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 (14244a - 6641a b + 14369a*b - 10181b - 8076a c + 6340a*b*c +
------------------------------------------------------------------------
2 2 2 3 2
9988b c - 2113a*c + 15291b*c - 15459c - 13695a d - 3900a*b*d -
------------------------------------------------------------------------
2 2 2 2
7207b d + 13860a*c*d + 15839b*c*d + 15806c d - 6585a*d - 6163b*d -
------------------------------------------------------------------------
2 3 2 2
13052c*d - 8673d + 5397a e + 14637a*b*e + 10765b e - 946a*c*e -
------------------------------------------------------------------------
2 2
14267b*c*e - 11898c e + 7278a*d*e + 11921b*d*e + 15869c*d*e + 12546d e +
------------------------------------------------------------------------
2 2 2 2 3 3 2
4443a*e - 14740b*e + 1384c*e - 6712d*e + 3169e , - 10303a - 1106a b
------------------------------------------------------------------------
2 3 2 2 2
- 8903a*b - 12760b + 4460a c - 12675a*b*c + 12597b c + 9409a*c -
------------------------------------------------------------------------
2 3 2 2
10837b*c + 8734c - 11759a d + 15764a*b*d + 1930b d + 4360a*c*d +
------------------------------------------------------------------------
2 2 2 2 3 2
1154b*c*d + 3154c d + 2329a*d + 4186b*d - 3752c*d + 5784d + 7910a e
------------------------------------------------------------------------
2 2
+ 11084a*b*e + 10891b e - 9089a*c*e - 85b*c*e + 11618c e - 3950a*d*e -
------------------------------------------------------------------------
2 2 2 2
2947b*d*e - 9558c*d*e + 7517d e - 11484a*e - 12291b*e + 8527c*e -
------------------------------------------------------------------------
2 3 3 2 2 3 2
12783d*e - 4825e , - 9418a - 5626a b - 4112a*b - 4913b + 13070a c -
------------------------------------------------------------------------
2 2 2 3 2
6403a*b*c - 4016b c + 13145a*c + 10223b*c + 12419c + 15759a d -
------------------------------------------------------------------------
2 2 2
8783a*b*d - 14299b d + 5729a*c*d + 6368b*c*d - 9034c d + 11333a*d +
------------------------------------------------------------------------
2 2 3 2 2
2218b*d - 3545c*d + 4127d + 1939a e - 917a*b*e - 6476b e + 12907a*c*e
------------------------------------------------------------------------
2 2
- 2506b*c*e - 3589c e + 3144a*d*e - 13965b*d*e - 5772c*d*e + 6335d e +
------------------------------------------------------------------------
2 2 2 2 3
4681a*e + 4744b*e + 5427c*e - 4939d*e - 3324e )
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 = | ab2-14197b3+5146a2c+5649abc+1515b2c-5908ac2-1718bc2-814c3+7320a2d+
------------------------------------------------------------------------
2526abd-14825b2d+5043acd+14232bcd+5589c2d+12004ad2-291bd2-2857cd2-
------------------------------------------------------------------------
14164d3-14724a2e-8550abe-13136b2e-7261ace-2456bce-1978c2e+15044ade+
------------------------------------------------------------------------
13487bde-8621cde-4250d2e-8055ae2-12942be2+2096ce2-6670de2+11471e3
------------------------------------------------------------------------
a2b+1763b3-5084a2c-11042abc-13983b2c-14340ac2+5505bc2-9443c3-10745a2d+
------------------------------------------------------------------------
7886abd+2805b2d-4473acd+9109bcd-14096c2d+7444ad2+3840bd2+12843cd2-1623d3
------------------------------------------------------------------------
+4874a2e+2830abe-14698b2e-4213ace+2766bce-11980c2e-1939ade+8825bde+
------------------------------------------------------------------------
1941cde+5614d2e-1265ae2-9261be2-3551ce2+7006de2-3255e3
------------------------------------------------------------------------
a3+14161b3-6551a2c+3760abc+15324b2c-3029ac2-14307bc2+14113c3+9273a2d+
------------------------------------------------------------------------
