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 (3570a + 10895a b - 15059a*b + 9135b - 8069a c - 2133a*b*c -
------------------------------------------------------------------------
2 2 2 3 2
7541b c - 13482a*c - 13618b*c + 4401c + 14166a d + 3027a*b*d +
------------------------------------------------------------------------
2 2 2 2
3887b d + 9742a*c*d + 14627b*c*d - 11948c d - 10677a*d + 3807b*d +
------------------------------------------------------------------------
2 3 2 2
1775c*d - 1466d - 5889a e + 14529a*b*e - 13014b e + 13935a*c*e -
------------------------------------------------------------------------
2 2
4143b*c*e - 8278c e - 4275a*d*e + 10949b*d*e + 11387c*d*e + 3290d e +
------------------------------------------------------------------------
2 2 2 2 3 3 2
2118a*e - 9219b*e + 6727c*e - 5634d*e - 10343e , 13002a - 1525a b +
------------------------------------------------------------------------
2 3 2 2 2
5645a*b - 6077b + 3426a c - 13901a*b*c + 4496b c - 14494a*c -
------------------------------------------------------------------------
2 3 2 2
1575b*c + 11469c + 11722a d + 7482a*b*d + 4421b d - 5975a*c*d -
------------------------------------------------------------------------
2 2 2 2 3 2
6865b*c*d + 7168c d - 6877a*d + 7051b*d + 1231c*d - 12830d + 4027a e
------------------------------------------------------------------------
2 2
+ 12432a*b*e - 3056b e + 15991a*c*e - 1726b*c*e - 15533c e - 14594a*d*e
------------------------------------------------------------------------
2 2 2 2
- 4877b*d*e - 2233c*d*e - 3038d e + 7892a*e - 14931b*e - 14615c*e +
------------------------------------------------------------------------
2 3 3 2 2 3 2
15017d*e + 9711e , 5525a + 13949a b + 10427a*b + 9481b - 7968a c +
------------------------------------------------------------------------
2 2 2 3 2
1800a*b*c - 253b c - 14755a*c - 9288b*c + 1828c - 15395a d -
------------------------------------------------------------------------
2 2 2
13268a*b*d - 15363b d + 12435a*c*d + 9212b*c*d - 9470c d + 5786a*d -
------------------------------------------------------------------------
2 2 3 2 2
4479b*d - 864c*d + 6629d + 14455a e - 9991a*b*e + 4888b e + 5724a*c*e
------------------------------------------------------------------------
2 2
- 1892b*c*e + 9140c e + 5237a*d*e + 4976b*d*e - 14622c*d*e + 5375d e -
------------------------------------------------------------------------
2 2 2 2 3
6150a*e - 1998b*e + 12225c*e - 1604d*e - 11785e )
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 = | ab2-12383b3-13634a2c-4418abc-12508b2c+14707ac2-2759bc2+13306c3+
------------------------------------------------------------------------
14133a2d+9074abd-8145b2d-1701acd+10756bcd-15891c2d-6491ad2-1943bd2+
------------------------------------------------------------------------
13026cd2+1687d3-8715a2e+2674abe+7408b2e+6447ace+8761bce-1629c2e-3761ade+
------------------------------------------------------------------------
11138bde+6940cde+11570d2e+257ae2+315be2+14555ce2-3226de2+11471e3
------------------------------------------------------------------------
a2b-15286b3-385a2c+8834abc-6824b2c-12549ac2-14127bc2-10315c3-1805a2d-
------------------------------------------------------------------------
10674abd+8104b2d+10967acd-13849bcd-3026c2d-7850ad2-8852bd2-6295cd2+
------------------------------------------------------------------------
10387d3+1590a2e+1437abe+8365b2e+15798ace-3352bce-11731c2e+2296ade+
------------------------------------------------------------------------
12511bde-11870cde-9790d2e+6891ae2-13638be2+15028ce2-7800de2+12131e3
------------------------------------------------------------------------
a3+4405b3+11612a2c-2612abc+13969b2c+10041ac2+12628bc2-4815c3+10302a2d+
------------------------------------------------------------------------
293abd+15460b2d-14878acd+4432bcd-9939c2d-7353ad2-9956bd2-8476cd2+11059d3
------------------------------------------------------------------------
+9105a2e-3411abe-10070b2e-4125ace+12474bce-2287c2e-4693ade+9593bde+
------------------------------------------------------------------------
2671cde+11629d2e+2627ae2+79be2+7252ce2+2808de2+7714e3
------------------------------------------------------------------------
b3c-11040a2c2+3996abc2+4410b2c2+6807ac3-13672bc3+8606c4-4409b3d-
------------------------------------------------------------------------
14749a2cd-15606abcd+12568b2cd+3614ac2d+9657bc2d+8287c3d-10164a2d2+
------------------------------------------------------------------------
2195abd2+9320b2d2+10740acd2-870bcd2+10837c2d2+14116ad3+7229bd3-4952cd3+
------------------------------------------------------------------------
6799d4-13719b3e-9465a2ce+15008abce-6606b2ce+4632ac2e-14964bc2e-4327c3e-
------------------------------------------------------------------------
406a2de+4551abde+4888b2de-997acde-12115bcde+7354c2de-525ad2e-1099bd2e+
