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];
|
i2 : I = ideal(random(3,R),random(3,R),random(3,R))
3 2 2 3 2
o2 = ideal (15652a + 15323a b + 4251a*b + 5777b - 14782a c - 1660a*b*c +
------------------------------------------------------------------------
2 2 2 3 2 2
11304b c + 8451a*c + 8673b*c - 5437c - 1094a d + 2411a*b*d + 5757b d
------------------------------------------------------------------------
2 2 2 2
+ 11084a*c*d + 1301b*c*d - 7837c d + 14441a*d + 12835b*d - 5794c*d +
------------------------------------------------------------------------
3 2 2
15824d + 2755a e - 14171a*b*e + 3409b e - 8171a*c*e + 10529b*c*e +
------------------------------------------------------------------------
2 2 2
6836c e + 4496a*d*e + 6518b*d*e - 10486c*d*e - 1015d e - 6780a*e -
------------------------------------------------------------------------
2 2 2 3 3 2 2
4426b*e - 7670c*e + 5721d*e + 3000e , - 7698a + 9028a b - 791a*b +
------------------------------------------------------------------------
3 2 2 2 2 3
11745b - 7942a c - 2708a*b*c + 7085b c - 86a*c - 8141b*c - 12870c +
------------------------------------------------------------------------
2 2 2
9939a d + 11819a*b*d + 4844b d - 10050a*c*d + 13308b*c*d - 12410c d -
------------------------------------------------------------------------
2 2 2 3 2 2
7802a*d - 937b*d - 7312c*d - 8414d + 9362a e + 4023a*b*e - 2378b e +
------------------------------------------------------------------------
2
5335a*c*e - 12402b*c*e - 15434c e - 7653a*d*e - 5343b*d*e - 5053c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3
11125d e - 10747a*e + 7222b*e + 15352c*e - 5997d*e + 11321e , -
------------------------------------------------------------------------
3 2 2 3 2 2
13958a - 15370a b + 3298a*b - 7403b + 7482a c - 1517a*b*c + 5671b c +
------------------------------------------------------------------------
2 2 3 2 2
6140a*c + 15741b*c + 10507c - 13352a d + 4310a*b*d - 14635b d -
------------------------------------------------------------------------
2 2 2 2
11997a*c*d + 4616b*c*d + 2444c d - 10051a*d + 409b*d - 6380c*d -
------------------------------------------------------------------------
3 2 2
14298d + 8159a e + 2138a*b*e + 13990b e + 8561a*c*e + 1962b*c*e -
------------------------------------------------------------------------
2 2 2
13174c e + 5948a*d*e + 8340b*d*e - 12016c*d*e - 5808d e - 3320a*e +
------------------------------------------------------------------------
2 2 2 3
8533b*e - 15334c*e - 4574d*e - 6474e )
o2 : Ideal of R
|
i3 : gens gb(I,PairLimit=>7);
1 7
o3 : Matrix R <--- R
|
Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
|
i5 : leadTerm gens g
o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o5 : Matrix R <--- R
|
We can make a Groebner basis snapshot by using StopBeforeComputation, or
gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)
o6 = | ab2-6453b3+15968a2c+1608abc+12996b2c+12886ac2-15531bc2+12542c3-6620a2d
------------------------------------------------------------------------
+15863abd-961b2d-10397acd+11503bcd+12230c2d-15686ad2+9688bd2-9618cd2+
------------------------------------------------------------------------
358d3-913a2e+3374abe-7892b2e-3101ace-8274bce+4350c2e+6407ade+11913bde+
------------------------------------------------------------------------
11233cde-13109d2e+1209ae2+12865be2-11984ce2+1861de2-14820e3
------------------------------------------------------------------------
a2b-6317b3-1293a2c-3307abc+6746b2c+10056ac2-14375bc2+11818c3+5104a2d+
------------------------------------------------------------------------
8892abd+1655b2d+14733acd+10144bcd+13221c2d+8920ad2+8412bd2+11928cd2+
------------------------------------------------------------------------
4006d3+1756a2e+12746abe-12233b2e+3926ace+11146bce-11952c2e-4835ade-
------------------------------------------------------------------------
5571bde+7530cde-5861d2e-8599ae2+11584be2-13805ce2-12341de2-9066e3
------------------------------------------------------------------------
a3+7837b3-1884a2c+13484abc-14889b2c-14724ac2-3114bc2-5761c3+9155a2d-
------------------------------------------------------------------------
11308abd+2434b2d-206acd+3924bcd+11947c2d-4547ad2-538bd2-10922cd2+2484d3-
------------------------------------------------------------------------
1336a2e-15577abe-5362b2e+12738ace+670bce-12957c2e-7974ade-14392bde+
------------------------------------------------------------------------
2223cde+14743d2e-2874ae2-9210be2+13467ce2-6349de2-9930e3
------------------------------------------------------------------------
b3c+11353a2c2-7685abc2+9001b2c2-11133ac3+13157bc3-4840c4+2179b3d+
------------------------------------------------------------------------
7850a2cd+13941abcd+1168b2cd+3193ac2d-13622bc2d-4924c3d-15499a2d2+
------------------------------------------------------------------------
7789abd2-1642b2d2-5970acd2+719bcd2-7289c2d2-4630ad3-13803bd3+333cd3-
------------------------------------------------------------------------
