D.5.6.3 jacoblift

Procedure from library mondromy.lib (see mondromy_lib).

Usage:

jacoblift(f); f poly

Assume:

The polynomial f in a series ring (local ordering) defines an isolated hypersurface singularity.

Return:

The procedure returns a list with entries kappa, xi, u of type int, vector, poly such that kappa is minimal with f^kappa in jacob(f), u is a unit, and u*f^kappa=(matrix(jacob(f))*xi)[1,1].

Display:

The procedure displays comments if printlevel>=1.

Example:

LIB "mondromy.lib";
ring R=0,(x,y),ds;
poly f=x2y2+x6+y6;
jacoblift(f);
→ [1]:
→    2
→ [2]:
→    1/2x2y3*gen(2)+1/6x7*gen(1)+5/6x6y*gen(2)-2/3xy6*gen(1)+1/6y7*gen(2)-4\
   x4y5*gen(2)-3/2x9y2*gen(1)-15/2x8y3*gen(2)+9/2x3y8*gen(1)-3/2x2y9*gen(2)
→ [3]:
→    1-9x2y2