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 (13598a - 6475a b + 3265a*b + 15784b - 9730a c + 11365a*b*c +
------------------------------------------------------------------------
2 2 2 3 2 2
5202b c + 13162a*c + 1623b*c + 4457c - 1995a d - 3448a*b*d - 12133b d
------------------------------------------------------------------------
2 2 2 2
+ 1557a*c*d - 11789b*c*d + 14744c d + 14570a*d + 1462b*d + 5438c*d +
------------------------------------------------------------------------
3 2 2
12334d + 6080a e + 1918a*b*e + 9537b e - 11447a*c*e - 6524b*c*e -
------------------------------------------------------------------------
2 2 2
7922c e + 1480a*d*e - 10432b*d*e + 2875c*d*e - 6443d e - 8320a*e -
------------------------------------------------------------------------
2 2 2 3 3 2 2
2859b*e - 14552c*e + 6521d*e + 15064e , 9435a + 14737a b - 6715a*b
------------------------------------------------------------------------
3 2 2 2 2
- 15038b + 12241a c + 10973a*b*c + 10209b c + 14789a*c + 5748b*c -
------------------------------------------------------------------------
3 2 2
12563c + 13725a d - 10733a*b*d + 1536b d + 5123a*c*d + 14385b*c*d -
------------------------------------------------------------------------
2 2 2 2 3 2
8366c d + 8001a*d - 5542b*d - 636c*d - 4057d - 730a e + 6568a*b*e -
------------------------------------------------------------------------
2 2
4125b e + 12916a*c*e + 11513b*c*e + 15406c e + 10602a*d*e + 12577b*d*e +
------------------------------------------------------------------------
2 2 2 2 2
5427c*d*e - 6804d e - 12027a*e + 4413b*e + 10511c*e - 12500d*e +
------------------------------------------------------------------------
3 3 2 2 3 2
7670e , 6582a - 12354a b - 15377a*b - 177b - 778a c - 9900a*b*c -
------------------------------------------------------------------------
2 2 2 3 2 2
14835b c - 6648a*c - 12664b*c - 4338c - 3232a d - 13397a*b*d + 812b d
------------------------------------------------------------------------
2 2 2 2
- 14720a*c*d - 6996b*c*d - 880c d + 15751a*d - 13616b*d - 4129c*d +
------------------------------------------------------------------------
3 2 2 2
271d - 5987a e - 9125a*b*e - 13807b e + 465a*c*e + 14381b*c*e - 4666c e
------------------------------------------------------------------------
2 2 2
+ 15525a*d*e - 8046b*d*e + 3769c*d*e + 12060d e + 10890a*e - 4248b*e +
------------------------------------------------------------------------
2 2 3
9876c*e - 11400d*e + 3308e )
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 = | ab2-10070b3-2095a2c-6657abc-14057b2c+1052ac2+7057bc2-9773c3-11328a2d-
------------------------------------------------------------------------
7145abd+323b2d-6625acd-8161bcd-13166c2d-9227ad2-13034bd2+15989cd2-
------------------------------------------------------------------------
15053d3+277a2e-14949abe-6395b2e+11197ace-1402bce-4856c2e-1317ade+3961bde
------------------------------------------------------------------------
-10551cde-10363d2e-2110ae2-11707be2+5697ce2-4500de2+9267e3
------------------------------------------------------------------------
a2b+128b3+2086a2c-5589abc-12302b2c-7608ac2+4125bc2-12374c3+728a2d+
------------------------------------------------------------------------
12373abd+12630b2d-1530acd-7244bcd-9176c2d-3272ad2+7378bd2-13748cd2-
------------------------------------------------------------------------
8530d3+12568a2e+13872abe+4430b2e+2418ace+10533bce-3398c2e+13251ade-50bde
------------------------------------------------------------------------
+1385cde+1352d2e-11841ae2-7825be2+13046ce2+9019de2-10916e3
------------------------------------------------------------------------
a3+2207b3-8608a2c-14856abc-3732b2c+15415ac2+8566bc2+5078c3-2509a2d-
------------------------------------------------------------------------
1727abd+9480b2d-4499acd-3077bcd+1749c2d-14684ad2+4167bd2-12548cd2-8672d3
------------------------------------------------------------------------
-5842a2e-7148abe-6112b2e-14920ace+12777bce-6793c2e-2096ade+2444bde-
------------------------------------------------------------------------
9923cde+13021d2e+13651ae2-607be2-11549ce2-13862de2+6758e3
------------------------------------------------------------------------
b3c-1540a2c2-4285abc2+629b2c2+5090ac3-4378bc3+6269c4+2320b3d-5484a2cd-
------------------------------------------------------------------------
1079abcd-766b2cd+4854ac2d+15885bc2d-3379c3d+412a2d2-11556abd2+4573b2d2-
------------------------------------------------------------------------
4821acd2+6810bcd2-10854c2d2-2934ad3+10202bd3-4273cd3+11747d4+344b3e-
------------------------------------------------------------------------
10243a2ce+11496abce+11241b2ce+1387ac2e+15859bc2e-6851c3e+9506a2de+
------------------------------------------------------------------------