------------------------------------------------------------------------
11493cd2e+5124d3e-13077a2e2-9637abe2-2847b2e2+4781ace2-2625bce2+
------------------------------------------------------------------------
13368c2e2+3275ade2+9725bde2-2961cde2+9663d2e2-14925ae3+261be3-11412ce3-
------------------------------------------------------------------------
1229de3-14282e4 b4-4737a2c2+13890abc2+3646b2c2+11723ac3+13849bc3+9101c4-
------------------------------------------------------------------------
1534b3d-48a2cd-7520abcd-8147b2cd-14620ac2d+8133bc2d+2218c3d+10631a2d2-
------------------------------------------------------------------------
12039abd2+9208b2d2+14315acd2+9128bcd2+15874c2d2-9811ad3+15790bd3+3089cd3
------------------------------------------------------------------------
+12985d4+6211b3e+9774a2ce-13706abce-5581b2ce+2013ac2e-11444bc2e-14102c3e
------------------------------------------------------------------------
-9840a2de+9953abde+8435b2de+15053acde+15045bcde+11592c2de-8619ad2e-
------------------------------------------------------------------------
12285bd2e+7102cd2e+774d3e+14218a2e2+8566abe2+11526b2e2-2409ace2+
------------------------------------------------------------------------
10370bce2+679c2e2+15690ade2+9097bde2-10672cde2+10625d2e2+13754ae3+986be3
------------------------------------------------------------------------
+2389ce3+15248de3+12984e4
------------------------------------------------------------------------
abc3-3026b2c3+7243ac4+2748bc4-5413c5+7167a2c2d-3359abc2d+105b2c2d-
------------------------------------------------------------------------
2192ac3d-10834bc3d+8960c4d-1783b3d2-3212a2cd2-10043abcd2+2875b2cd2-
------------------------------------------------------------------------
8186ac2d2-5917bc2d2-533c3d2+15081a2d3+335abd3-12446b2d3+12425acd3-
------------------------------------------------------------------------
6621bcd3-2266c2d3-13989ad4+11969bd4-11653cd4-1752d5+10410a2c2e+
------------------------------------------------------------------------
14251abc2e+1461b2c2e+14772ac3e+15043bc3e+7074c4e-3764b3de+12994a2cde+
------------------------------------------------------------------------
15794abcde-8142b2cde+9308ac2de-13187bc2de-15540c3de+14474a2d2e+9565abd2e
------------------------------------------------------------------------
-11619b2d2e-4839acd2e+13738bcd2e-15642c2d2e+5900ad3e+15436bd3e-12453cd3e
------------------------------------------------------------------------
+12948d4e-14141b3e2-10256a2ce2-9762abce2+3117b2ce2-15152ac2e2-2521bc2e2+
------------------------------------------------------------------------
1421c3e2+1584a2de2-10400abde2-7859b2de2-11255acde2-5949bcde2+9472c2de2+
------------------------------------------------------------------------
6852ad2e2-711bd2e2-1896cd2e2-9838d3e2+15237a2e3-1564abe3+15394b2e3+
------------------------------------------------------------------------
12499ace3-3384bce3+15829c2e3-15540ade3+15460bde3-12646cde3-15415d2e3-
------------------------------------------------------------------------
6349ae4+13284be4+10024ce4-540de4+5549e5
------------------------------------------------------------------------
a2c3-5216b2c3+9385ac4+1230bc4+14437c5-8761a2c2d-7284abc2d+7490b2c2d+
------------------------------------------------------------------------
13739ac3d+13586bc3d-11647c4d+13633b3d2-876a2cd2+14382abcd2-9890b2cd2+
------------------------------------------------------------------------
1757ac2d2-12694bc2d2-6238c3d2-2738a2d3+7389abd3-15823b2d3-7569acd3-
------------------------------------------------------------------------
14598bcd3-4907c2d3+15968ad4+10553bd4+13956cd4+5703d5+6973a2c2e-
------------------------------------------------------------------------
12766abc2e-4776b2c2e-158ac3e-11749bc3e-7399c4e+14885b3de+14848a2cde-
------------------------------------------------------------------------
6835abcde-4917b2cde-6268ac2de-4450bc2de+11031c3de+7389a2d2e+4874abd2e+
------------------------------------------------------------------------
14508b2d2e-8199acd2e+13249bcd2e+10025c2d2e+15652ad3e-10752bd3e-13098cd3e
------------------------------------------------------------------------
-3528d4e-12661b3e2+840a2ce2+5614abce2+12954b2ce2-13500ac2e2-12878bc2e2-
------------------------------------------------------------------------
14913c3e2-10293a2de2-14125abde2-10705b2de2+3354acde2-1394bcde2+8238c2de2
------------------------------------------------------------------------
-15975ad2e2+2898bd2e2-2079cd2e2-7224d3e2+5251a2e3+4426abe3-13974b2e3+
------------------------------------------------------------------------
3658ace3-4152bce3-9117c2e3+14310ade3+14983bde3-13295cde3+8467d2e3-
------------------------------------------------------------------------
13318ae4-7676be4-14548ce4-1732de4-10023e5 |
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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