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question-multiplicative subsets
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1686		 Page 1 of 1
Author:  gema [ Thu Oct 23, 2008 11:37 am ]
Post subject:  question-multiplicative subsets
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.
Author:  greuel [ Sat Nov 15, 2008 2:57 am ]
Post subject: 
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
*/
Author:  gema [ Sat Nov 15, 2008 11:22 am ]
Post subject:  thanks -multiplicative subsets
thanks a lot for your answer,

kind regards,
gema m.
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