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 (12627a + 7498a b + 4059a*b + 1522b - 10435a c + 11541a*b*c +
------------------------------------------------------------------------
2 2 2 3 2
11658b c - 14933a*c - 10286b*c + 4972c + 13523a d - 12706a*b*d -
------------------------------------------------------------------------
2 2 2 2
3348b d + 10993a*c*d + 5852b*c*d - 3655c d + 12147a*d + 1135b*d +
------------------------------------------------------------------------
2 3 2 2
10079c*d - 3322d - 172a e - 8105a*b*e + 9913b e - 2369a*c*e -
------------------------------------------------------------------------
2 2
8859b*c*e + 15089c e + 12315a*d*e + 7118b*d*e - 710c*d*e + 10677d e +
------------------------------------------------------------------------
2 2 2 2 3 3 2
2428a*e - 15078b*e - 6049c*e - 7675d*e - 2258e , - 5642a + 4757a b
------------------------------------------------------------------------
2 3 2 2 2
- 8746a*b + 3171b + 2534a c - 4464a*b*c + 11422b c - 6317a*c +
------------------------------------------------------------------------
2 3 2 2
10185b*c + 14969c - 9634a d - 10058a*b*d + 5891b d + 11492a*c*d +
------------------------------------------------------------------------
2 2 2 2 3
4954b*c*d - 14933c d - 10221a*d + 7489b*d + 4526c*d + 1886d +
------------------------------------------------------------------------
2 2 2
6538a e + 1060a*b*e + 1001b e - 14482a*c*e - 11385b*c*e + 14847c e +
------------------------------------------------------------------------
2 2 2
1672a*d*e + 14373b*d*e - 2054c*d*e + 1257d e - 11434a*e - 14846b*e +
------------------------------------------------------------------------
2 2 3 3 2 2 3
12362c*e + 4644d*e - 980e , - 15615a - 6540a b + 5340a*b - 1328b -
------------------------------------------------------------------------
2 2 2 2 3 2
1669a c + 340a*b*c - 14729b c - 8053a*c - 13270b*c + 757c + 15734a d
------------------------------------------------------------------------
2 2 2
+ 5471a*b*d + 1451b d - 4740a*c*d + 15191b*c*d - 1406c d + 8351a*d +
------------------------------------------------------------------------
2 2 3 2 2
5572b*d - 8004c*d + 2089d - 641a e + 15597a*b*e + 7572b e -
------------------------------------------------------------------------
2
13288a*c*e + 7920b*c*e + 13285c e - 9013a*d*e - 8836b*d*e - 4119c*d*e -
------------------------------------------------------------------------
2 2 2 2 2 3
5809d e - 2247a*e - 4373b*e - 9033c*e + 15014d*e - 3046e )
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 = | ab2-15141b3+2034a2c-14447abc-1453b2c+23ac2+9236bc2+13221c3+1075a2d-
------------------------------------------------------------------------
14576abd-1525b2d-911acd+9280bcd+3330c2d-12552ad2-12577bd2+5933cd2+7625d3
------------------------------------------------------------------------
-14215a2e+14176abe+6057b2e+6678ace-11702bce+8468c2e-9613ade-4678bde+
------------------------------------------------------------------------
2409cde+10058d2e+13220ae2+7612be2+6986ce2-11200de2-13462e3
------------------------------------------------------------------------
a2b-15922b3+12986a2c-14487abc+14227b2c-14573ac2-13478bc2-5257c3+11465a2d
------------------------------------------------------------------------
+13714abd+2047b2d+6515acd+7940bcd+13913c2d+10606ad2+6558bd2+15581cd2-
------------------------------------------------------------------------
8476d3-10175a2e+11220abe-9664b2e+7451ace+1351bce-6766c2e-8686ade+
------------------------------------------------------------------------
13074bde-5023cde-4225d2e+851ae2+8882be2+1411ce2+15145de2-5392e3
------------------------------------------------------------------------
a3-13114b3+9259a2c+3074abc+1727b2c-6638ac2-152bc2-3670c3+1371a2d-
------------------------------------------------------------------------
11729abd+12654b2d-7805acd-4504bcd-1075c2d+14828ad2-7665bd2+12283cd2+
------------------------------------------------------------------------
15827d3+585a2e+14984abe+5645b2e-5593ace-8411bce-2254c2e-6773ade-5296bde-
------------------------------------------------------------------------
8576cde-11746d2e+2025ae2-6929be2-9035ce2-7596de2+4660e3
------------------------------------------------------------------------
b3c+13183a2c2+8293abc2+10325b2c2+5942ac3+3092bc3-2278c4-5480b3d+9627a2cd
------------------------------------------------------------------------
+3243abcd-8761b2cd+11444ac2d+10666bc2d+1298c3d-7925a2d2-6246abd2-
------------------------------------------------------------------------
14317b2d2+14172acd2+15011bcd2-6418c2d2+898ad3-4042bd3+13477cd3-11935d4+
------------------------------------------------------------------------
13490b3e+15028a2ce-11959abce-8922b2ce-12407ac2e-5652bc2e+8031c3e+
------------------------------------------------------------------------
15433a2de-10906abde+15433b2de+14362acde-9341bcde-13330c2de+11396ad2e+
