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| Remembering basis transformations https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2002 |
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| Author: | Jerry [ Thu Oct 27, 2011 5:55 pm ] |
| Post subject: | Remembering basis transformations |
If I take some ideal I=(f_1,...,f_n) and then generate it by a Groebner basis I=(g_1,...,g_m) is there some way to automatically have it also return how to express g_i's in terms of f_i's? This information is at least implicitly contained in the computation of the Groebner basis but I was wonder if there is any explicit way to extract it in plural. Thanks. |
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| Author: | gorzel [ Fri Oct 28, 2011 12:39 pm ] |
| Post subject: | Re: Remembering basis transformations |
Use the command lift http://www.singular.uni-kl.de/Manual/3-0-4/sing_235.htm Code: > ring r = 0,(x,y,z),dp; > ideal I=3x2+yz,7y6+2x2y,4x2y3-5xz; > ideal J = std(I); > J; J[1]=3x2+yz J[2]=8xz2-105yz2 J[3]=33075y2z2+64yz3 J[4]=315xy2z+8y2z2 J[5]=4y4z+15xz J[6]=8388608yz5-56987567117578125yz2 J[7]=21y6-2y2z > matrix T = lift(J,I); > matrix(J)*T; // This is I again, now as a matrix _[1,1]=3x2+yz _[1,2]=7y6+2x2y _[1,3]=4x2y3-5xz > _ == I; 1 > I; I[1]=3x2+yz I[2]=7y6+2x2y I[3]=4x2y3-5xz Note: lift makes again a std-basis computation; there is no direct way to obtain automatically the transformation matrix from the initial std computation. |
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| Author: | hannes [ Fri Oct 28, 2011 5:42 pm ] |
| Post subject: | Re: Remembering basis transformations |
liftstd produces both: the standard basis and the transformation matrix |
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| Author: | Jerry [ Tue Nov 08, 2011 7:14 pm ] |
| Post subject: | Re: Remembering basis transformations |
Thanks for the responses. Is there also a way to do it with twostd()? |
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