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 (11760a + 10052a b + 14506a*b + 5599b - 8705a c + 3371a*b*c -
------------------------------------------------------------------------
2 2 2 3 2
13032b c - 6118a*c + 14051b*c + 15640c - 14774a d - 12210a*b*d -
------------------------------------------------------------------------
2 2 2 2
7433b d + 14822a*c*d + 2579b*c*d - 11651c d + 13367a*d - 2375b*d -
------------------------------------------------------------------------
2 3 2 2
6039c*d + 9121d - 335a e - 10710a*b*e - 15700b e + 4017a*c*e +
------------------------------------------------------------------------
2 2
10446b*c*e + 15648c e + 15556a*d*e - 6254b*d*e - 14908c*d*e - 10751d e +
------------------------------------------------------------------------
2 2 2 2 3 3 2
4799a*e + 9010b*e - 4205c*e + 13399d*e - 14860e , 14049a - 8900a b
------------------------------------------------------------------------
2 3 2 2 2
- 8154a*b + 8715b - 14257a c + 5697a*b*c + 11659b c + 12648a*c -
------------------------------------------------------------------------
2 3 2 2
4253b*c + 7694c + 5439a d + 4276a*b*d - 7803b d - 1799a*c*d +
------------------------------------------------------------------------
2 2 2 2 3
12800b*c*d - 6444c d - 1318a*d + 13633b*d - 5732c*d - 6419d +
------------------------------------------------------------------------
2 2 2
12487a e - 15244a*b*e + 6562b e - 11556a*c*e - 8057b*c*e + 5326c e -
------------------------------------------------------------------------
2 2 2
10211a*d*e + 10395b*d*e + 137c*d*e + 4163d e + 8123a*e + 4038b*e -
------------------------------------------------------------------------
2 2 3 3 2 2 3
9181c*e + 11813d*e - 12880e , 11310a + 9569a b + 592a*b + 11370b +
------------------------------------------------------------------------
2 2 2 2 3
3723a c - 1280a*b*c - 13324b c + 2235a*c + 13607b*c + 15223c -
------------------------------------------------------------------------
2 2 2
12191a d + 13217a*b*d - 948b d - 3966a*c*d + 5713b*c*d - 12215c d -
------------------------------------------------------------------------
2 2 2 3 2 2
13276a*d - 958b*d - 8439c*d - 14359d - 6240a e - 6598a*b*e - 1833b e
------------------------------------------------------------------------
2
+ 4166a*c*e + 48b*c*e + 15044c e - 15766a*d*e - 12988b*d*e - 3321c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3
4520d e - 7018a*e - 4424b*e - 10817c*e + 5194d*e + 3678e )
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 = | ab2-13320b3+14718a2c+5510abc-9828b2c+13613ac2-10016bc2-7898c3+2457a2d+
------------------------------------------------------------------------
2925abd+15855b2d+9569acd-2875bcd+4285c2d+4090ad2-7956bd2-10254cd2+7008d3
------------------------------------------------------------------------
-13601a2e+3946abe-13313b2e-14407ace-10459bce+12497c2e-362ade-13996bde+
------------------------------------------------------------------------
3665cde-4008d2e+569ae2+11772be2+1880ce2-13295de2-4944e3
------------------------------------------------------------------------
a2b+356b3-12674a2c+14905abc+11212b2c+446ac2+3754bc2+4020c3+12843a2d+
------------------------------------------------------------------------
8865abd-7799b2d-2346acd-1788bcd+13379c2d-10928ad2+3769bd2-4716cd2+2808d3
------------------------------------------------------------------------
-1777a2e+13117abe+5227b2e+2837ace+1939bce+4359c2e-11306ade-14385bde+
------------------------------------------------------------------------
4560cde-11775d2e+13773ae2+6518be2-15961ce2-2175de2-11194e3
------------------------------------------------------------------------
a3-3655b3-859a2c+14053abc-6562b2c-8857ac2-15217bc2-12078c3+6248a2d+
------------------------------------------------------------------------
4815abd+12104b2d-14532acd+6177bcd-10945c2d-2237ad2-1983bd2-14124cd2-
------------------------------------------------------------------------
4020d3+5002a2e+1799abe-14167b2e-7472ace-7870bce+8384c2e-1209ade-4169bde+
------------------------------------------------------------------------
13966cde-14380d2e+2213ae2-7829be2+2754ce2-11139de2+4116e3
------------------------------------------------------------------------
b3c-6343a2c2+1302abc2+6821b2c2-10498ac3+5211bc3+5341c4-9361b3d+1993a2cd+
------------------------------------------------------------------------
15096abcd+7155b2cd-5175ac2d-1953bc2d-10175c3d+13060a2d2+4767abd2-
------------------------------------------------------------------------
8893b2d2-6320acd2-6234bcd2+4300c2d2-11189ad3-10309bd3-436cd3-5070d4+
------------------------------------------------------------------------
11309b3e+7471a2ce+5988abce-2735b2ce+3145ac2e-13245bc2e+2520c3e-15424a2de
------------------------------------------------------------------------
-11950abde+14726b2de-11039acde-540bcde+8796c2de-14722ad2e-10608bd2e+
