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| why different length minimal resolution for different order? https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2803 |
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| Author: | janstevens [ Thu Nov 22, 2018 2:14 pm ] |
| Post subject: | why different length minimal resolution for different order? |
I have a graded ring and compute syzygies with Singular online (version 4.1.1). Depending on the order I write the variables I get a different number of syzygies. This looks like a bug. More precisely: I generate an ideal with: ring re = 0, (s,t,w,z(0..3),y(5..7),x(0..2)),wp(1,1,9,15,15,15,15,10,10,10,5,5,5); ideal parm = w^2-(s^3-t^3)*(s^15+t^15), z(0)-(s^3-t^3)*w*s^3,z(1)-(s^3-t^3)*w*s^2*t,z(2)-(s^3-t^3)*w*s*t^2,z(3)-(s^3-t^3)*w*t^3, y(5)-(s^3-t^3)*s^2*t^5,y(6)-(s^3-t^3)*s*t^6,y(7)-(s^3-t^3)*t^7, x(0)-(s^3-t^3)*s^2,x(1)-(s^3-t^3)*s*t,x(2)-(s^3-t^3)*t^2; ideal krom= eliminate(parm,w*s*t); ring r = 0,(z(0..3),y(5..7),x(0..2)),wp(3,3,3,3,2,2,2,1,1,1); ideal kr = imap(re,krom); list T = mres(kr,2); print(betti(T),"betti"); I get 161 syzygies (also not all degrees in the Betti table are OK). But with ring r = 0,(x(0..2),y(5..7),z(0..3)),wp(1,1,1,2,2,2,3,3,3,3); I get 169 syzygies. But there should only be 160 syzygies. Can somebody explain me what is happening here? Best, Jan Stevens |
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| Author: | hannes [ Fri Dec 14, 2018 6:32 pm ] |
| Post subject: | Re: why different length minimal resolution for different order? |
You get a generating set of the syszygy module: different order of variables may produce a different number of generators. betti works only for homogeneous input (wrt. weight 1). |
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