6816abde-13544b2de+2648acde+15015bcde-7604c2de-2261ad2e-7170bd2e-
------------------------------------------------------------------------
13175cd2e+2315d3e-471a2e2-8252abe2+847b2e2-12563ace2+15218bce2+3453c2e2-
------------------------------------------------------------------------
585ade2-7206bde2+14847cde2-13779d2e2-1999ae3-5428be3-2142ce3-14548de3-
------------------------------------------------------------------------
15697e4 b4+2890a2c2+13211abc2+11301b2c2-12856ac3-333bc3-1827c4-9386b3d+
------------------------------------------------------------------------
14937a2cd+14923abcd-9471b2cd-5234ac2d-9739bc2d+5645c3d+8068a2d2-
------------------------------------------------------------------------
11202abd2-640b2d2+1476acd2+1108bcd2-12320c2d2+946ad3-6858bd3+6026cd3+
------------------------------------------------------------------------
2175d4+6561b3e+15374a2ce+7207abce-6542b2ce+14446ac2e+4294bc2e-12300c3e+
------------------------------------------------------------------------
15904a2de-2603abde+15217b2de-5002acde-13563bcde+9954c2de-3737ad2e-
------------------------------------------------------------------------
7313bd2e-10333cd2e+11464d3e+14249a2e2-9533abe2+13267b2e2+6841ace2-
------------------------------------------------------------------------
2219bce2-4062c2e2+2087ade2+5854bde2-14746cde2+11219d2e2-2315ae3-13923be3
------------------------------------------------------------------------
+2680ce3+640de3+1963e4 abc3-10285b2c3-12394ac4+4675bc4-3527c5+2702a2c2d-
------------------------------------------------------------------------
2199abc2d+2321b2c2d+1135ac3d+5469bc3d+5074c4d+8459b3d2-6894a2cd2+
------------------------------------------------------------------------
2171abcd2+2414b2cd2+3104ac2d2-3712bc2d2+12797c3d2+4155a2d3-2443abd3-
------------------------------------------------------------------------
3481b2d3-9206acd3-6801bcd3-15054c2d3-8778ad4-7433bd4-5037cd4-12362d5-
------------------------------------------------------------------------
8502a2c2e+6520abc2e-7616b2c2e-13182ac3e+8885bc3e-13989c4e-15467b3de-
------------------------------------------------------------------------
3788a2cde+114abcde+14844b2cde+9838ac2de-1310bc2de+11929c3de+7957a2d2e+
------------------------------------------------------------------------
4029abd2e-3552b2d2e+13960acd2e-8703bcd2e-13030c2d2e-4044ad3e+1768bd3e-
------------------------------------------------------------------------
8570cd3e+7732d4e+13839b3e2-2901a2ce2-8004abce2-2673b2ce2-7494ac2e2+
------------------------------------------------------------------------
3876bc2e2+2222c3e2+8397a2de2-10142abde2-5521b2de2-3449acde2+13755bcde2-
------------------------------------------------------------------------
4590c2de2+8488ad2e2-2883bd2e2+4547cd2e2+13870d3e2-6833a2e3+1211abe3-
------------------------------------------------------------------------
7571b2e3-6988ace3+14063bce3-12262c2e3+6612ade3+10871bde3+4384cde3-
------------------------------------------------------------------------
6906d2e3+3151ae4-4933be4+170ce4+8840de4+6741e5
------------------------------------------------------------------------
a2c3-3238b2c3+12022ac4-13964bc4-6525c5+10728a2c2d+13246abc2d+13066b2c2d+
------------------------------------------------------------------------
5341ac3d-14984bc3d+5709c4d+11282b3d2+1625a2cd2+10106abcd2+12534b2cd2+
------------------------------------------------------------------------
10420ac2d2-9999bc2d2-12172c3d2-15535a2d3-13647abd3+12261b2d3+2816acd3-
------------------------------------------------------------------------
1553bcd3-10631c2d3+12829ad4-5135bd4-3832cd4+5097d5+12156a2c2e+8092abc2e+
------------------------------------------------------------------------
1647b2c2e-5570ac3e+8674bc3e-6754c4e-4329b3de-8935a2cde-7586abcde-
------------------------------------------------------------------------
7554b2cde+9521ac2de+3386bc2de+10981c3de+6193a2d2e+7125abd2e+12199b2d2e-
------------------------------------------------------------------------
258acd2e-1686bcd2e+11541c2d2e+4491ad3e+1396bd3e-11578cd3e+14790d4e+
------------------------------------------------------------------------
2059b3e2-6796a2ce2+10968abce2-9325b2ce2-7955ac2e2+5193bc2e2-4480c3e2+
------------------------------------------------------------------------
11359a2de2+12429abde2-13606b2de2-11084acde2-15772bcde2+10176c2de2+
------------------------------------------------------------------------
12909ad2e2-2794bd2e2+2383cd2e2-15306d3e2+10478a2e3+13522abe3-6255b2e3-
------------------------------------------------------------------------
8703ace3+9675bce3-1967c2e3+2091ade3+670bde3+4667cde3-7647d2e3+7569ae4+
------------------------------------------------------------------------
5951be4-9142ce4-2830de4+9694e5 |
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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