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 (- 4238a + 7951a b - 9243a*b - 12104b - 5305a c + 9443a*b*c -
------------------------------------------------------------------------
2 2 2 3 2
11278b c + 11541a*c - 8297b*c - 12185c + 10185a d + 4157a*b*d +
------------------------------------------------------------------------
2 2 2 2
5503b d + 12592a*c*d + 4036b*c*d - 2095c d + 9839a*d - 1887b*d -
------------------------------------------------------------------------
2 3 2 2
8728c*d - 10185d + 3633a e - 168a*b*e - 2743b e + 10992a*c*e +
------------------------------------------------------------------------
2 2
13130b*c*e - 10045c e + 6397a*d*e + 3986b*d*e + 2498c*d*e - 12955d e +
------------------------------------------------------------------------
2 2 2 2 3 3 2
4070a*e - 11301b*e - 7780c*e + 15771d*e - 158e , - 13873a + 268a b
------------------------------------------------------------------------
2 3 2 2 2
+ 13267a*b + 6733b + 3908a c + 2187a*b*c - 12738b c - 4141a*c -
------------------------------------------------------------------------
2 3 2 2
6737b*c + 11857c + 3556a d + 3052a*b*d + 1737b d - 11156a*c*d -
------------------------------------------------------------------------
2 2 2 2 3
3014b*c*d + 13974c d + 6733a*d + 2453b*d - 7346c*d - 11301d -
------------------------------------------------------------------------
2 2 2
13972a e + 10583a*b*e + 15450b e - 10883a*c*e - 12350b*c*e + 15352c e +
------------------------------------------------------------------------
2 2 2
8785a*d*e - 3197b*d*e - 4734c*d*e + 2369d e - 13041a*e - 11729b*e +
------------------------------------------------------------------------
2 2 3 3 2 2 3
1542c*e + 14291d*e + 1545e , - 4111a - 107a b - 4997a*b - 9556b -
------------------------------------------------------------------------
2 2 2 2 3 2
4118a c + 755a*b*c - 6948b c - 14791a*c - 11709b*c - 1302c - 9224a d
------------------------------------------------------------------------
2 2 2
+ 5151a*b*d + 7673b d - 6009a*c*d + 6916b*c*d + 10896c d - 7026a*d +
------------------------------------------------------------------------
2 2 3 2 2
9332b*d + 12320c*d - 5009d - 15761a e + 3676a*b*e + 5850b e +
------------------------------------------------------------------------
2
11835a*c*e - 14596b*c*e - 3830c e - 7247a*d*e + 9867b*d*e - 8312c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3
6280d e - 4758a*e - 37b*e + 7121c*e + 200d*e - 8262e )
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 = | ab2-13330b3-13710a2c-1253abc-11534b2c-10779ac2-8308bc2+9233c3-15642a2d
------------------------------------------------------------------------
+4577abd+8148b2d-11498acd+4072bcd+235c2d+14115ad2+3734bd2-11293cd2-
------------------------------------------------------------------------
10110d3-9352a2e-15577abe+14086b2e-7477ace-4317bce+4005c2e+9898ade+
------------------------------------------------------------------------
11433bde-14858cde-15387d2e+3627ae2-3642be2-1612ce2-13887de2-7747e3
------------------------------------------------------------------------
a2b+4868b3+3384a2c-7414abc-14000b2c-4813ac2+2391bc2+1532c3+15802a2d-
------------------------------------------------------------------------
14316abd-9657b2d-3486acd-7375bcd+13831c2d+8716ad2+773bd2-2547cd2+9608d3-
------------------------------------------------------------------------
10417a2e+2786abe-14010b2e-6431ace-10902bce+9860c2e+850ade-14946bde-
------------------------------------------------------------------------
4659cde-15795d2e+3387ae2+4632be2-9685ce2+11792de2-1518e3
------------------------------------------------------------------------
a3+10419b3-13339a2c+9376abc-1168b2c+8926ac2-11797bc2+4307c3+5409a2d+
------------------------------------------------------------------------
6594abd-15244b2d+15921acd+9549bcd+10009c2d-4950ad2-5651bd2+416cd2-1085d3
------------------------------------------------------------------------
+4356a2e+13427abe-543b2e+13301ace+3752bce+6670c2e-4189ade+12366bde-
------------------------------------------------------------------------
10114cde-6787d2e-5967ae2-4576be2+3720ce2-6283de2-1168e3
------------------------------------------------------------------------
b3c-13223a2c2-10079abc2-15661b2c2+3977ac3+14016bc3-4664c4-10018b3d-
------------------------------------------------------------------------
199a2cd+11285abcd-7781b2cd-12769ac2d-8001bc2d-6221c3d+11864a2d2-
------------------------------------------------------------------------
11903abd2-6633b2d2-15203acd2+6284bcd2+6321c2d2-6400ad3+12295bd3+4790cd3-
------------------------------------------------------------------------
11786d4-11597b3e-1263a2ce+10263abce-7621b2ce+670ac2e-1800bc2e-6659c3e-
------------------------------------------------------------------------
8121a2de-8242abde-6769b2de+2781acde-2135bcde-12630c2de+15062ad2e+
