Sometimes a Groebner basis computation doesn't finish quickly enough. If so then this section might be of use. THIS PAGE IS UNDER CONSTRUCTION.
Partially computed Groebner bases
Suppose that you have computed part of a Groebner basis. For example, you may have interrupted the computation using CTRL-C (typing 'c' while holding the CTRL key down, in emacs, you have to type CTRL-C twice), or you may have given options requesting only partial computation.
i1 : R = ZZ/32003[a..e];
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i2 : I = ideal(random(3,R),random(3,R),random(3,R))
3 2 2 3 2
o2 = ideal (13140a + 15925a b + 11783a*b + 13940b - 12751a c - 15360a*b*c
------------------------------------------------------------------------
2 2 2 3 2
- 1489b c + 3002a*c + 9560b*c + 6345c - 10852a d - 10433a*b*d +
------------------------------------------------------------------------
2 2 2 2
14821b d + 8524a*c*d - 1479b*c*d + 4411c d - 1658a*d + 15585b*d +
------------------------------------------------------------------------
2 3 2 2
1247c*d + 8498d + 8843a e + 12520a*b*e - 11972b e - 11617a*c*e +
------------------------------------------------------------------------
2 2
15531b*c*e - 2175c e + 8452a*d*e - 10309b*d*e - 13814c*d*e - 14470d e -
------------------------------------------------------------------------
2 2 2 2 3 3
11712a*e - 12488b*e + 15353c*e + 9326d*e + 6655e , 12102a +
------------------------------------------------------------------------
2 2 3 2 2
15956a b - 9879a*b - 4147b + 13753a c - 4735a*b*c - 10818b c +
------------------------------------------------------------------------
2 2 3 2 2
15333a*c - 10018b*c + 8880c - 11652a d - 9657a*b*d + 4072b d +
------------------------------------------------------------------------
2 2 2 2
11296a*c*d - 11038b*c*d + 10491c d - 4097a*d + 12819b*d - 12946c*d -
------------------------------------------------------------------------
3 2 2
14004d + 8546a e - 10549a*b*e + 9538b e + 14973a*c*e - 14106b*c*e -
------------------------------------------------------------------------
2 2 2
15636c e - 3367a*d*e - 4860b*d*e - 11209c*d*e + 5261d e - 2482a*e -
------------------------------------------------------------------------
2 2 2 3 3 2
1316b*e + 13093c*e + 1397d*e + 11040e , - 6997a + 13846a b +
------------------------------------------------------------------------
2 3 2 2 2 2
11883a*b - 9668b + 10983a c - 2466a*b*c + 7304b c + 303a*c + 6243b*c
------------------------------------------------------------------------
3 2 2
+ 13129c - 12817a d + 10362a*b*d - 4950b d - 12549a*c*d - 12410b*c*d +
------------------------------------------------------------------------
2 2 2 2 3 2
15304c d + 15718a*d - 8477b*d + 6705c*d + 2289d + 15271a e +
------------------------------------------------------------------------
2 2
8370a*b*e + 9376b e - 15690a*c*e - 4708b*c*e - 14383c e - 5951a*d*e -
------------------------------------------------------------------------
2 2 2 2
13726b*d*e + 2684c*d*e - 698d e - 4543a*e - 3554b*e - 3663c*e +
------------------------------------------------------------------------
2 3
15027d*e + 137e )
o2 : Ideal of R
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i3 : gens gb(I,PairLimit=>7);
1 7
o3 : Matrix R <--- R
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Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
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i5 : leadTerm gens g
o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o5 : Matrix R <--- R
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We can make a Groebner basis snapshot by using StopBeforeComputation, or
gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)
o6 = | ab2-3541b3-10558a2c-951abc-6377b2c+7741ac2+4420bc2-11840c3+15948a2d-
------------------------------------------------------------------------
15796abd-1672b2d+8559acd+2748bcd+4456c2d+6873ad2-7092bd2+1501cd2+7783d3+
------------------------------------------------------------------------
1573a2e-13558abe+14222b2e+5911ace-3786bce-2361c2e-3384ade+5712bde+
------------------------------------------------------------------------
1784cde-4640d2e-8528ae2-2967be2+8954ce2-2426de2+3168e3
------------------------------------------------------------------------
a2b+12278b3+11864a2c-534abc+2568b2c-11910ac2-11459bc2-3283c3+11461a2d+
------------------------------------------------------------------------
15015abd+1905b2d+9893acd+7698bcd-15310c2d-15400ad2-2731bd2+1480cd2+
------------------------------------------------------------------------
7427d3+9989a2e-10831abe-9800b2e-10750ace-8153bce-7146c2e-1115ade+3254bde
------------------------------------------------------------------------
-8440cde-2663d2e+10848ae2-8936be2+10940ce2+1231de2-3568e3
------------------------------------------------------------------------
a3-5788b3-1261a2c-11412abc-302b2c-15311ac2+2119bc2-5521c3+4851a2d+
------------------------------------------------------------------------
3127abd-15480b2d+3488acd+6743bcd-12307c2d-14244ad2-11012bd2+11990cd2+
------------------------------------------------------------------------
4094d3+10759a2e+533abe+6639b2e+11770ace+4368bce-3558c2e+1968ade-4573bde-
------------------------------------------------------------------------
10754cde+3746d2e+8713ae2+12927be2-14801ce2-9942de2+10454e3
------------------------------------------------------------------------
b3c-998a2c2+8770abc2+4257b2c2-8543ac3+9571bc3-318c4-10640b3d-710a2cd-
