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 (- 10369a - 9374a b - 14199a*b + 14416b - 14554a c - 572a*b*c +
------------------------------------------------------------------------
2 2 2 3 2
11457b c - 1420a*c + 13413b*c - 2089c + 14300a d + 354a*b*d +
------------------------------------------------------------------------
2 2 2 2
12493b d - 2361a*c*d - 4679b*c*d - 6338c d - 1204a*d - 13566b*d +
------------------------------------------------------------------------
2 3 2 2
10778c*d + 9462d + 4265a e + 7767a*b*e - 1089b e + 4391a*c*e -
------------------------------------------------------------------------
2 2
3335b*c*e - 12087c e - 10587a*d*e - 14142b*d*e - 1252c*d*e + 12147d e -
------------------------------------------------------------------------
2 2 2 2 3 3 2
115a*e + 9061b*e + 4370c*e + 2330d*e + 2585e , - 6716a + 6402a b +
------------------------------------------------------------------------
2 3 2 2 2 2
2076a*b + 1550b + 8864a c - 11547a*b*c + 14569b c + 474a*c - 5657b*c
------------------------------------------------------------------------
3 2 2
+ 498c + 2057a d + 1198a*b*d + 15100b d + 15539a*c*d + 9965b*c*d -
------------------------------------------------------------------------
2 2 2 2 3 2
4763c d - 7908a*d - 14606b*d - 3607c*d - 12578d - 5273a e - 265a*b*e
------------------------------------------------------------------------
2 2
+ 5844b e + 3934a*c*e - 5572b*c*e + 13650c e - 4136a*d*e - 4087b*d*e +
------------------------------------------------------------------------
2 2 2 2 2
8386c*d*e + 2540d e - 15761a*e - 5673b*e + 4232c*e + 12217d*e +
------------------------------------------------------------------------
3 3 2 2 3 2
11172e , 9175a - 12854a b + 3709a*b + 6550b + 8809a c - 12111a*b*c -
------------------------------------------------------------------------
2 2 2 3 2 2
7416b c + 14270a*c - 3190b*c - 9178c + 13579a d - 6715a*b*d - 9564b d
------------------------------------------------------------------------
2 2 2 2
- 8357a*c*d + 9604b*c*d - 2985c d + 11849a*d + 2857b*d + 8425c*d +
------------------------------------------------------------------------
3 2 2
14629d + 12592a e - 7797a*b*e + 2769b e - 596a*c*e + 876b*c*e -
------------------------------------------------------------------------
2 2 2
11420c e + 2527a*d*e + 9337b*d*e + 6093c*d*e - 7333d e - 1446a*e +
------------------------------------------------------------------------
2 2 2 3
3605b*e - 14363c*e - 8050d*e - 14720e )
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 = | ab2-5493b3-10299a2c+554abc-9803b2c+11644ac2+2604bc2-11672c3-12222a2d-
------------------------------------------------------------------------
1037abd+9724b2d-11207acd-5094bcd+7466c2d-9826ad2+1933bd2+9064cd2+7739d3+
------------------------------------------------------------------------
319a2e-5517abe+4035b2e+9788ace+2499bce+7312c2e-12535ade+9891bde+14396cde
------------------------------------------------------------------------
+12987d2e+7793ae2+1344be2+5780ce2-4038de2+11772e3
------------------------------------------------------------------------
a2b-15872b3-1106a2c+15878abc-4966b2c-1961ac2-60bc2-8394c3-3011a2d+
------------------------------------------------------------------------
3159abd-225b2d+4747acd+4818bcd-15849c2d-15030ad2-1176bd2-3237cd2+12630d3
------------------------------------------------------------------------
+341a2e+14302abe-13472b2e+6698ace+4588bce+11360c2e+1347ade-8959bde-
------------------------------------------------------------------------
14285cde-11984d2e+7077ae2-5577be2+1109ce2+10924de2-10190e3
------------------------------------------------------------------------
a3-8794b3+4910a2c+8137abc+14187b2c+186ac2-4374bc2-4681c3-5157a2d-5334abd
------------------------------------------------------------------------
+1979b2d+13367acd-7929bcd-14148c2d-10006ad2-11243bd2-14536cd2+10326d3-
------------------------------------------------------------------------
9835a2e-3678abe+870b2e-740ace+4270bce+9456c2e+7007ade+9371bde-10617cde+
------------------------------------------------------------------------
8163d2e+3625ae2+6932be2-4276ce2-1973de2+10354e3
------------------------------------------------------------------------
b3c-2077a2c2-948abc2-7553b2c2-12337ac3-4596bc3+13056c4-8846b3d-15766a2cd
------------------------------------------------------------------------
-128abcd-14630b2cd+717ac2d-10334bc2d-2425c3d-7531a2d2+10200abd2+654b2d2-
------------------------------------------------------------------------
7598acd2+8032bcd2+2896c2d2+348ad3+3850bd3-9011cd3-13594d4+9436b3e-
------------------------------------------------------------------------
1718a2ce+3693abce-8020b2ce-4954ac2e-4633bc2e-12877c3e+3012a2de-12592abde
------------------------------------------------------------------------
