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 (4902a - 3777a b + 15249a*b - 2640b - 6061a c + 1053a*b*c -
------------------------------------------------------------------------
2 2 2 3 2
6853b c - 15795a*c + 11885b*c - 14300c + 11407a d - 10292a*b*d -
------------------------------------------------------------------------
2 2 2 2
13797b d + 1867a*c*d - 4488b*c*d + 293c d + 15228a*d - 4227b*d -
------------------------------------------------------------------------
2 3 2 2
9850c*d - 6618d + 2548a e + 12611a*b*e - 1311b e + 11144a*c*e +
------------------------------------------------------------------------
2 2
2735b*c*e + 7775c e - 7130a*d*e - 5010b*d*e + 7086c*d*e - 3309d e +
------------------------------------------------------------------------
2 2 2 2 3 3 2
12114a*e - 7701b*e - 8321c*e - 3168d*e + 14304e , 12537a + 5957a b
------------------------------------------------------------------------
2 3 2 2 2
+ 15670a*b + 3347b - 15027a c - 12681a*b*c + 8326b c + 10628a*c -
------------------------------------------------------------------------
2 3 2 2
2506b*c + 7333c - 11872a d + 5327a*b*d + 11409b d - 12926a*c*d +
------------------------------------------------------------------------
2 2 2 2 3
15742b*c*d - 10002c d - 1254a*d + 499b*d + 5726c*d + 1012d -
------------------------------------------------------------------------
2 2 2
15011a e + 11501a*b*e - 6175b e - 2490a*c*e + 15527b*c*e + 7735c e +
------------------------------------------------------------------------
2 2 2
4377a*d*e + 3257b*d*e + 1414c*d*e - 15712d e + 10080a*e - 14022b*e +
------------------------------------------------------------------------
2 2 3 3 2 2
8205c*e - 5772d*e + 13721e , - 14928a - 11780a b - 14170a*b -
------------------------------------------------------------------------
3 2 2 2 2 3
10530b + 12305a c - 7779a*b*c - 4784b c + 12517a*c - 6278b*c - 6986c
------------------------------------------------------------------------
2 2 2
- 14761a d + 13697a*b*d - 3412b d - 36a*c*d + 7433b*c*d + 8149c d +
------------------------------------------------------------------------
2 2 2 3 2 2
8544a*d + 12160b*d - 12522c*d + 362d + 1969a e + 2625a*b*e - 9381b e
------------------------------------------------------------------------
2
- 12483a*c*e + 14602b*c*e + 14841c e + 6848a*d*e + 13188b*d*e -
------------------------------------------------------------------------
2 2 2 2 2
6363c*d*e + 11198d e + 2782a*e - 10603b*e + 280c*e + 118d*e -
------------------------------------------------------------------------
3
6526e )
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+8755b3+2194a2c+7453abc+163b2c-14093ac2-8781bc2-11432c3-198a2d-
------------------------------------------------------------------------
10951abd+9755b2d-6848acd-5082bcd-3851c2d+3291ad2-3772bd2+12254cd2+2856d3
------------------------------------------------------------------------
-11921a2e+456abe+1556b2e+4195ace-12736bce+30c2e-2130ade+468bde+12675cde-
------------------------------------------------------------------------
14423d2e-2478ae2-5913be2-5236ce2+300de2-13231e3
------------------------------------------------------------------------
a2b-3508b3-12149a2c-5378abc+11624b2c-6870ac2-11599bc2+4636c3-11348a2d+
------------------------------------------------------------------------
10176abd-9823b2d-9025acd-1783bcd-10768c2d+12387ad2+284bd2-6987cd2+
------------------------------------------------------------------------
14743d3+14798a2e-11441abe-9126b2e+6954ace+12079bce-8177c2e+14675ade-
------------------------------------------------------------------------
3828bde-11145cde-10009d2e-14535ae2+13458be2+12473ce2-9744de2+8079e3
------------------------------------------------------------------------
a3-7591b3+10580a2c-15185abc-6150b2c-2038ac2-6891bc2-4636c3-13407a2d+
------------------------------------------------------------------------
7597abd+3350b2d+9283acd+783bcd+13998c2d-4294ad2-2287bd2+7333cd2-7652d3-
------------------------------------------------------------------------
10813a2e+9485abe+12982b2e+961ace+2012bce-15506c2e+11279ade+10988bde-
------------------------------------------------------------------------
11938cde-5484d2e+6520ae2+14856be2+8805ce2-3036de2+7745e3
------------------------------------------------------------------------
b3c+8881a2c2-13100abc2+14249b2c2+7292ac3-9643bc3+6665c4+947b3d-4926a2cd+
------------------------------------------------------------------------
14497abcd-5861b2cd+2861ac2d-2225bc2d-10880c3d+5279a2d2+6256abd2+
------------------------------------------------------------------------
12791b2d2+4440acd2-1055bcd2+10812c2d2-8741ad3-9385bd3-15986cd3-5884d4-
------------------------------------------------------------------------
8815b3e-12504a2ce+11483abce+3614b2ce+5400ac2e+11217bc2e+7512c3e+6997a2de
