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| does a ring function related to "kbase" exist? https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1787 |
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| Author: | Guest [ Wed Nov 25, 2009 1:18 am ] |
| Post subject: | does a ring function related to "kbase" exist? |
hi, i need following computation: let r be the polynomial ring: r=Q[a,b] let R be the polynomial ring: R=r[x,y,z] let I be an Ideal in R: compute a set of generators of R/I as an free r module (if finite dimentional). in the past i used "work-arounds" like R=(0,a,b),(x,y,z),Dp; to be able to use "kbase(I)", but for many reasons a mathematical correct definition like R=0,(a,b,x,y,z),Dp; would help much. i've read in the online manual that such computations can be done but did not find a function doing it. best regards, peter |
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| Author: | greuel [ Thu Jan 07, 2010 6:27 pm ] |
| Post subject: | Re: does a ring function related to "kbase" exist? |
No, such a function does not exist (not every module over r is free). In fact, what you do is computing a basis of the module over the quotient field, which is a basis over the ring iff the module is free. In this case your way should be the fastest possibility to compute it (except you choose random values for a and b). Checking whether a module is free, is however another story. |
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