------------------------------------------------------------------------
6073bd2e+7979cd2e+15468d3e+4004a2e2-5425abe2-4232b2e2-6951ace2+11705bce2
------------------------------------------------------------------------
-8076c2e2+6143ade2-13694bde2-3931cde2-12568d2e2+6101ae3-14825be3-
------------------------------------------------------------------------
14958ce3-15470de3+11780e4
------------------------------------------------------------------------
b4-6726a2c2-4451abc2+1953b2c2+2568ac3+373bc3+11319c4-11936b3d+11211a2cd+
------------------------------------------------------------------------
14808abcd-6914b2cd+15780ac2d-1329bc2d+729c3d+5897a2d2+11132abd2+
------------------------------------------------------------------------
12962b2d2-11112acd2-5439bcd2-2134c2d2-411ad3+15747bd3-4081cd3-9288d4-
------------------------------------------------------------------------
6069b3e-11359a2ce+3777abce+10593b2ce-4666ac2e-8925bc2e+3402c3e+12750a2de
------------------------------------------------------------------------
-4624abde+8346b2de+12138acde-13059bcde-4742c2de-6830ad2e-9641bd2e-
------------------------------------------------------------------------
15679cd2e-4181d3e+236a2e2-3032abe2+11860b2e2+283ace2-15967bce2+11441c2e2
------------------------------------------------------------------------
+6022ade2+7891bde2+8853cde2-13558d2e2-12975ae3-11950be3+2637ce3+11278de3
------------------------------------------------------------------------
+7824e4 abc3+15703b2c3-98ac4-8378bc4-6609c5-4161a2c2d+4982abc2d-
------------------------------------------------------------------------
1390b2c2d-7801ac3d-12114bc3d-3048c4d+13527b3d2+11963a2cd2+3931abcd2+
------------------------------------------------------------------------
9409b2cd2-13782ac2d2+15387bc2d2-3469c3d2+8158a2d3+4311abd3+12745b2d3-
------------------------------------------------------------------------
2554acd3+1318bcd3+13095c2d3+7151ad4+12099bd4+6462cd4-5226d5-3941a2c2e+
------------------------------------------------------------------------
10684abc2e-10589b2c2e+9155ac3e+8292bc3e+10917c4e-7180b3de+6506a2cde+
------------------------------------------------------------------------
7000abcde+12783b2cde+12633ac2de-3978bc2de+377c3de+5541a2d2e+6357abd2e+
------------------------------------------------------------------------
12783b2d2e-9329acd2e-8196bcd2e-13691c2d2e-11507ad3e-8075bd3e-4461cd3e+
------------------------------------------------------------------------
13054d4e+3941b3e2+15998a2ce2-5045abce2+11527b2ce2+13973ac2e2-15384bc2e2-
------------------------------------------------------------------------
12342c3e2+6394a2de2-9365abde2+6047b2de2+4313acde2+2025bcde2+10925c2de2+
------------------------------------------------------------------------
15050ad2e2-13518bd2e2-10552cd2e2-7157d3e2-6874a2e3+4608abe3+11404b2e3-
------------------------------------------------------------------------
9488ace3+12126bce3+7218c2e3+5026ade3+14205bde3-7794cde3-1836d2e3+2365ae4
------------------------------------------------------------------------
+10769be4+3597ce4+12079de4-5189e5
------------------------------------------------------------------------
a2c3+11518b2c3+11347ac4+815bc4-3058c5-5259a2c2d-2701abc2d-14635b2c2d+
------------------------------------------------------------------------
10235ac3d-8563bc3d-14611c4d-9774b3d2-13927a2cd2-13401abcd2-11536b2cd2+
------------------------------------------------------------------------
8287ac2d2+11108bc2d2-7835c3d2+11792a2d3-8298abd3-3160b2d3-8514acd3+
------------------------------------------------------------------------
4459bcd3+1942c2d3-10329ad4+14173bd4-12390cd4+31d5+6901a2c2e-15023abc2e+
------------------------------------------------------------------------
7916b2c2e-10919ac3e+11572bc3e-14352c4e+10004b3de-11319a2cde-7722abcde+
------------------------------------------------------------------------
5174b2cde+6611ac2de-8922bc2de-8523c3de-12558a2d2e+1200abd2e-4877b2d2e+
------------------------------------------------------------------------
4441acd2e-2022bcd2e+11768c2d2e-14082ad3e+3138bd3e+8686cd3e+8695d4e-
------------------------------------------------------------------------
3548b3e2-4473a2ce2-57abce2-4254b2ce2-1403ac2e2-4227bc2e2-11134c3e2-
------------------------------------------------------------------------
6763a2de2+13293abde2-5637b2de2-5558acde2-10333bcde2+14537c2de2-7480ad2e2
------------------------------------------------------------------------
+14136bd2e2+11412cd2e2-636d3e2-12237a2e3+8116abe3+13051b2e3+2920ace3+
------------------------------------------------------------------------
6015bce3+779c2e3-15459ade3-6963bde3+8423cde3-8744d2e3+10524ae4+5726be4+
------------------------------------------------------------------------
13025ce4-12458de4-6421e5 |
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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