------------------------------------------------------------------------
9743abcd+2070b2cd-920ac2d+10815bc2d-12467c3d+753a2d2-6356abd2+8690b2d2-
------------------------------------------------------------------------
2292acd2+6461bcd2-13832c2d2-4353ad3+9385bd3+6019cd3-6201d4-10600b3e+
------------------------------------------------------------------------
5955a2ce+8246abce-10420b2ce+8234ac2e+7575bc2e+6130c3e-4689a2de+7790abde+
------------------------------------------------------------------------
4425b2de+9955acde-10488bcde+7648c2de-14754ad2e+4536bd2e-9717cd2e-9588d3e
------------------------------------------------------------------------
+11957a2e2+11755abe2+11354b2e2-6176ace2+7792bce2+8589c2e2-13336ade2+
------------------------------------------------------------------------
14839bde2-12627cde2-10080d2e2-11616ae3-3991be3+7843ce3-8832de3-2286e4
------------------------------------------------------------------------
b4+256a2c2-12114abc2+1036b2c2-8931ac3+10231bc3+13723c4+12656b3d+
------------------------------------------------------------------------
12686a2cd-6188abcd-13938b2cd-13793ac2d+5243bc2d-14364c3d+3367a2d2-
------------------------------------------------------------------------
3511abd2-2505b2d2+5395acd2-5193bcd2-12564c2d2+6675ad3-9059bd3+12468cd3-
------------------------------------------------------------------------
13615d4+9361b3e+4889a2ce+9387abce-8163b2ce-4427ac2e-9357bc2e+3073c3e-
------------------------------------------------------------------------
8956a2de+15510abde+1859b2de-13689acde+4671bcde+12187c2de-11434ad2e-
------------------------------------------------------------------------
1528bd2e+3366cd2e+789d3e+9023a2e2-6799abe2-10061b2e2-4873ace2+2614bce2+
------------------------------------------------------------------------
6446c2e2-4515ade2+11418bde2-1541cde2-12390d2e2+5500ae3+2472be3-6988ce3+
------------------------------------------------------------------------
15499de3+14457e4 abc3+15364b2c3+6443ac4-4641bc4+6025c5-2897a2c2d+
------------------------------------------------------------------------
8574abc2d+9771b2c2d-8403ac3d+9441bc3d+4242c4d-4271b3d2-2864a2cd2-
------------------------------------------------------------------------
111abcd2+7477b2cd2-11433ac2d2+12303bc2d2-12056c3d2-15145a2d3-9631abd3+
------------------------------------------------------------------------
3866b2d3+9232acd3+4786bcd3-12422c2d3-13370ad4+2080bd4-2714cd4-2077d5-
------------------------------------------------------------------------
2063a2c2e+7167abc2e-11399b2c2e+10902ac3e+1790bc3e-9744c4e+7995b3de-
------------------------------------------------------------------------
11429a2cde+8294abcde+1300b2cde-12403ac2de-8059bc2de-14616c3de-15999a2d2e
------------------------------------------------------------------------
-13761abd2e+9716b2d2e+2536acd2e+15053bcd2e-4367c2d2e+9890ad3e+11210bd3e-
------------------------------------------------------------------------
7596cd3e-2492d4e+5452b3e2+6355a2ce2-8883abce2+1831b2ce2-14527ac2e2+
------------------------------------------------------------------------
8137bc2e2-15598c3e2+113a2de2-15764abde2+3519b2de2+5231acde2-339bcde2+
------------------------------------------------------------------------
480c2de2-573ad2e2-11376bd2e2-13688cd2e2-12271d3e2-9460a2e3+864abe3-
------------------------------------------------------------------------
14694b2e3+10426ace3+6690bce3-1222c2e3+13791ade3-1385bde3-15513cde3+
------------------------------------------------------------------------
3785d2e3+8580ae4+13070be4+5915ce4+14077de4+8821e5
------------------------------------------------------------------------
a2c3-5219b2c3-8437ac4-7780bc4+880c5+12065a2c2d-1614abc2d-5985b2c2d-
------------------------------------------------------------------------
12466ac3d+11789bc3d+8180c4d+7098b3d2+11828a2cd2+15900abcd2+2301b2cd2+
------------------------------------------------------------------------
7831ac2d2-8169bc2d2-10838c3d2+15505a2d3-6778abd3+7450b2d3+7529acd3-
------------------------------------------------------------------------
3905bcd3+7050c2d3+9801ad4+9002bd4+15933cd4-3828d5+1376a2c2e+9603abc2e-
------------------------------------------------------------------------
4558b2c2e-7205ac3e+14650bc3e-14412c4e-6968b3de+829a2cde-11552abcde+
------------------------------------------------------------------------
5009b2cde-113ac2de-71bc2de-5684c3de-727a2d2e+11448abd2e+11318b2d2e+
------------------------------------------------------------------------
9166acd2e+15422bcd2e+7352c2d2e+9969ad3e-14062bd3e-9978cd3e-4339d4e-
------------------------------------------------------------------------
9638b3e2+12465a2ce2+9086abce2-6471b2ce2-581ac2e2-14338bc2e2+5502c3e2-
------------------------------------------------------------------------
3762a2de2-11518abde2+15251b2de2+6738acde2-1072bcde2+53c2de2+9654ad2e2+
------------------------------------------------------------------------
4737bd2e2-2698cd2e2-14309d3e2+5633a2e3-9440abe3-12131b2e3-7020ace3+
------------------------------------------------------------------------
2366bce3+11481c2e3-3459ade3+15528bde3+9792cde3-6073d2e3-4277ae4+118be4-
------------------------------------------------------------------------
6263ce4+5011de4-3549e5 |
1 7
o6 : Matrix R <--- R
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i7 : leadTerm gbSnapshot(I)
o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o7 : Matrix R <--- R
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