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 (- 12046a + 219a b + 1155a*b + 10273b - 15164a c + 6956a*b*c +
------------------------------------------------------------------------
2 2 2 3 2
9628b c + 4502a*c - 10776b*c + 10178c + 8294a d + 10131a*b*d -
------------------------------------------------------------------------
2 2 2 2
6375b d + 5360a*c*d - 14176b*c*d - 9808c d - 120a*d - 3744b*d +
------------------------------------------------------------------------
2 3 2 2
9358c*d - 13603d - 11548a e + 7284a*b*e + 904b e + 4243a*c*e +
------------------------------------------------------------------------
2 2
14472b*c*e - 9770c e - 2307a*d*e + 2539b*d*e - 15271c*d*e - 522d e +
------------------------------------------------------------------------
2 2 2 2 3 3 2
527a*e - 6937b*e + 5694c*e - 15520d*e + 12935e , 12265a - 13450a b
------------------------------------------------------------------------
2 3 2 2 2
- 12905a*b - 2815b - 6506a c + 14326a*b*c - 8955b c - 9376a*c -
------------------------------------------------------------------------
2 3 2 2
386b*c + 13410c + 13395a d - 183a*b*d + 9649b d + 2803a*c*d -
------------------------------------------------------------------------
2 2 2 2 3
5512b*c*d - 15125c d + 1241a*d + 9991b*d - 11358c*d - 11965d +
------------------------------------------------------------------------
2 2 2
10407a e - 351a*b*e + 4192b e + 14904a*c*e - 6113b*c*e - 7638c e -
------------------------------------------------------------------------
2 2 2
15344a*d*e + 12997b*d*e - 1176c*d*e + 4111d e + 3352a*e + 12794b*e -
------------------------------------------------------------------------
2 2 3 3 2 2 3
10721c*e + 8246d*e - 1626e , 7684a + 12337a b - 2296a*b + 3113b -
------------------------------------------------------------------------
2 2 2 2 3
5097a c - 14648a*b*c + 11415b c - 9857a*c + 4143b*c + 14962c +
------------------------------------------------------------------------
2 2 2
4026a d - 7550a*b*d - 7758b d + 10587a*c*d - 3222b*c*d + 15712c d -
------------------------------------------------------------------------
2 2 2 3 2 2
42a*d - 825b*d - 4324c*d - 9686d + 904a e - 8778a*b*e - 8793b e +
------------------------------------------------------------------------
2
14013a*c*e + 9179b*c*e + 5314c e - 13331a*d*e + 8997b*d*e + 5529c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3
11332d e + 13617a*e + 6692b*e + 14935c*e + 9896d*e + 12733e )
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+848b3-466a2c+12888abc-7505b2c+11118ac2+1629bc2-6741c3-14822a2d+
------------------------------------------------------------------------
11096abd-1558b2d+13885acd+3366bcd-8127c2d+5525ad2-11781bd2+4044cd2+809d3
------------------------------------------------------------------------
+577a2e-7801abe+15581b2e+6019ace+7879bce-2421c2e-7350ade-14781bde+
------------------------------------------------------------------------
1585cde-3307d2e+15094ae2-14722be2-8847ce2+4066de2+5378e3
------------------------------------------------------------------------
a2b+10698b3-11333a2c+14228abc+12168b2c-10177ac2+14298bc2+9430c3+13521a2d
------------------------------------------------------------------------
+1190abd-11463b2d-2067acd-1315bcd-12833c2d+6190ad2-11489bd2-1663cd2-
------------------------------------------------------------------------
15440d3-8297a2e-14324abe+4387b2e-6459ace+12090bce+471c2e+636ade+11877bde
------------------------------------------------------------------------
+13615cde+14049d2e-1835ae2-8220be2+9888ce2-11911de2+14581e3
------------------------------------------------------------------------
a3-13378b3-13031a2c+13125abc-10353b2c-11343ac2-4389bc2-7540c3-11439a2d+
------------------------------------------------------------------------
471abd+12411b2d-2102acd+1105bcd+1289c2d-1507ad2-12879bd2-3190cd2+5680d3+
------------------------------------------------------------------------
10899a2e-13578abe+13954b2e-8454ace+1524bce+13927c2e+11079ade+1155bde-
------------------------------------------------------------------------
5367cde-407d2e+14655ae2-6494be2+7984ce2-5370de2-13572e3
------------------------------------------------------------------------
b3c-10792a2c2+5923abc2-13168b2c2-8594ac3+10566bc3+12456c4-5219b3d-
------------------------------------------------------------------------
13757a2cd-5970abcd-8465b2cd-5622ac2d+12450bc2d+9744c3d-15213a2d2-
------------------------------------------------------------------------
2411abd2+1611b2d2+6854acd2+4695bcd2+12329c2d2-3540ad3+5877bd3-5034cd3-
------------------------------------------------------------------------
15365d4-10986b3e-3943a2ce+14991abce-4080b2ce-4570ac2e-13483bc2e+5266c3e+
------------------------------------------------------------------------
7523a2de+7246abde+9010b2de-14971acde+5652bcde-4589c2de-336ad2e-9941bd2e+
