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 (- 14738a - 5799a b + 490a*b - 5498b + 12559a c - 381a*b*c -
------------------------------------------------------------------------
2 2 2 3 2 2
9424b c - 3641a*c + 13107b*c - 14140c + 218a d + 3974a*b*d - 5014b d
------------------------------------------------------------------------
2 2 2 2
- 638a*c*d - 9375b*c*d - 1908c d + 12478a*d + 4628b*d + 3883c*d -
------------------------------------------------------------------------
3 2 2
11234d - 12599a e + 5995a*b*e + 7732b e + 12305a*c*e + 10477b*c*e +
------------------------------------------------------------------------
2 2 2
11747c e - 12013a*d*e + 11368b*d*e + 2834c*d*e + 8884d e + 9762a*e +
------------------------------------------------------------------------
2 2 2 3 3 2
14856b*e + 11947c*e - 5148d*e + 14951e , - 11241a - 16000a b -
------------------------------------------------------------------------
2 3 2 2 2 2
7831a*b + 4532b - 10818a c + 7616a*b*c - 973b c + 11610a*c - 461b*c
------------------------------------------------------------------------
3 2 2
- 11066c - 10443a d - 4999a*b*d + 198b d + 3614a*c*d + 15629b*c*d -
------------------------------------------------------------------------
2 2 2 2 3 2
9381c d + 6882a*d - 12781b*d + 10062c*d + 5966d - 11948a e -
------------------------------------------------------------------------
2 2
1191a*b*e + 10851b e + 12704a*c*e + 8698b*c*e - 2677c e - 203a*d*e -
------------------------------------------------------------------------
2 2 2 2
13915b*d*e - 7037c*d*e + 5283d e + 6730a*e + 4222b*e + 6856c*e -
------------------------------------------------------------------------
2 3 3 2 2 3 2
8749d*e + 1828e , - 11739a + 7441a b - 5895a*b + 6499b + 1788a c -
------------------------------------------------------------------------
2 2 2 3 2
9461a*b*c + 11995b c - 13701a*c - 11547b*c - 13166c - 11696a d +
------------------------------------------------------------------------
2 2 2
9296a*b*d + 1214b d + 7076a*c*d + 13792b*c*d + 1345c d - 11376a*d -
------------------------------------------------------------------------
2 2 3 2 2
6315b*d - 9184c*d + 15979d + 4090a e + 6347a*b*e - 13682b e +
------------------------------------------------------------------------
2
8553a*c*e - 11770b*c*e + 6914c e + 5218a*d*e - 5799b*d*e + 4211c*d*e -
------------------------------------------------------------------------
2 2 2 2 2 3
9148d e - 7083a*e + 13490b*e + 14345c*e - 11621d*e - 9956e )
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+11961b3+15959a2c-2681abc+11586b2c-7845ac2+302bc2-1355c3-14196a2d-
------------------------------------------------------------------------
13602abd-12967b2d-1298acd+6688bcd+2087c2d-10838ad2-1769bd2+12323cd2+
------------------------------------------------------------------------
14789d3+8673a2e+3582abe-9596b2e-13138ace-10150bce+367c2e-4358ade-9820bde
------------------------------------------------------------------------
-3061cde-8332d2e+4175ae2+11400be2-8419ce2-4967de2+13550e3
------------------------------------------------------------------------
a2b-10974b3+1913a2c-1448abc-14566b2c-115ac2-13306bc2-1462c3+3158a2d+
------------------------------------------------------------------------
2967abd+3917b2d+12191acd+3036bcd-15024c2d+14422ad2+6928bd2+6138cd2-
------------------------------------------------------------------------
2824d3+10025a2e-11260abe-4710b2e-11837ace+872bce-11173c2e+5107ade-
------------------------------------------------------------------------
6660bde+11995cde-5951d2e+5718ae2-13444be2+13555ce2-9055de2+4271e3
------------------------------------------------------------------------
a3+30b3+5349a2c-13319abc-12375b2c+6425ac2+4400bc2-14187c3+4587a2d-
------------------------------------------------------------------------
13500abd-14421b2d+2302acd+7673bcd-6722c2d-10635ad2+2396bd2+15290cd2+
------------------------------------------------------------------------
7510d3+14016a2e+7257abe-8138b2e-4036ace+10239bce-6163c2e-5984ade-4017bde
------------------------------------------------------------------------
-15464cde-3115d2e+10296ae2+1807be2+10346ce2+11578de2-14047e3
------------------------------------------------------------------------
b3c-11409a2c2-12561abc2+13754b2c2-12223ac3-13825bc3+13653c4-12090b3d-
------------------------------------------------------------------------
5055a2cd+7746abcd+12307b2cd-8397ac2d-946bc2d+4207c3d+12430a2d2+14805abd2
------------------------------------------------------------------------
-8851b2d2+1419acd2+11903bcd2-11703c2d2+4066ad3-5925bd3+7489cd3-13059d4-
------------------------------------------------------------------------
4508b3e-7028a2ce-2389abce+9886b2ce-2010ac2e+7358bc2e+372c3e-6918a2de-
------------------------------------------------------------------------
3987abde+4819b2de+7155acde+6364bcde-15413c2de+4735ad2e+1316bd2e+
