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 (2137a - 8520a b - 5402a*b + 1589b - 10352a c + 2030a*b*c -
------------------------------------------------------------------------
2 2 2 3 2
12895b c + 11234a*c + 5346b*c + 13995c + 13917a d - 6985a*b*d +
------------------------------------------------------------------------
2 2 2 2
14751b d + 740a*c*d - 3207b*c*d + 7627c d - 1201a*d - 8296b*d +
------------------------------------------------------------------------
2 3 2 2
13141c*d + 12286d - 1840a e - 128a*b*e - 2b e - 635a*c*e + 6473b*c*e -
------------------------------------------------------------------------
2 2 2
303c e - 4135a*d*e - 5292b*d*e + 195c*d*e + 7585d e + 13138a*e -
------------------------------------------------------------------------
2 2 2 3 3 2 2
3147b*e - 3435c*e + 3110d*e - 3252e , 6345a + 12016a b - 2335a*b +
------------------------------------------------------------------------
3 2 2 2 2 3
1877b - 14855a c - 361a*b*c - 3984b c - 1813a*c - 4408b*c + 12611c -
------------------------------------------------------------------------
2 2 2
4940a d - 4316a*b*d - 12207b d - 11382a*c*d + 5836b*c*d - 12315c d -
------------------------------------------------------------------------
2 2 2 3 2
7876a*d + 14566b*d - 4395c*d - 14322d + 6843a e + 3260a*b*e -
------------------------------------------------------------------------
2 2
7583b e - 1699a*c*e + 664b*c*e - 9212c e - 8004a*d*e + 2628b*d*e +
------------------------------------------------------------------------
2 2 2 2 2
14650c*d*e + 8330d e - 11800a*e - 2050b*e + 14953c*e - 5676d*e -
------------------------------------------------------------------------
3 3 2 2 3 2
13129e , 11275a + 3630a b - 6078a*b + 2742b + 1413a c - 140a*b*c +
------------------------------------------------------------------------
2 2 2 3 2 2
8917b c - 3970a*c - 3470b*c + 5091c - 10231a d + 5715a*b*d - 1945b d
------------------------------------------------------------------------
2 2 2 2
- 11134a*c*d + 12146b*c*d - 12647c d - 13799a*d + 3245b*d - 8561c*d +
------------------------------------------------------------------------
3 2 2
7483d + 14044a e + 8543a*b*e + 14060b e + 11248a*c*e + 10602b*c*e -
------------------------------------------------------------------------
2 2 2
5865c e + 282a*d*e + 14789b*d*e + 13811c*d*e + 9071d e - 241a*e +
------------------------------------------------------------------------
2 2 2 3
12593b*e + 12252c*e + 10409d*e - 10004e )
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+10530b3+12295a2c+14061abc-770b2c+9891ac2-2344bc2-8524c3+3586a2d-
------------------------------------------------------------------------
4201abd-15882b2d-12154acd-5647bcd-7814c2d-1776ad2-3182bd2-1439cd2+4126d3
------------------------------------------------------------------------
+5486a2e-2182abe+6654b2e+8029ace+11627bce-3292c2e-14171ade-13827bde+
------------------------------------------------------------------------
12778cde+3569d2e+14860ae2-7610be2+975ce2-6079de2-15562e3
------------------------------------------------------------------------
a2b+10145b3+15472a2c+10464abc-10278b2c-12189ac2+14035bc2+8022c3+15932a2d
------------------------------------------------------------------------
-1798abd+2296b2d-11455acd+7439bcd-14808c2d-14011ad2-10554bd2+5264cd2-
------------------------------------------------------------------------
4533d3+15218a2e-9015abe+482b2e+15994ace+1351bce-15466c2e-1256ade+
------------------------------------------------------------------------
10473bde-15842cde-948d2e+394ae2+3851be2-195ce2+9903de2+9630e3
------------------------------------------------------------------------
a3+8601b3-14166a2c+3314abc+2117b2c-11368ac2-2067bc2+7432c3-10120a2d-
------------------------------------------------------------------------
3130abd-14603b2d+4251acd+182bcd+3699c2d-4611ad2+837bd2+10347cd2-7008d3-
------------------------------------------------------------------------
9474a2e-12959abe+6402b2e+14635ace-8574bce-15921c2e+4380ade+2996bde+
------------------------------------------------------------------------
2027cde+2071d2e+1432ae2+4846be2+5744ce2+81de2+15063e3
------------------------------------------------------------------------
b3c-2659a2c2+11636abc2+1339b2c2+14948ac3-3034bc3-10409c4+4415b3d-
------------------------------------------------------------------------
4674a2cd+4461abcd-3183b2cd+259ac2d-10929bc2d-3856c3d-5076a2d2+211abd2+
------------------------------------------------------------------------
11544b2d2+5492acd2+5897bcd2-11901c2d2-12857ad3-8630bd3+11334cd3+15687d4-
------------------------------------------------------------------------
11243b3e+7417a2ce+700abce+6914b2ce-14944ac2e-4449bc2e-9475c3e+12139a2de-
------------------------------------------------------------------------
7363abde+14769b2de-9989acde+2355bcde-15964c2de-3843ad2e+95bd2e-7992cd2e-
