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D.5.3.1 esStratum
Procedure from library equising.lib (see equising_lib).
- Usage:
- esStratum(F[,m]); F poly, m int
- Assume:
- F defines a deformation of an irreducible 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.
- Return:
- list l of an ideal and an integer, where
| l[1] is the ideal in the deformation parameters, defining the ES-stratum of F,
l[2]=1 if some error has occured, l[2]=0 otherwise.
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- Note:
- If m is given, the computation stops after m steps of the iteration.
printlevel > 0 displays comments and pauses after intermediate
computations (default: printlevel=0)
This procedure uses execute or calls a procedure using
execute .
Example:
| LIB "equising.lib";
ring r = 11,(a,b,c,d,e,f,g,x,y),ds;
poly F = (x2+2xy+y2+x5)+ax+by+cx2+dxy+ey2+fx3+gx4;
esStratum(F);
==> [1]:
==> _[1]=g
==> _[2]=f
==> _[3]=b
==> _[4]=a
==> _[5]=-4c+4d-4e+d2-4ce
==> [2]:
==> 0
esStratum(F,2);
==> [1]:
==> _[1]=g
==> _[2]=f
==> _[3]=b
==> _[4]=a
==> _[5]=-4c+4d-4e+d2-4ce
==> [2]:
==> 0
ideal I = f-fa,e+b;
qring q = std(I);
poly F = imap(r,F);
esStratum(F);
==> [1]:
==> _[1]=a
==> _[2]=-e
==> _[3]=c-d-3d2
==> _[4]=g
==> [2]:
==> 0
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