Singular

Hello everybody,

I would like to know if given a zero dimensional ideal J in Q[x1,...,xn] and a multiplicative subset S of Q[x1,...,xn] , it is possible to define in SINGULAR S-1(Q[x1,...,xn]/J).

And given g in Q[x1,...,xn] , is it possible to define in SINGULAR the saturation of J with respect to g?

thanks in advance for your help,
best wishes,
gema m.

Hi,
You can localize in the maximal ideal <x1,...,xn> just by defining a local ring (local ordering, ends with an s = referring to series) eg.
ring r = 0,x(1..n),ds;
Localization in any other maximal ideal <x1-p1,...,xn-pn> is possible by translation of p to 0 (apply the translation to your ideal) and then as above.
Localizations w.r.t. arbitrary mlutiplicative sets are not possible.

If you wish to analyse a 0-dim ideal you should try a primary decomposition first.

sat(J,g); does the saturation.

Here is an example:

ring r = 0,(x,y,z),dp;
poly g = x3+y5+z2 +xyz;
ideal J = jacob(g);
LIB"primdec.lib";
primdecGTZ(J);
/*
[1]:
[1]:
_[1]=z2
_[2]=y3z
_[3]=30y4+y2z
_[4]=-y2z+6xz
_[5]=xy+2z
_[6]=3x2+yz
[2]:
_[1]=z
_[2]=y
_[3]=x
[2]:
[1]:
_[1]=z+3888000
_[2]=y-360
_[3]=x-21600
[2]:
_[1]=z+3888000
_[2]=y-360
_[3]=x-21600
*/
sat(J,g);
/*
[1]:
_[1]=z+3888000
_[2]=y-360
_[3]=x-21600
[2]:
1
*/

thanks a lot for your answer,

kind regards,
gema m.