------------------------------------------------------------------------
2355cd2e+11306d3e+13471a2e2-15414abe2+12455b2e2+7889ace2+8611bce2-
------------------------------------------------------------------------
12302c2e2+12686ade2+15374bde2+97cde2+6200d2e2+3613ae3+2290be3+8678ce3+
------------------------------------------------------------------------
15806de3+6555e4 b4-6834a2c2+11236abc2+13008b2c2-7624ac3-11732bc3-10914c4
------------------------------------------------------------------------
+8394b3d+558a2cd+15804abcd-6747b2cd+10851ac2d-4991bc2d-11148c3d-1127a2d2
------------------------------------------------------------------------
+15476abd2+2092b2d2+10397acd2+720bcd2+8898c2d2-5171ad3-1437bd3-7123cd3+
------------------------------------------------------------------------
1200d4-12585b3e-14405a2ce-11516abce-10804b2ce+12165ac2e-7591bc2e+7219c3e
------------------------------------------------------------------------
+7714a2de-13857abde-10074b2de-6743acde-14398bcde+12567c2de-14474ad2e-
------------------------------------------------------------------------
3671bd2e+2668cd2e+5245d3e-8440a2e2-14962abe2-6064b2e2+9787ace2+9365bce2-
------------------------------------------------------------------------
1626c2e2+11562ade2-5347bde2-6611cde2+1297d2e2+6083ae3-2910be3+9336ce3+
------------------------------------------------------------------------
4500de3+5824e4 abc3+10205b2c3+129ac4+10383bc4-8995c5+11833a2c2d+
------------------------------------------------------------------------
8750abc2d-3986b2c2d-7688ac3d+13715bc3d-3801c4d+14284b3d2+5583a2cd2-
------------------------------------------------------------------------
10680abcd2-3580b2cd2+1819ac2d2-11397bc2d2+5022c3d2+4921a2d3-6346abd3+
------------------------------------------------------------------------
588b2d3-9801acd3+5283bcd3-15602c2d3-15745ad4-10724bd4-5110cd4+4865d5-
------------------------------------------------------------------------
9419a2c2e+5219abc2e+4904b2c2e+2962ac3e-9674bc3e+14661c4e+12409b3de-
------------------------------------------------------------------------
313a2cde+6087abcde+1654b2cde+10375ac2de+4782bc2de+13568c3de+6761a2d2e-
------------------------------------------------------------------------
12681abd2e-12155b2d2e-1284acd2e-1608bcd2e+8800c2d2e+9832ad3e-4279bd3e-
------------------------------------------------------------------------
3534cd3e+12319d4e-2285b3e2+1166a2ce2-10962abce2+1912b2ce2+360ac2e2-
------------------------------------------------------------------------
12380bc2e2+5852c3e2-10532a2de2-12331abde2+3893b2de2-5214acde2-7314bcde2+
------------------------------------------------------------------------
14154c2de2-8680ad2e2-6985bd2e2+14152cd2e2+6713d3e2+9190a2e3-3024abe3-
------------------------------------------------------------------------
895b2e3+6116ace3+14642bce3+10573c2e3-12549ade3-12131bde3+6219cde3+
------------------------------------------------------------------------
1982d2e3+4618ae4+201be4+11618ce4+644de4-13377e5
------------------------------------------------------------------------
a2c3-10186b2c3-8459ac4-12619bc4+9858c5-10977a2c2d-9530abc2d-10791b2c2d-
------------------------------------------------------------------------
4374ac3d+7212bc3d+11559c4d-3944b3d2+15534a2cd2+15407abcd2-472b2cd2-
------------------------------------------------------------------------
459ac2d2-13931bc2d2-15944c3d2-8354a2d3-5810abd3+15064b2d3+905acd3+
------------------------------------------------------------------------
1316bcd3-14896c2d3-5815ad4+10407bd4-534cd4-3965d5-2533a2c2e+6498abc2e+
------------------------------------------------------------------------
4114b2c2e-1161ac3e+9529bc3e+2934c4e-7672b3de-7580a2cde+13351abcde-
------------------------------------------------------------------------
200b2cde-10316ac2de+7066bc2de-14177c3de-14662a2d2e-6024abd2e-15461b2d2e-
------------------------------------------------------------------------
710acd2e-7835bcd2e+10254c2d2e-15854ad3e+13473bd3e-11164cd3e+12677d4e+
------------------------------------------------------------------------
15698b3e2+6870a2ce2+6983abce2-14369b2ce2-12916ac2e2-9711bc2e2-4762c3e2+
------------------------------------------------------------------------
6939a2de2-1176abde2+14807b2de2+11773acde2+1321bcde2-3747c2de2+9891ad2e2+
------------------------------------------------------------------------
2313bd2e2-15317cd2e2-13439d3e2-11254a2e3+14880abe3+7100b2e3-792ace3-
------------------------------------------------------------------------
14548bce3+15471c2e3-6301ade3+8988bde3+4801cde3+5511d2e3+5980ae4-6871be4+
------------------------------------------------------------------------
15307ce4-7552de4-6757e5 |
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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