet) -- decompose a witness set into irreducibles

The source of this document is in NumericalAlgebraicGeometry/doc.m2:630:0.

decompose(WitnessSet) -- decompose a witness set into irreducibles

Description

Caveat

See also

Ways to use this method: