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A.1.5 Parameters
Let us deform the ideal in Long coefficients by
introducing a parameter t and compute over the ground field Q(t).
We compute the dimension at the generic point,
i.e.,
436#436.(This gives the
same result as for the deformed ideal above. Hence, the above small
deformation was "generic".)
For almost all
437#437this is the same as
438#438,where
439#439.
| ring Rt = (0,t),(x,y),lp;
Rt;
==> // coefficients: QQ(t)
==> // 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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