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D.5.3.3 esStratum
Procedure from library equising.lib (see equising_lib).
- Usage:
esStratum(F[,m,L]); F poly, m int, L list
- Assume:
F defines a deformation of a reduced bivariate polynomial f and the characteristic of the basering does not divide mult(f).
If nv is the number of variables of the basering, then the first nv-2 variables are the deformation parameters.
If the basering is a qring, ideal(basering) must only depend on the deformation parameters.- Compute:
equations for the stratum of equisingular deformations with fixed (trivial) section.
- Return:
list l: either consisting of an ideal and an integer, where
l[1]=ideal defining the equisingular stratum l[2]=1 if some error has occured, l[2]=0 otherwise;
or consisting of a ring and an integer, where
l[1]=ESSring is a ring extension of basering containing the ideal ES (describing the ES-stratum) and the poly p_F=F, l[2]=1 if some error has occured, l[2]=0 otherwise.- Note:
L is supposed to be the output of reddevelop (with the given ordering of the variables appearing in f).
If m is given, the ES Stratum over A/maxideal(m) is computed.
This procedure usesexecuteor calls a procedure usingexecute. printlevel>=2 displays additional information.
Example:
LIB "equising.lib"; int p=printlevel; printlevel=1; ring r = 0,(a,b,c,d,e,f,g,x,y),ds; poly F = (x2+2xy+y2+x5)+ax+by+cx2+dxy+ey2+fx3+gx4; list M = esStratum(F); M[1]; → _[1]=g → _[2]=f → _[3]=b → _[4]=a → _[5]=-4c+4d-4e+d2-4ce printlevel=3; // displays additional information esStratum(F,2); // es stratum over Q[a,b,c,d,e,f,g] / <a,b,c,d,e,f,g>^2 → // → // Compute HN development → // ---------------------- → // finished → // → // Blowup Step 1 completed → // Blowup Step 2 completed → // Blowup Step 3 completed → // 1 branch finished → // → // Elimination starts: → // ------------------- → // finished → // → // output of 'esStratum' is list consisting of: → // _[1] = ideal defining equisingular stratum → // _[2] = 0 → [1]: → _[1]=b → _[2]=a → _[3]=c-d+e → _[4]=g → _[5]=f → [2]: → 0 ideal I = f-fa,e+b; qring q = std(I); poly F = imap(r,F); esStratum(F); → // → // Compute HN development → // ---------------------- → // finished → // → // Blowup Step 1 completed → // Blowup Step 2 completed → // Blowup Step 3 completed → // 1 branch finished → // → // Elimination starts: → // ------------------- → // finished → // → // output of 'esStratum' is list consisting of: → // _[1] = ideal defining equisingular stratum → // _[2] = 0 → [1]: → _[1]=e → _[2]=a → _[3]=-4c+4d+d2 → _[4]=g → [2]: → 0 printlevel=p; |
See also: esIdeal; isEquising.