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| Basis of Quotient Ring https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1381 |
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| Author: | Sheng Mao [ Thu Aug 11, 2005 5:32 pm ] |
| Post subject: | Basis of Quotient Ring |
Let S be the polynomial ring of n- variables, J be a homogenous ideal generated by homogenous elements f_1,..,f_m. Consider the quotient ring S/J of S modulo J. Can one find a basis of the graded piece of (S/J)_i of given degree i by exploiting commands of SINGULAR? If so, what are the appropriate SINGULAR commands? email: msheng@math.cuhk.edu.hk Posted in old Singular Forum on: 2004-01-05 13:14:24+01 |
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| Author: | levandov [ Thu Aug 11, 2005 8:51 pm ] |
| Post subject: | Re: Basis of Quotient Ring |
Quote: > Let S be the polynomial ring of n- variables, J be a homogenous ideal generated by homogenous elements f_1,..,f_m. >Consider the quotient ring S/J of S modulo J. Can one find a basis of the graded piece of (S/J)_i of given degree i by exploiting commands of SINGULAR? If so, what are the appropriate SINGULAR commands? There are two commands you can use: kbase and jet. We recommend to use kbase with the second argument, for example Code: ring r=32003,(x,y,z),ds; ideal i=x2,y3,xyz; kbase(std(i),2); ==> _[1]=z2 ==> _[2]=yz ==> _[3]=xz ==> _[4]=y2 ==> _[5]=xy More information you can find in the documentation. kbase: http://www.singular.uni-kl.de/Manual/3-0-0/sing_218.htm jet: http://www.singular.uni-kl.de/Manual/3-0-0/sing_217.htm Have fun, |
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