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.
setRandomSeed 7
R = CC[x,y]
F = {x^2+y^2-1, x*y};
W = first regeneration F
decompose W
R = CC[x,y,z]
sph = (x^2+y^2+z^2-1);
I = ideal {sph*(x-0.5)*(y-x^2), sph*(y-0.5)*(z-x^3), sph*(z-0.5)*(z-x^3)*(y-x^3)};
regeneration I_* / decompose
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).
See also
regeneration -- solve a system of polynomial equations with regeneration method