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 (- 5854a - 7749a b + 9127a*b + 7806b + 11938a c + 12655a*b*c +
------------------------------------------------------------------------
2 2 2 3 2
14937b c - 4203a*c + 12589b*c - 8816c - 7554a d + 2429a*b*d +
------------------------------------------------------------------------
2 2 2 2
14386b d - 9151a*c*d + 10096b*c*d + 8532c d - 5574a*d + 9598b*d +
------------------------------------------------------------------------
2 3 2 2
7268c*d - 14798d - 15064a e - 14934a*b*e - 15649b e - 6477a*c*e +
------------------------------------------------------------------------
2 2
3155b*c*e + 2226c e - 12967a*d*e - 3287b*d*e + 9661c*d*e + 13911d e +
------------------------------------------------------------------------
2 2 2 2 3 3 2
165a*e - 2801b*e + 9141c*e - 9188d*e - 13413e , 9681a + 8809a b -
------------------------------------------------------------------------
2 3 2 2 2
11953a*b + 2273b - 11682a c + 9806a*b*c + 3157b c - 11304a*c +
------------------------------------------------------------------------
2 3 2 2
10584b*c + 9824c - 7882a d - 4841a*b*d - 11993b d + 1773a*c*d -
------------------------------------------------------------------------
2 2 2 2 3 2
3981b*c*d + 11231c d - 8750a*d + 3962b*d + 6155c*d + 8966d - 5120a e
------------------------------------------------------------------------
2 2
+ 13171a*b*e + 13031b e - 3598a*c*e - 14833b*c*e - 2179c e + 13646a*d*e
------------------------------------------------------------------------
2 2 2 2
+ 6752b*d*e + 3652c*d*e + 6249d e - 8582a*e - 1454b*e + 9596c*e +
------------------------------------------------------------------------
2 3 3 2 2 3 2
9599d*e + 8354e , - 2098a - 6228a b + 6862a*b + 10026b + 8403a c -
------------------------------------------------------------------------
2 2 2 3 2
13075a*b*c + 4368b c + 2474a*c + 10476b*c - 14808c + 441a d +
------------------------------------------------------------------------
2 2 2
14355a*b*d + 8171b d + 1474a*c*d - 15209b*c*d + 4996c d - 6295a*d +
------------------------------------------------------------------------
2 2 3 2 2
211b*d + 7354c*d - 773d - 7388a e + 300a*b*e + 6962b e + 11007a*c*e +
------------------------------------------------------------------------
2 2
9900b*c*e + 123c e - 8770a*d*e - 418b*d*e - 9428c*d*e + 15333d e +
------------------------------------------------------------------------
2 2 2 2 3
10696a*e - 13211b*e - 8166c*e - 11242d*e - 6058e )
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+4888b3-14221a2c+2909abc-7353b2c+11624ac2-13893bc2-10808c3-1251a2d+
------------------------------------------------------------------------
14abd+372b2d+10810acd+12082bcd-8480c2d+3154ad2-4275bd2-5266cd2-11460d3+
------------------------------------------------------------------------
8522a2e+10074abe+14590b2e-10975ace-7294bce-9112c2e+1288ade+3968bde-
------------------------------------------------------------------------
5201cde-8537d2e+5234ae2+8086be2+3397ce2-7764de2+4451e3
------------------------------------------------------------------------
a2b+14501b3-6539a2c+4920abc+7521b2c-6557ac2-10540bc2-779c3+5277a2d+
------------------------------------------------------------------------
15855abd-5377b2d-15980acd-14061bcd-3708c2d-7338ad2-5256bd2-15198cd2+
------------------------------------------------------------------------
2317d3+9493a2e-4361abe+7708b2e-5221ace-652bce+8379c2e-4637ade-7945bde+
------------------------------------------------------------------------
10488cde-14351d2e-14795ae2+14922be2+11412ce2+13241de2+11741e3
------------------------------------------------------------------------
a3-7295b3+7048a2c-2537abc+14577b2c+10195ac2-5218bc2-6519c3+12780a2d+
------------------------------------------------------------------------
9550abd-8864b2d+6645acd-11617bcd+14723c2d-6689ad2-11239bd2-4877cd2+
------------------------------------------------------------------------
3095d3+7781a2e+560abe-4056b2e-5164ace+528bce+467c2e-4655ade-3097bde-
------------------------------------------------------------------------
487cde-12526d2e+13990ae2-12672be2-9888ce2-15455de2+1246e3
------------------------------------------------------------------------
b3c-12225a2c2-7748abc2+4276b2c2-7519ac3+13509bc3-2325c4+14688b3d-
------------------------------------------------------------------------
4573a2cd+9736abcd-4978b2cd-7860ac2d+8753bc2d+1726c3d-3031a2d2-2622abd2+
------------------------------------------------------------------------
8896b2d2-5334acd2-9876bcd2-9223c2d2+15552ad3-86bd3+3042cd3-10155d4+
------------------------------------------------------------------------
6709b3e+12422a2ce+1944abce+15969b2ce+5613ac2e-7637bc2e-5106c3e-14015a2de
------------------------------------------------------------------------
