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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 uses execute or calls a procedure using execute. 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.


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