------------------------------------------------------------------------
3386bd2e-13813cd2e+15604d3e-1799a2e2+2594abe2+6791b2e2-5699ace2+
------------------------------------------------------------------------
10657bce2-6531c2e2-13511ade2+13023bde2+2924cde2+8087d2e2+6272ae3+6666be3
------------------------------------------------------------------------
-4306ce3+8299de3+14295e4
------------------------------------------------------------------------
b4+2137a2c2-2524abc2-8716b2c2-4171ac3+12164bc3-11140c4-887b3d+14183a2cd-
------------------------------------------------------------------------
970abcd-3629b2cd-4316ac2d-1698bc2d+1049c3d-4677a2d2+11136abd2+13825b2d2+
------------------------------------------------------------------------
12326acd2-8188bcd2+90c2d2+9789ad3+3759bd3-3970cd3-12068d4+8603b3e+
------------------------------------------------------------------------
4256a2ce+780abce+11672b2ce-14046ac2e+4465bc2e+10769c3e+1755a2de-
------------------------------------------------------------------------
12562abde+8073b2de-11729acde-13212bcde-2215c2de-1276ad2e+9033bd2e+
------------------------------------------------------------------------
13956cd2e-2293d3e-15908a2e2-12906abe2-4096b2e2-7343ace2-5032bce2-
------------------------------------------------------------------------
13090c2e2-6323ade2+6062bde2+9364cde2-12216d2e2-9964ae3+12409be3+1737ce3-
------------------------------------------------------------------------
3153de3-748e4 abc3-6589b2c3+15548ac4-10100bc4-6452c5-11017a2c2d+
------------------------------------------------------------------------
2103abc2d-8369b2c2d-14255ac3d+8000bc3d+12882c4d+9773b3d2-6533a2cd2+
------------------------------------------------------------------------
2211abcd2-6723b2cd2-7810ac2d2+10861bc2d2+5809c3d2-126a2d3+1505abd3+
------------------------------------------------------------------------
1993b2d3-11839acd3+1767bcd3-4805c2d3+7010ad4-12453bd4+296cd4+2122d5-
------------------------------------------------------------------------
4998a2c2e+13524abc2e+9924b2c2e-6006ac3e+8363bc3e+302c4e-7029b3de+
------------------------------------------------------------------------
2450a2cde+1925abcde+7909b2cde-12373ac2de+4480bc2de-6638c3de+12100a2d2e-
------------------------------------------------------------------------
4988abd2e+14595b2d2e-6933acd2e+1770bcd2e+1657c2d2e-612ad3e+5628bd3e-
------------------------------------------------------------------------
12026cd3e+10208d4e-10142b3e2-2021a2ce2+9731abce2-9669b2ce2-10591ac2e2+
------------------------------------------------------------------------
14083bc2e2-1893c3e2-4331a2de2-2739abde2+2870b2de2-5337acde2+8887bcde2+
------------------------------------------------------------------------
12353c2de2+11092ad2e2-13241bd2e2+8879cd2e2-14983d3e2+606a2e3+11162abe3+
------------------------------------------------------------------------
4298b2e3+12946ace3-10294bce3+6744c2e3+5ade3-3335bde3-5764cde3-136d2e3-
------------------------------------------------------------------------
4817ae4+5075be4+6733ce4-13446de4+15583e5
------------------------------------------------------------------------
a2c3+1625b2c3-5972ac4+8929bc4+1591c5+7244a2c2d-2847abc2d+4700b2c2d+
------------------------------------------------------------------------
1963ac3d-15656bc3d+6405c4d+13247b3d2+6272a2cd2+13822abcd2+14081b2cd2-
------------------------------------------------------------------------
6229ac2d2-11346bc2d2+6640c3d2+14965a2d3-6619abd3+7395b2d3+15895acd3+
------------------------------------------------------------------------
7045bcd3+8618c2d3-7795ad4+9781bd4-10900cd4-1756d5+5542a2c2e+297abc2e+
------------------------------------------------------------------------
11149b2c2e+11572ac3e-1648bc3e-5069c4e+12235b3de-10391a2cde+13870abcde-
------------------------------------------------------------------------
15572b2cde-11750ac2de-2591bc2de+8716c3de+4328a2d2e-6399abd2e+3649b2d2e-
------------------------------------------------------------------------
4213acd2e-8313bcd2e+13244c2d2e+4351ad3e-15240bd3e-2613cd3e-10581d4e+
------------------------------------------------------------------------
4684b3e2+2620a2ce2-3947abce2-7912b2ce2+6311ac2e2-10434bc2e2-4936c3e2+
------------------------------------------------------------------------
9387a2de2+12963abde2+9293b2de2+4394acde2+9507bcde2-569c2de2+14034ad2e2-
------------------------------------------------------------------------
15322bd2e2+6308cd2e2-6841d3e2+15132a2e3+5437abe3-9611b2e3-6838ace3+
------------------------------------------------------------------------
6140bce3-15666c2e3+4887ade3+14618bde3-869cde3-4005d2e3-321ae4-8398be4-
------------------------------------------------------------------------
15224ce4+118de4-3741e5 |
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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