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A.6 Parameters
Let us deform the above ideal now by introducing a parameter t
and compute over the ground field Q(t).
We compute the dimension at the generic point,
i.e.,
.(This gives the
same result as for the deformed ideal above. Hence, the above small
deformation was "generic".)
For almost all
this is the same as
,where
.
| ring Rt = (0,t),(x,y),lp;
Rt;
==> // characteristic : 0
==> // 1 parameter : t
==> // minpoly : 0
==> // number of vars : 2
==> // block 1 : ordering lp
==> // : names x y
==> // block 2 : ordering C
poly f = x5+y11+xy9+x3y9;
ideal i = jacob(f);
ideal j = i,i[1]*i[2]+t*x5y8; // deformed ideal, parameter t
vdim(std(j));
==> 40
ring R=0,(x,y),lp;
ideal i=imap(Rt,i);
int a=random(1,30000);
ideal j=i,i[1]*i[2]+a*x5y8; // deformed ideal, fixed integer a
vdim(std(j));
==> 40
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