ring r = 0,(x,y,z),ds;
matrix M2[3][2] = z, 0, y^2, z-x^7, x^9, y;
LIB "spcurve.lib";
LIB "stratify.lib";
minor(M2,2);

==>

_[1]=z2-x7z _[2]=yz _[3]=-y3+x9z-x16

The corresponding space curve has 2 branches given by (y³+x¹⁶,z), resp. by (z-x⁷,y). This can be seen, for instance by using primdecGTZ(minor(M2,2)). We compute a monomial basis of T¹: list li=matrixT1(M2,3);
vdim(std(li[2])); // Tjurina number

==>

44

Next, we compute a versal family with fixed quasihomogeneous initial part: posweight(li[1],std(li[2]),0);

==>

[1]: _[1,1]=z _[1,2]=x^4*T(3)+x^5*T(2)+x^6*T(1) _[2,1]=y^2+x^6*y*T(4)+x^11*T(8)+x^12*T(7)+x^13*T(6)+x^14*T(5) _[2,2]=z-x^7 _[3,1]=x^9 _[3,2]=y [2]: 8,5,2,2,10,7,4,1

The kernel of the Kodaira-Spencer map can be computed by setring r;
def KS=KSpencerKernel(M2); We change to the ring in the variables T(i) and define the integer vectors indicating the filtration ring rt=0,(T(1..8)),wp(8,5,2,2,10,7,4,1);
def KS=imap(reneu,KS);
intvec wr=10,8,7,5,4,2,2,1;
intvec ws=9,6,3,0;
int step=3; Finally, we compute the stratification: list l=stratify(KS,wr,ws,step);
size(l);

==>

12

Result: 12 Strata