-335b2de-2362acde-15594bcde-7622c2de+15557ad2e-819bd2e-9924cd2e-5185d3e-
------------------------------------------------------------------------
11716a2e2+4029abe2+5904b2e2-9322ace2-14236bce2+1379c2e2-4779ade2-
------------------------------------------------------------------------
10620bde2+6255cde2-1478d2e2+13793ae3-11964be3-15442ce3+10867de3-10272e4
------------------------------------------------------------------------
b4-4150a2c2-9925abc2-3706b2c2-9196ac3-8261bc3-13621c4+2598b3d-4663a2cd+
------------------------------------------------------------------------
10343abcd+1897b2cd-1878ac2d-14421bc2d+536c3d-10282a2d2+5866abd2+7606b2d2
------------------------------------------------------------------------
+10956acd2+4120bcd2+10017c2d2-3486ad3+2810bd3-12378cd3-5716d4+11283b3e+
------------------------------------------------------------------------
3500a2ce-6212abce-4673b2ce+9340ac2e-14478bc2e-40c3e-10726a2de-5107abde-
------------------------------------------------------------------------
14959b2de+6856acde-6428bcde+11789c2de+14313ad2e+8781bd2e-10308cd2e+
------------------------------------------------------------------------
11914d3e-9799a2e2+12163abe2+1806b2e2+14066ace2+8979bce2-8927c2e2-
------------------------------------------------------------------------
5698ade2-15125bde2+12454cde2-1685d2e2-10159ae3+11785be3+1658ce3-8905de3-
------------------------------------------------------------------------
8038e4 abc3-4193b2c3+4794ac4-14838bc4+1146c5+2810a2c2d+11558abc2d+
------------------------------------------------------------------------
12724b2c2d+3274ac3d+5290bc3d+13746c4d+10692b3d2-5592a2cd2-10429abcd2-
------------------------------------------------------------------------
5764b2cd2+13741ac2d2+11346bc2d2+4731c3d2-9875a2d3+3339abd3-12827b2d3-
------------------------------------------------------------------------
165acd3-1457bcd3+9279c2d3-2546ad4-9240bd4-10899cd4+14198d5-14989a2c2e+
------------------------------------------------------------------------
14781abc2e+6516b2c2e+11030ac3e-4564bc3e+11248c4e-3231b3de+1884a2cde-
------------------------------------------------------------------------
9612abcde+6475b2cde-5791ac2de+8435bc2de+5606c3de-13347a2d2e-1080abd2e+
------------------------------------------------------------------------
6232b2d2e-5831acd2e+14876bcd2e+7220c2d2e-7767ad3e+8322bd3e-8286cd3e-
------------------------------------------------------------------------
6346d4e-549b3e2+15717a2ce2+10805abce2-1701b2ce2-7337ac2e2-12982bc2e2-
------------------------------------------------------------------------
4311c3e2+1494a2de2+5579abde2-10349b2de2+515acde2-1736bcde2+10140c2de2+
------------------------------------------------------------------------
7029ad2e2-14410bd2e2+2605cd2e2-6112d3e2+8575a2e3-11247abe3-10238b2e3+
------------------------------------------------------------------------
1608ace3-13317bce3-14272c2e3+1881ade3-7117bde3+12430cde3-8064d2e3-
------------------------------------------------------------------------
11512ae4-7053be4-8307ce4+13656de4-7435e5
------------------------------------------------------------------------
a2c3+2650b2c3+13675ac4+97bc4-5214c5+11868a2c2d-13524abc2d+9883b2c2d-
------------------------------------------------------------------------
7057ac3d+3118bc3d-12057c4d+6742b3d2-9246a2cd2-1603abcd2-11811b2cd2-
------------------------------------------------------------------------
12129ac2d2-4751bc2d2+7198c3d2+2403a2d3-5916abd3+6124b2d3-15949acd3+
------------------------------------------------------------------------
504bcd3+15219c2d3-9906ad4+14457bd4-7935cd4+10461d5-10441a2c2e-8507abc2e+
------------------------------------------------------------------------
3523b2c2e+11515ac3e+4538bc3e+14029c4e+2978b3de+15123a2cde-9963abcde-
------------------------------------------------------------------------
13048b2cde+6718ac2de-2561bc2de+7396c3de-10115a2d2e+15942abd2e-3312b2d2e-
------------------------------------------------------------------------
4837acd2e-14267bcd2e+13118c2d2e+6360ad3e+13030bd3e+10938cd3e-6281d4e+
------------------------------------------------------------------------
8062b3e2-6778a2ce2+8557abce2+9524b2ce2+13084ac2e2+1142bc2e2+3985c3e2-
------------------------------------------------------------------------
4840a2de2-3001abde2-14584b2de2+3958acde2+9781bcde2+5836c2de2-5381ad2e2+
------------------------------------------------------------------------
11169bd2e2-12514cd2e2-13373d3e2-6310a2e3-12294abe3-13719b2e3-157ace3+
------------------------------------------------------------------------
2977bce3+11628c2e3+15282ade3+3863bde3-14017cde3+2321d2e3+11211ae4+
------------------------------------------------------------------------
13505be4-6783ce4+10673de4-13620e5 |
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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