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 (- 12761a - 9909a b + 1372a*b + 11726b - 10155a c + 11565a*b*c
------------------------------------------------------------------------
2 2 2 3 2 2
+ 2144b c - 7907a*c + 123b*c - 2812c + 6279a d - 13664a*b*d - 7388b d
------------------------------------------------------------------------
2 2 2 2
- 2747a*c*d - 12778b*c*d + 6637c d - 12558a*d - 10480b*d + 15866c*d -
------------------------------------------------------------------------
3 2 2
2851d - 13385a e - 10110a*b*e - 12045b e - 12233a*c*e + 2645b*c*e +
------------------------------------------------------------------------
2 2 2
5974c e - 12230a*d*e + 11645b*d*e + 616c*d*e + 10139d e - 10927a*e -
------------------------------------------------------------------------
2 2 2 3 3 2 2
1309b*e - 14486c*e + 7937d*e - 4554e , 8340a + 11164a b - 7199a*b +
------------------------------------------------------------------------
3 2 2 2 2 3
496b + 15335a c - 15148a*b*c - 7657b c + 10639a*c + 7481b*c - 9544c
------------------------------------------------------------------------
2 2 2
- 11030a d - 4584a*b*d - 15464b d - 1339a*c*d + 9415b*c*d - 6901c d +
------------------------------------------------------------------------
2 2 2 3 2
12993a*d - 4415b*d - 10193c*d - 13208d - 5939a e - 5380a*b*e -
------------------------------------------------------------------------
2 2
12509b e - 8115a*c*e + 4810b*c*e + 3198c e + 12070a*d*e - 3118b*d*e -
------------------------------------------------------------------------
2 2 2 2 2
4379c*d*e - 5863d e + 13833a*e - 5641b*e - 9614c*e + 6306d*e -
------------------------------------------------------------------------
3 3 2 2 3 2
1686e , - 5977a + 5492a b - 11997a*b + 2112b + 13719a c + 5999a*b*c +
------------------------------------------------------------------------
2 2 2 3 2
11644b c - 2426a*c - 12514b*c + 2491c + 3668a d - 10898a*b*d -
------------------------------------------------------------------------
2 2 2 2
8935b d - 13147a*c*d - 7049b*c*d + 10692c d - 11022a*d - 7971b*d +
------------------------------------------------------------------------
2 3 2 2
1091c*d + 9207d + 8790a e + 13331a*b*e - 1321b e - 391a*c*e -
------------------------------------------------------------------------
2 2
9830b*c*e - 7697c e + 15427a*d*e + 9277b*d*e + 12266c*d*e + 12243d e +
------------------------------------------------------------------------
2 2 2 2 3
15475a*e + 9672b*e - 5627c*e - 4315d*e - 15546e )
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+5797b3-4161a2c-13165abc+3020b2c+1834ac2-6935bc2+6776c3+6259a2d+
------------------------------------------------------------------------
4892abd+76b2d+15730acd-5887bcd-7547c2d+15671ad2+677bd2-2023cd2-4548d3+
------------------------------------------------------------------------
3316a2e+9367abe+9351b2e+12974ace-11214bce-1381c2e-11539ade-3297bde-
------------------------------------------------------------------------
12589cde+11770d2e+12748ae2+4216be2-7311ce2-14384de2+5605e3
------------------------------------------------------------------------
a2b+13207b3-15738a2c-13818abc-1537b2c-15766ac2-15187bc2+310c3-9638a2d-
------------------------------------------------------------------------
3809abd+4401b2d-9903acd+12448bcd-8039c2d+13320ad2+9290bd2+1225cd2+9449d3
------------------------------------------------------------------------
+218a2e-760abe-14501b2e-9357ace+8487bce-1503c2e+3535ade+8179bde-7155cde+
------------------------------------------------------------------------
2707d2e+15795ae2-10368be2-11767ce2-3849de2+7823e3
------------------------------------------------------------------------
a3-4068b3-5608a2c-3241abc-2309b2c+6484ac2-9708bc2-15442c3+5636a2d+
------------------------------------------------------------------------
3565abd+12085b2d-1182acd+8456bcd-4250c2d+6696ad2-2320bd2-10256cd2+124d3-
------------------------------------------------------------------------
4840a2e+8753abe+2892b2e-12397ace+14524bce+5590c2e-12707ade-7045bde-
------------------------------------------------------------------------
12149cde-15694d2e-1830ae2-5737ce2-6887de2+10333e3
------------------------------------------------------------------------
b3c-11044a2c2-15491abc2-10778b2c2-1782ac3-11003bc3+13459c4+8422b3d-
------------------------------------------------------------------------
2133a2cd-13989abcd+7884b2cd-880ac2d+7203bc2d+14378c3d+12446a2d2-
------------------------------------------------------------------------
15526abd2+6405b2d2-12710acd2+2543bcd2+11879c2d2-11183ad3-830bd3+5991cd3-
------------------------------------------------------------------------
10571d4-4248b3e+12596a2ce-6934abce+6908b2ce-6047ac2e-3832bc2e+3442c3e+
------------------------------------------------------------------------