------------------------------------------------------------------------
10690cd2e+15970d3e+15987a2e2+3444abe2-1236b2e2-4416ace2+14728bce2+
------------------------------------------------------------------------
13510c2e2+12766ade2-6694bde2+10599cde2-11496d2e2+2572ae3+14977be3+
------------------------------------------------------------------------
10306ce3-14914de3-1640e4
------------------------------------------------------------------------
b4+14776a2c2-14245abc2-11058b2c2-6281ac3-8392bc3+7322c4+2168b3d-7583a2cd
------------------------------------------------------------------------
+10730abcd+10571b2cd-15698ac2d+4886bc2d+10207c3d-9535a2d2+10104abd2-
------------------------------------------------------------------------
4488b2d2+9904acd2+11213bcd2+13193c2d2-13563ad3+9276bd3+9787cd3+3224d4+
------------------------------------------------------------------------
3624b3e+2492a2ce-7732abce+9386b2ce-5076ac2e+339bc2e+15710c3e+14243a2de+
------------------------------------------------------------------------
7887abde+6033b2de+8295acde+13790bcde+12712c2de-6690ad2e-10503bd2e-
------------------------------------------------------------------------
3587cd2e-307d3e-2693a2e2+3071abe2-546b2e2-12823ace2+8803bce2-14330c2e2-
------------------------------------------------------------------------
5712ade2+12852bde2-2931cde2+15715d2e2+14331ae3-10329be3+5369ce3-13854de3
------------------------------------------------------------------------
-2709e4 abc3+5747b2c3-15574ac4+3904bc4-270c5+11332a2c2d+9892abc2d+
------------------------------------------------------------------------
720b2c2d-2082ac3d-5247bc3d-3625c4d-2615b3d2-13776a2cd2+14788abcd2+
------------------------------------------------------------------------
11870b2cd2+9076ac2d2-2918bc2d2-4573c3d2-6722a2d3-6513abd3-5012b2d3+
------------------------------------------------------------------------
7101acd3-11537bcd3-962c2d3-3597ad4-14851bd4-6915cd4+9788d5+5510a2c2e-
------------------------------------------------------------------------
10346abc2e-12525b2c2e+8803ac3e-14314bc3e+11090c4e+3762b3de-4970a2cde+
------------------------------------------------------------------------
5752abcde-11859b2cde+14578ac2de+11590bc2de-6771c3de-3227a2d2e-11370abd2e
------------------------------------------------------------------------
-6088b2d2e-9314acd2e-6665bcd2e+9606c2d2e+15231ad3e-12941bd3e-4527cd3e-
------------------------------------------------------------------------
10093d4e-2b3e2-15736a2ce2-5104abce2-2936b2ce2+5919ac2e2+10676bc2e2-
------------------------------------------------------------------------
10157c3e2-8101a2de2-3155abde2-4846b2de2-10630acde2-7162bcde2+111c2de2+
------------------------------------------------------------------------
4953ad2e2-2506bd2e2+5997cd2e2+14440d3e2-7805a2e3+3336abe3-3892b2e3+
------------------------------------------------------------------------
14334ace3+13977bce3-2563c2e3+14076ade3-3330bde3-9640cde3-9256d2e3+
------------------------------------------------------------------------
8419ae4-9611be4-10378ce4-6974de4+10406e5
------------------------------------------------------------------------
a2c3+4555b2c3+4987ac4-3236bc4+6678c5+3809a2c2d+2347abc2d-12151b2c2d-
------------------------------------------------------------------------
2479ac3d-9619bc3d-14548c4d-3249b3d2-13660a2cd2-7550abcd2-10510b2cd2-
------------------------------------------------------------------------
5147ac2d2-13596bc2d2-6532c3d2+12516a2d3-15341abd3-9540b2d3+11784acd3-
------------------------------------------------------------------------
10194bcd3+14553c2d3+9445ad4+2011bd4-14066cd4-7225d5-10453a2c2e+9986abc2e
------------------------------------------------------------------------
+14609b2c2e+10488ac3e+14045bc3e-2877c4e+2377b3de+13707a2cde+5296abcde+
------------------------------------------------------------------------
10605b2cde-14292ac2de-14334bc2de-4956c3de+5320a2d2e-6868abd2e-12425b2d2e
------------------------------------------------------------------------
+13744acd2e-13782bcd2e-9106c2d2e-3568ad3e+14846bd3e-7652cd3e-6164d4e-
------------------------------------------------------------------------
14608b3e2+11252a2ce2+7473abce2-261b2ce2-9379ac2e2+14041bc2e2-14080c3e2+
------------------------------------------------------------------------
13742a2de2+12271abde2+6467b2de2-6680acde2-9853bcde2+1035c2de2+5568ad2e2+
------------------------------------------------------------------------
5909bd2e2+2073cd2e2+1267d3e2-14539a2e3+13818abe3-15572b2e3+10449ace3+
------------------------------------------------------------------------
3167bce3-3960c2e3-5113ade3+935bde3-13031cde3-12307d2e3-3229ae4+13176be4+
------------------------------------------------------------------------
3991ce4-15683de4-5268e5 |
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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