------------------------------------------------------------------------
+4727abde-3526b2de+2653acde+14411bcde+321c2de+4121ad2e-4548bd2e-1137cd2e
------------------------------------------------------------------------
-9640d3e-13672a2e2-1123abe2+7439b2e2+12810ace2+8122bce2-13826c2e2-
------------------------------------------------------------------------
888ade2+5913bde2-7884cde2-3009d2e2+538ae3-8751be3-11313ce3-15282de3+
------------------------------------------------------------------------
3804e4 b4+6666a2c2+2813abc2-8942b2c2-8133ac3-9695bc3+2586c4+409b3d+
------------------------------------------------------------------------
10453a2cd-9700abcd+1296b2cd-1514ac2d+5772bc2d-1432c3d+12130a2d2-1786abd2
------------------------------------------------------------------------
+5596b2d2+2777acd2-8864bcd2+9429c2d2+12416ad3-9115bd3+2629cd3+8074d4+
------------------------------------------------------------------------
6189b3e-3254a2ce-6123abce-14449b2ce+15617ac2e+6234bc2e+12674c3e+1484a2de
------------------------------------------------------------------------
+3812abde+7736b2de-9266acde+11334bcde+3661c2de+1650ad2e-1505bd2e-144cd2e
------------------------------------------------------------------------
+13020d3e-11493a2e2-7972abe2+15171b2e2-12338ace2-8653bce2+6916c2e2+
------------------------------------------------------------------------
586ade2-13816bde2+1429cde2-3107d2e2+13004ae3-2209be3+6116ce3-11854de3-
------------------------------------------------------------------------
12617e4 abc3-2369b2c3+4721ac4+14125bc4+13406c5+12517a2c2d+4952abc2d+
------------------------------------------------------------------------
422b2c2d-7127ac3d-15695bc3d+7033c4d+4974b3d2-6261a2cd2+2987abcd2-
------------------------------------------------------------------------
8154b2cd2+14217ac2d2+11323bc2d2+8656c3d2-4386a2d3-7313abd3+2430b2d3+
------------------------------------------------------------------------
3706acd3-4182bcd3-13524c2d3-5155ad4+4171bd4-7310cd4-14088d5-11338a2c2e-
------------------------------------------------------------------------
8154abc2e-9445b2c2e-10680ac3e+9361bc3e-207c4e-14718b3de-12525a2cde+
------------------------------------------------------------------------
11876abcde-4974b2cde-4849ac2de-4851bc2de-8896c3de+10723a2d2e+13385abd2e-
------------------------------------------------------------------------
2045b2d2e+5317acd2e-15526bcd2e+3272c2d2e-12126ad3e+9386bd3e+7099cd3e-
------------------------------------------------------------------------
12681d4e-3703b3e2+10412a2ce2-5004abce2+15016b2ce2+14962ac2e2-285bc2e2-
------------------------------------------------------------------------
11719c3e2+10007a2de2-8437abde2-12974b2de2-11931acde2+4009bcde2-453c2de2-
------------------------------------------------------------------------
726ad2e2-7018bd2e2+4348cd2e2-8988d3e2+13580a2e3-10620abe3+7352b2e3-
------------------------------------------------------------------------
3580ace3+8052bce3-1144c2e3-4974ade3-11892bde3+5587cde3-4663d2e3-2302ae4+
------------------------------------------------------------------------
2965be4+10174ce4+1443de4+13694e5
------------------------------------------------------------------------
a2c3+11914b2c3+3153ac4-14200bc4-204c5+9712a2c2d-11350abc2d-12340b2c2d-
------------------------------------------------------------------------
11381ac3d+11064bc3d+9453c4d-13797b3d2+12946a2cd2-5109abcd2-5508b2cd2+
------------------------------------------------------------------------
3784ac2d2-482bc2d2-13359c3d2+13400a2d3+8596abd3+3193b2d3-7718acd3-
------------------------------------------------------------------------
9305bcd3-5487c2d3-14659ad4+9859bd4+1530cd4-11361d5+2821a2c2e-5310abc2e-
------------------------------------------------------------------------
4819b2c2e-14384ac3e+378bc3e+13974c4e+13503b3de+2258a2cde-942abcde-
------------------------------------------------------------------------
3959b2cde-5008ac2de+1993bc2de+12521c3de+6005a2d2e-8107abd2e-3433b2d2e+
------------------------------------------------------------------------
13006acd2e-1235bcd2e-1871c2d2e+6425ad3e+8322bd3e-7641cd3e+3343d4e+
------------------------------------------------------------------------
15838b3e2+14841a2ce2+1507abce2+1637b2ce2+9363ac2e2-15619bc2e2+5235c3e2+
------------------------------------------------------------------------
5366a2de2-343abde2-10084b2de2-14828acde2-3240bcde2-4185c2de2+14331ad2e2+
------------------------------------------------------------------------
6858bd2e2+7928cd2e2+3783d3e2-9119a2e3-11433abe3+142b2e3-12061ace3-
------------------------------------------------------------------------
12795bce3-4979c2e3+9278ade3-6166bde3+12507cde3+15226d2e3+12460ae4+
------------------------------------------------------------------------
4397be4-4945ce4-12586de4-5421e5 |
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
|