------------------------------------------------------------------------
10040cd2e-14564d3e+710a2e2+8621abe2+13318b2e2-9398ace2+15916bce2-
------------------------------------------------------------------------
3168c2e2+916ade2-2668bde2+5512cde2-4214d2e2-11890ae3-14168be3+13994ce3+
------------------------------------------------------------------------
630de3-10056e4 b4-14953a2c2-7545abc2-12136b2c2-6462ac3-3279bc3+6688c4-
------------------------------------------------------------------------
4203b3d+1509a2cd+714abcd+1381b2cd-5504ac2d-14467bc2d+5010c3d+10332a2d2-
------------------------------------------------------------------------
8541abd2+8175b2d2-6529acd2+3511bcd2+4823c2d2-1417ad3-6269bd3-3038cd3+
------------------------------------------------------------------------
10659d4+15345b3e-15351a2ce+2670abce+6429b2ce-8294ac2e+12727bc2e+12517c3e
------------------------------------------------------------------------
+15217a2de+7167abde-9331b2de+7743acde+10543bcde-2078c2de-14906ad2e-
------------------------------------------------------------------------
14423bd2e-15403cd2e-11886d3e+15825a2e2-7440abe2+8086b2e2+8109ace2+
------------------------------------------------------------------------
326bce2+10389c2e2+11765ade2-12481bde2-8806cde2-14547d2e2-10995ae3+163be3
------------------------------------------------------------------------
+10536ce3-13698de3+5295e4
------------------------------------------------------------------------
abc3+7520b2c3+9765ac4-15596bc4+14922c5-8895a2c2d+11516abc2d+2939b2c2d+
------------------------------------------------------------------------
15527ac3d-12241bc3d+325c4d-1164b3d2+6913a2cd2+3509abcd2+11351b2cd2+
------------------------------------------------------------------------
9237ac2d2+5448bc2d2+8781c3d2-8348a2d3+5896abd3+1031b2d3+4679acd3+
------------------------------------------------------------------------
6078bcd3+10439c2d3+9533ad4+10498bd4+613cd4-2062d5-970a2c2e-7805abc2e-
------------------------------------------------------------------------
9286b2c2e-8074ac3e-12055bc3e-14655c4e-925b3de-13160a2cde-9007abcde-
------------------------------------------------------------------------
2458b2cde-11066ac2de-7456bc2de+3665c3de-8441a2d2e-15327abd2e-8485b2d2e-
------------------------------------------------------------------------
2585acd2e-6856bcd2e-5455c2d2e+15016ad3e-9057bd3e+2505cd3e-5648d4e-
------------------------------------------------------------------------
8650b3e2-2401a2ce2-4952abce2+12233b2ce2+1326ac2e2+8655bc2e2-4991c3e2-
------------------------------------------------------------------------
2751a2de2-3680abde2-10824b2de2-6614acde2+1508bcde2+7593c2de2+2330ad2e2+
------------------------------------------------------------------------
14220bd2e2-10272cd2e2-982d3e2-3441a2e3+1456abe3+3590b2e3+3962ace3+
------------------------------------------------------------------------
5984bce3-3898c2e3+4037ade3-9949bde3-15095cde3+9757d2e3-2153ae4+12964be4+
------------------------------------------------------------------------
11997ce4+8056de4+4832e5
------------------------------------------------------------------------
a2c3-12549b2c3-9812ac4+11966bc4+15876c5+4654a2c2d+13401abc2d+548b2c2d+
------------------------------------------------------------------------
1089ac3d-5365bc3d+9570c4d-5503b3d2-240a2cd2-4959abcd2-3005b2cd2+
------------------------------------------------------------------------
4016ac2d2+12043bc2d2+10653c3d2-9131a2d3-11989abd3-7953b2d3+5890acd3+
------------------------------------------------------------------------
10312bcd3-11337c2d3+13678ad4+4209bd4+14293cd4+10152d5-3445a2c2e-
------------------------------------------------------------------------
12080abc2e+1267b2c2e+11967ac3e-7936bc3e+12587c4e-942b3de+6556a2cde+
------------------------------------------------------------------------
418abcde+14158b2cde-4104ac2de-7493bc2de-9695c3de-7598a2d2e-11349abd2e-
------------------------------------------------------------------------
12573b2d2e-13676acd2e+14803bcd2e-3447c2d2e+7330ad3e+6529bd3e+3610cd3e-
------------------------------------------------------------------------
15294d4e-8963b3e2-12422a2ce2+13675abce2-1745b2ce2-13043ac2e2-8313bc2e2-
------------------------------------------------------------------------
6018c3e2-11312a2de2+13949abde2+6383b2de2+3273acde2+11075bcde2+5238c2de2+
------------------------------------------------------------------------
15537ad2e2-4122bd2e2+10727cd2e2+6073d3e2-9647a2e3+4245abe3+11588b2e3-
------------------------------------------------------------------------
9708ace3-7460bce3+14574c2e3-226ade3-5716bde3+13511cde3-8529d2e3+8583ae4+
------------------------------------------------------------------------
6738be4+5114ce4+6683de4-267e5 |
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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