------------------------------------------------------------------------
14923d3e+8591a2e2-9631abe2-14919b2e2-10508ace2-13600bce2+6420c2e2+
------------------------------------------------------------------------
12694ade2+2041bde2-12436cde2+870d2e2+15270ae3-9465be3-12662ce3+12753de3-
------------------------------------------------------------------------
576e4 b4-6820a2c2+14706abc2-4092b2c2+5658ac3-6155bc3+7516c4-3590b3d+
------------------------------------------------------------------------
15512a2cd+3253abcd+8448b2cd+170ac2d-296bc2d-11945c3d+10069a2d2-11877abd2
------------------------------------------------------------------------
-10923b2d2+9986acd2+14554bcd2-4340c2d2+7643ad3+5956bd3-6458cd3+11265d4+
------------------------------------------------------------------------
11914b3e-10253a2ce-13193abce+10379b2ce-6074ac2e-9377bc2e-7575c3e+
------------------------------------------------------------------------
3338a2de+12101abde-309b2de-13323acde+5350bcde-11244c2de-1443ad2e-
------------------------------------------------------------------------
10300bd2e-287cd2e+12325d3e-9057a2e2+11367abe2+2049b2e2-13439ace2+
------------------------------------------------------------------------
1919bce2-8608c2e2-4447ade2+9300bde2-5761cde2+1708d2e2-10629ae3-14254be3-
------------------------------------------------------------------------
7429ce3-797de3+10444e4 abc3-14929b2c3-6294ac4-12490bc4+10715c5+9338a2c2d
------------------------------------------------------------------------
-6225abc2d+6432b2c2d-7237ac3d+393bc3d-9342c4d+3867b3d2+4289a2cd2+
------------------------------------------------------------------------
8087abcd2-15792b2cd2+8406ac2d2-3017bc2d2-4574c3d2-9558a2d3+3499abd3+
------------------------------------------------------------------------
5596b2d3-6223acd3+10909bcd3-15430c2d3-4014ad4+95bd4-9509cd4+12062d5+
------------------------------------------------------------------------
2603a2c2e-12633abc2e-1465b2c2e+9589ac3e-2131bc3e+13501c4e-9951b3de-
------------------------------------------------------------------------
1112a2cde-3702abcde-1321b2cde-12185ac2de-4346bc2de+215c3de+15823a2d2e-
------------------------------------------------------------------------
15106abd2e-8052b2d2e+296acd2e-352bcd2e+6240c2d2e-13030ad3e+11690bd3e-
------------------------------------------------------------------------
5307cd3e-2830d4e-15687b3e2-9318a2ce2+2567abce2+10906b2ce2+5018ac2e2+
------------------------------------------------------------------------
2588bc2e2-6780c3e2+4034a2de2+2769abde2+14470b2de2-2677acde2+5228bcde2-
------------------------------------------------------------------------
1421c2de2+5465ad2e2-4313bd2e2+7605cd2e2+335d3e2-9185a2e3-3298abe3+
------------------------------------------------------------------------
1532b2e3+7828ace3+7562bce3-5264c2e3+2832ade3-356bde3-4469cde3+1512d2e3+
------------------------------------------------------------------------
7022ae4-13688be4-13640ce4-11486de4-2999e5
------------------------------------------------------------------------
a2c3+6327b2c3+9999ac4+6906bc4+9538c5-15090a2c2d-14895abc2d-3633b2c2d-
------------------------------------------------------------------------
4152ac3d+12212bc3d-9214c4d-12906b3d2-11841a2cd2+12808abcd2+12413b2cd2-
------------------------------------------------------------------------
4237ac2d2+7780bc2d2+6684c3d2-3463a2d3+9701abd3-4580b2d3-7722acd3-
------------------------------------------------------------------------
2947bcd3+5795c2d3+10012ad4-10039bd4-14166cd4+12709d5+9671a2c2e-5739abc2e
------------------------------------------------------------------------
-1541b2c2e+409ac3e-1556bc3e+8034c4e+14976b3de-14139a2cde-7323abcde-
------------------------------------------------------------------------
8713b2cde-13571ac2de-11523bc2de+6202c3de+4589a2d2e+1417abd2e-14389b2d2e-
------------------------------------------------------------------------
5095acd2e+7811bcd2e+13875c2d2e-6310ad3e-15214bd3e-5207cd3e-8011d4e-
------------------------------------------------------------------------
6850b3e2+6357a2ce2+2917abce2-11412b2ce2-4432ac2e2+3572bc2e2+14326c3e2-
------------------------------------------------------------------------
15522a2de2+13624abde2+11131b2de2-11731acde2-5742bcde2-9501c2de2+
------------------------------------------------------------------------
7336ad2e2-13471bd2e2-2079cd2e2+1734d3e2-15597a2e3+652abe3-11022b2e3+
------------------------------------------------------------------------
14849ace3+10987bce3-7077c2e3-1906ade3-474bde3+4896cde3-7096d2e3+6981ae4-
------------------------------------------------------------------------
7203be4-9767ce4+9297de4+9503e5 |
1 7
o6 : Matrix R <--- R
|
i7 : leadTerm gbSnapshot(I)
o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o7 : Matrix R <--- R
|