2213d4+4744b3e+3840a2ce+3912abce-520b2ce+3915ac2e-1932bc2e-9310c3e+
------------------------------------------------------------------------
14505a2de-6810abde-4784b2de+14720acde-8025bcde+12037c2de+9736ad2e-
------------------------------------------------------------------------
8406bd2e+13451cd2e-9766d3e+6117a2e2-9775abe2-1845b2e2+2670ace2+15836bce2
------------------------------------------------------------------------
-3993c2e2+15688ade2-1194bde2+11631cde2-2418d2e2-13566ae3-4750be3-2883ce3
------------------------------------------------------------------------
-10629de3-15360e4 b4-12783a2c2-3344abc2-1982b2c2-9882ac3-4410bc3-4339c4+
------------------------------------------------------------------------
7782b3d-8609a2cd-14510abcd+246b2cd-1433ac2d-9954bc2d+6193c3d+8477a2d2-
------------------------------------------------------------------------
6182abd2-6486b2d2-7719acd2-5324bcd2-7052c2d2-12010ad3-4999bd3+3449cd3-
------------------------------------------------------------------------
4993d4-9145b3e-3180a2ce+13720abce+8333b2ce+3215ac2e+9964bc2e+13820c3e-
------------------------------------------------------------------------
4437a2de+10869abde-8149b2de+12793acde-12701bcde-2565c2de-6160ad2e+
------------------------------------------------------------------------
11442bd2e-12474cd2e+5702d3e+2366a2e2+8197abe2-2542b2e2+6492ace2-6671bce2
------------------------------------------------------------------------
+3126c2e2+14490ade2-13332bde2+15029cde2+1757d2e2-13287ae3+7463be3+
------------------------------------------------------------------------
11188ce3+3510de3+225e4 abc3-15935b2c3-1445ac4-5138bc4+7037c5+8470a2c2d+
------------------------------------------------------------------------
98abc2d+4531b2c2d+7632ac3d+2371bc3d-116c4d-11969b3d2-4423a2cd2-5038abcd2
------------------------------------------------------------------------
+4061b2cd2+10167ac2d2-12013bc2d2-22c3d2-3645a2d3+14154abd3-6169b2d3+
------------------------------------------------------------------------
10221acd3-253bcd3-14660c2d3-10292ad4+6080bd4-625cd4-6235d5-11602a2c2e-
------------------------------------------------------------------------
11239abc2e+13136b2c2e-1920ac3e+9992bc3e-15391c4e+12558b3de+11068a2cde+
------------------------------------------------------------------------
13178abcde+14350b2cde+9607ac2de+9882bc2de-7903c3de+13199a2d2e+2576abd2e-
------------------------------------------------------------------------
6102b2d2e+583acd2e-6856bcd2e+9700c2d2e-11264ad3e-8051bd3e-11391cd3e-
------------------------------------------------------------------------
1383d4e-403b3e2-6989a2ce2+6385abce2-7435b2ce2-9955ac2e2+14807bc2e2-
------------------------------------------------------------------------
8100c3e2-9217a2de2+14577abde2+13681b2de2-12691acde2+13015bcde2-
------------------------------------------------------------------------
12656c2de2-12184ad2e2+6625bd2e2-2865cd2e2+15423d3e2+12398a2e3+4670abe3+
------------------------------------------------------------------------
1021b2e3+5672ace3+11782bce3-4303c2e3-4363ade3+11937bde3+1750cde3-
------------------------------------------------------------------------
1249d2e3-9072ae4+12727be4-14758ce4+13288de4+169e5
------------------------------------------------------------------------
a2c3-2709b2c3-9375ac4+14293bc4+6739c5+2880a2c2d-829abc2d-10787b2c2d+
------------------------------------------------------------------------
4989ac3d+13200bc3d+10724c4d+3826b3d2-13775a2cd2+4756abcd2+2707b2cd2-
------------------------------------------------------------------------
15495ac2d2+15604bc2d2-14575c3d2-4030a2d3+6741abd3+12202b2d3+4723acd3+
------------------------------------------------------------------------
15064bcd3-3969c2d3+15331ad4-3008bd4+12785cd4-6553d5-15018a2c2e+4324abc2e
------------------------------------------------------------------------
-1008b2c2e-7833ac3e+4044bc3e-8068c4e+4250b3de+11482a2cde-6812abcde+
------------------------------------------------------------------------
15606b2cde-7933ac2de+148bc2de+2905c3de+8896a2d2e+1125abd2e-9689b2d2e+
------------------------------------------------------------------------
11981acd2e+4347bcd2e+8237c2d2e-2475ad3e+257bd3e+7241cd3e+8707d4e+
------------------------------------------------------------------------
6130b3e2+3527a2ce2+2540abce2-3827b2ce2+3112ac2e2+15670bc2e2-5784c3e2+
------------------------------------------------------------------------
13802a2de2+4808abde2+5526b2de2+621acde2-6296bcde2+13313c2de2+7829ad2e2-
------------------------------------------------------------------------
2490bd2e2-3182cd2e2+3688d3e2-7333a2e3+11082abe3+6956b2e3+14831ace3-
------------------------------------------------------------------------
5895bce3+4933c2e3-11502ade3-10680bde3+159cde3+9785d2e3-6540ae4+13602be4+
------------------------------------------------------------------------
3915ce4-12383de4+12258e5 |
1 7
o6 : Matrix R <--- R
|
i7 : leadTerm gbSnapshot(I)
o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o7 : Matrix R <--- R
|