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Ring Normalization problem and using Singular in Sage.
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2897		 Page 1 of 1
Author:  azerbajdzan [ Sat Dec 28, 2019 7:38 pm ]
Post subject:  Ring Normalization problem and using Singular in Sage.
Here .../DEMOS/GMG-Mainz_DMV-99/Examples/normal.html you can find this code:
Code:
LIB "normal.lib";
ring r=0,(x,y,z),dp;
ideal i=y^2-x^2*z;
list NN=normal(i);
def N=NN[1];
setring N;
PP;
=> PP[1]=T(1)
=> PP[2]=T(1)*T(2)
=> PP[3]=T(2)^2

But it does not work any more when I write it in Singular. Maybe it was written in old version of Singular and does not work any more, but I can not figure out how to amend it to work with current version of Singular.
Another question is how I would use the same code inside Sage?
Author:  Guest [ Sat Dec 28, 2019 7:40 pm ]
Post subject:  Re: Ring Normalization problem and using Singular in Sage.
Three dots represent "www(dot)singular(dot)uni-kl(dot)de". I was not allowed to post url's.
Author:  hannes [ Fri Jan 10, 2020 4:10 pm ]
Post subject:  Re: Ring Normalization problem and using Singular in Sage.
Translating your example to newer version of normal.lib:
Code:
LIB "normal.lib";
ring r=0,(x,y,z),dp;
ideal i=y^2-x^2*z;
list NN=normal(i);
def N=NN[1][1];
setring N;
norid;
=> norid[1]=T(1)*x-y
=> norid[2]=-T(1)*y+x*z
=> norid[3]=T(1)^2-z
=> norid[4]=x^2*z-y^2


To use the code in sage: unfortunatly, normal does not return all results
as a return value - yu need to change the ring and then acces the Singular variable norid and normap.
Author:  Guest [ Fri Jan 10, 2020 5:52 pm ]
Post subject:  Re: Ring Normalization problem and using Singular in Sage.
But the output is not like it was in the original. In the original I got parametrization of $y^2-x^2*z$
Author:  azerbajdzan [ Fri Jan 10, 2020 5:56 pm ]
Post subject:  Re: Ring Normalization problem and using Singular in Sage.
But the output is not like it was in the original. In the original I got parametrization of y^2-x^2*z=0 as x=T(1), y=T(1)*T(2), z=T(2)^2.
I have no idea what the new output should represent?
Author:  azerbajdzan [ Fri Jan 10, 2020 6:25 pm ]
Post subject:  Re: Ring Normalization problem and using Singular in Sage.
Is it a good idea to block your own URL-s in the forum?

None of these codes on your site work anymore:
already mentioned one on
www*singular*uni-kl*de/DEMOS/GMG-Mainz_DMV-99/Examples/normal*html
and the new version of it on
www*singular*uni-kl*de/Overview/Examples/Normalize/index*html
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