14939a2de+12368abde-7834b2de+977acde-4158bcde+15639c2de-4754ad2e+62bd2e-
------------------------------------------------------------------------
11371cd2e-9510d3e-5234a2e2+8085abe2+8642b2e2+14851ace2+418bce2-3178c2e2-
------------------------------------------------------------------------
11700ade2-360bde2-6849cde2+2594d2e2+14156ae3+6351be3+12164ce3+9919de3-
------------------------------------------------------------------------
8988e4 b4+5373a2c2-13061abc2+13079b2c2+11318ac3-10847bc3+3372c4+11506b3d
------------------------------------------------------------------------
-11538a2cd-481abcd-6750b2cd-3694ac2d+1882bc2d+10907c3d+4709a2d2-
------------------------------------------------------------------------
14553abd2-202b2d2-8134acd2+2984bcd2-13894c2d2-1463ad3+6487bd3-4964cd3+
------------------------------------------------------------------------
6133d4+1366b3e-6439a2ce+776abce+2999b2ce-3957ac2e-1064bc2e+4420c3e-
------------------------------------------------------------------------
6258a2de+6728abde+2408b2de-10552acde+9689bcde+1884c2de-4530ad2e-
------------------------------------------------------------------------
13312bd2e-1076cd2e+2301d3e+1589a2e2+11670abe2-8043b2e2+9088ace2+3877bce2
------------------------------------------------------------------------
-5054c2e2-4580ade2+2451bde2-15519cde2-11578d2e2+15406ae3-14306be3+
------------------------------------------------------------------------
3787ce3-53de3-5520e4 abc3-4568b2c3-14492ac4+7537bc4-8160c5+498a2c2d+
------------------------------------------------------------------------
15063abc2d+1507b2c2d+7084ac3d-1142bc3d+1876c4d+13237b3d2+1843a2cd2-
------------------------------------------------------------------------
5981abcd2+5919b2cd2+11348ac2d2+3657bc2d2-5078c3d2-10125a2d3+757abd3+
------------------------------------------------------------------------
10610b2d3-2761acd3+3775bcd3+11170c2d3-6850ad4-6938bd4-8131cd4+9446d5+
------------------------------------------------------------------------
12725a2c2e-10870abc2e-1745b2c2e+4252ac3e-4456bc3e-3685c4e+15125b3de-
------------------------------------------------------------------------
15367a2cde-6205abcde-14278b2cde+5241ac2de-11255bc2de-9008c3de-4833a2d2e+
------------------------------------------------------------------------
12741abd2e-9628b2d2e-5419acd2e+13770bcd2e-6398c2d2e-13855ad3e-6409bd3e+
------------------------------------------------------------------------
6253cd3e+14061d4e-1230b3e2+11601a2ce2+16001abce2+12560b2ce2+12602ac2e2-
------------------------------------------------------------------------
6958bc2e2-7267c3e2+14439a2de2-3366abde2-9523b2de2-3656acde2-7550bcde2+
------------------------------------------------------------------------
12731c2de2-13244ad2e2-3023bd2e2-13564cd2e2-12458d3e2+502a2e3-7770abe3+
------------------------------------------------------------------------
14186b2e3+14808ace3-2530bce3-8731c2e3-2592ade3+15598bde3-2321cde3+
------------------------------------------------------------------------
8983d2e3+8644ae4+6938be4-12425ce4-10277de4+8660e5
------------------------------------------------------------------------
a2c3+2070b2c3-11834ac4-4135bc4-174c5+6160a2c2d+6748abc2d-13747b2c2d+
------------------------------------------------------------------------
11759ac3d-6561bc3d-11834c4d+13792b3d2+348a2cd2+9990abcd2+11568b2cd2-
------------------------------------------------------------------------
15935ac2d2+8208bc2d2+3842c3d2-6212a2d3+15155abd3-11510b2d3+8051acd3-
------------------------------------------------------------------------
9238bcd3-8282c2d3-13266ad4-8648bd4+3267cd4+3224d5-1877a2c2e-13750abc2e-
------------------------------------------------------------------------
10207b2c2e-14462ac3e-673bc3e-6557c4e+14710b3de-13133a2cde+9635abcde-
------------------------------------------------------------------------
10341b2cde-7598ac2de-2942bc2de+1438c3de+3806a2d2e-11582abd2e-854b2d2e-
------------------------------------------------------------------------
4154acd2e+88bcd2e-1714c2d2e+2684ad3e-12342bd3e-10575cd3e+14933d4e-
------------------------------------------------------------------------
4915b3e2-4187a2ce2-9311abce2+5831b2ce2+2745ac2e2+3819bc2e2-14081c3e2-
------------------------------------------------------------------------
9330a2de2-11794abde2-4253b2de2+11778acde2-7648bcde2-8077c2de2-7419ad2e2+
------------------------------------------------------------------------
7849bd2e2-7299cd2e2-10167d3e2-7569a2e3-11572abe3-1242b2e3-10663ace3+
------------------------------------------------------------------------
12149bce3-8836c2e3+4004ade3-12114bde3+13144cde3+13094d2e3-6341ae4+
------------------------------------------------------------------------
7940be4-12124ce4+9935de4-6675e5 |
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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