-13459abde+1361b2de-2049acde+8640bcde-11113c2de+9400ad2e+4219bd2e+
------------------------------------------------------------------------
951cd2e-12742d3e+2406a2e2+4012abe2-9371b2e2+3430ace2+7083bce2+462c2e2-
------------------------------------------------------------------------
5733ade2+15457bde2+2613cde2+1764d2e2-15373ae3+9287be3+4859ce3-2078de3+
------------------------------------------------------------------------
11730e4 b4+15262a2c2+15523abc2+8027b2c2+11997ac3+1477bc3+13171c4-
------------------------------------------------------------------------
14332b3d-1568a2cd+11806abcd-6613b2cd-6812ac2d-1449bc2d+13055c3d-4603a2d2
------------------------------------------------------------------------
+3222abd2+29b2d2-10674acd2-2847bcd2-5900c2d2+2137ad3-3176bd3+10354cd3-
------------------------------------------------------------------------
6511d4-1811b3e-11466a2ce+6719abce+11035b2ce-2311ac2e-12486bc2e+4860c3e+
------------------------------------------------------------------------
6541a2de-1175abde+8601b2de+2847acde+1749bcde+854c2de+460ad2e+10422bd2e-
------------------------------------------------------------------------
4611cd2e-9066d3e+9407a2e2+408abe2+8700b2e2+659ace2+1204bce2-8312c2e2-
------------------------------------------------------------------------
1823ade2+15668bde2+5558cde2+1241d2e2+1669ae3-9291be3+3518ce3+14602de3-
------------------------------------------------------------------------
31e4 abc3+12156b2c3+8614ac4+11316bc4-15974c5+6304a2c2d+9446abc2d+
------------------------------------------------------------------------
12271b2c2d-5228ac3d-3147bc3d+14866c4d+4158b3d2-8038a2cd2-2327abcd2-
------------------------------------------------------------------------
8846b2cd2-10970ac2d2-4927bc2d2-12478c3d2-165a2d3+13102abd3+8433b2d3-
------------------------------------------------------------------------
5556acd3+300bcd3-11007c2d3-4795ad4+13040bd4-907cd4+5821d5-5303a2c2e-
------------------------------------------------------------------------
14057abc2e-14267b2c2e-15500ac3e-7610bc3e+4920c4e+674b3de-12870a2cde-
------------------------------------------------------------------------
3756abcde-10462b2cde+1717ac2de-4507bc2de-10875c3de-3840a2d2e+935abd2e-
------------------------------------------------------------------------
3881b2d2e-10350acd2e-8331bcd2e-12437c2d2e+4188ad3e-3847bd3e+4075cd3e-
------------------------------------------------------------------------
9119d4e-5029b3e2+6487a2ce2-14746abce2+11659b2ce2+1201ac2e2+7488bc2e2-
------------------------------------------------------------------------
11652c3e2+2927a2de2+6060abde2+4679b2de2+577acde2-4727bcde2+12726c2de2-
------------------------------------------------------------------------
10784ad2e2+2850bd2e2+6861cd2e2-385d3e2-14907a2e3+10361abe3+1044b2e3+
------------------------------------------------------------------------
928ace3+5440bce3+13176c2e3-70ade3+2484bde3-9131cde3-5492d2e3-64ae4-
------------------------------------------------------------------------
11394be4+7746ce4+2479de4+8019e5
------------------------------------------------------------------------
a2c3-2118b2c3+5674ac4-5859bc4+3586c5-4490a2c2d+4030abc2d-13452b2c2d-
------------------------------------------------------------------------
12087ac3d+2937bc3d+3482c4d+14535b3d2+13027a2cd2+5180abcd2+13582b2cd2-
------------------------------------------------------------------------
14492ac2d2-6886bc2d2+7607c3d2+11807a2d3+15717abd3+996b2d3+6077acd3-
------------------------------------------------------------------------
12089bcd3-8905c2d3-13665ad4-2890bd4+12822cd4+4562d5+15091a2c2e-7889abc2e
------------------------------------------------------------------------
+2192b2c2e+661ac3e+8389bc3e-3414c4e+2069b3de+1540a2cde-9144abcde-
------------------------------------------------------------------------
4326b2cde+14406ac2de+6786bc2de-11616c3de-8879a2d2e+1056abd2e-13939b2d2e+
------------------------------------------------------------------------
5751acd2e-2753bcd2e+3772c2d2e+6466ad3e-10497bd3e-3701cd3e-9848d4e-
------------------------------------------------------------------------
3812b3e2-7147a2ce2+5966abce2-7282b2ce2-9358ac2e2+11968bc2e2-2333c3e2-
------------------------------------------------------------------------
10697a2de2-12025abde2-9385b2de2+8558acde2-14436bcde2-6855c2de2+9685ad2e2
------------------------------------------------------------------------
+2822bd2e2-9245cd2e2+2698d3e2-783a2e3+14899abe3+8565b2e3-14543ace3+
------------------------------------------------------------------------
2236bce3+6085c2e3+11488ade3-2416bde3-13870cde3+7367d2e3-14431ae4-
------------------------------------------------------------------------
11444be4-11841ce4+10976de4+4569e5 |
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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