6179abd+1737b2d-11162acd-286bcd+13056c2d+7760ad2+12832bd2-8548cd2+
------------------------------------------------------------------------
10745d3+9997a2e+13246abe-5349b2e+8088ace-1871bce-7716c2e-11058ade+
------------------------------------------------------------------------
4231bde+13411cde-6939d2e+2991ae2-8642be2-6994ce2+15198de2+13852e3
------------------------------------------------------------------------
b3c-9030a2c2+3068abc2-299b2c2-9237ac3+12481bc3+2156c4-4718b3d-10185a2cd+
------------------------------------------------------------------------
15641abcd+4960b2cd-4545ac2d+3941bc2d-9618c3d-8299a2d2-7515abd2-13504b2d2
------------------------------------------------------------------------
+3052acd2-3609bcd2-8963c2d2+13362ad3+3935bd3-4860cd3-12659d4-10294b3e+
------------------------------------------------------------------------
11806a2ce-4506abce+9453b2ce+10106ac2e-12210bc2e-12433c3e-2427a2de+
------------------------------------------------------------------------
6091abde-6101b2de+15066acde+994bcde+6737c2de-14003ad2e+5817bd2e-
------------------------------------------------------------------------
15553cd2e-7748d3e-2389a2e2+665abe2+1550b2e2-13669ace2+7605bce2+7991c2e2+
------------------------------------------------------------------------
14142ade2-10317bde2-1820cde2-975d2e2+10489ae3-12358be3+1894ce3+15212de3+
------------------------------------------------------------------------
13681e4 b4-13476a2c2+8195abc2-15554b2c2-13683ac3-10556bc3+3111c4+8322b3d
------------------------------------------------------------------------
-2839a2cd+10977abcd-8599b2cd+1639ac2d-1442bc2d+12976c3d+10153a2d2+
------------------------------------------------------------------------
12921abd2-6031b2d2-5989acd2+11570bcd2-846c2d2-8452ad3-10976bd3-6334cd3-
------------------------------------------------------------------------
2310d4-1858b3e+13182a2ce+1028abce-2039b2ce-13601ac2e+2048bc2e+7175c3e+
------------------------------------------------------------------------
6222a2de-7086abde-6529b2de-6973acde+10771bcde-12089c2de-7330ad2e-
------------------------------------------------------------------------
3704bd2e-7688cd2e-6841d3e+6306a2e2+8464abe2+10170b2e2+3593ace2+281bce2+
------------------------------------------------------------------------
3330c2e2+3163ade2-8492bde2-9002cde2-6623d2e2+193ae3-1679be3+2935ce3+
------------------------------------------------------------------------
7484de3+7350e4 abc3-10062b2c3-11236ac4-2460bc4+8969c5-6160a2c2d+
------------------------------------------------------------------------
4772abc2d-54b2c2d-11949ac3d+5958bc3d-9529c4d+4460b3d2+3471a2cd2+
------------------------------------------------------------------------
12147abcd2+6548b2cd2-13163ac2d2+4965bc2d2-11188c3d2+14783a2d3-300abd3+
------------------------------------------------------------------------
12508b2d3-8109acd3+14076bcd3-1937c2d3-8666ad4+5993bd4+8754cd4+1038d5+
------------------------------------------------------------------------
3677a2c2e+2373abc2e+4907b2c2e-9671ac3e-8594bc3e+12403c4e+1833b3de+
------------------------------------------------------------------------
923a2cde-3265abcde-5957b2cde-13860ac2de+13001bc2de-268c3de+15980a2d2e+
------------------------------------------------------------------------
4418abd2e+10042b2d2e-3171acd2e-6937bcd2e+9c2d2e-743ad3e-11985bd3e-
------------------------------------------------------------------------
1027cd3e-7242d4e-7812b3e2+10280a2ce2-2275abce2+12501b2ce2-8602ac2e2+
------------------------------------------------------------------------
3134bc2e2+1708c3e2+13329a2de2+5400abde2+11581b2de2-2428acde2-14305bcde2-
------------------------------------------------------------------------
5088c2de2+9561ad2e2+14974bd2e2-11241cd2e2-7630d3e2-12822a2e3-9071abe3-
------------------------------------------------------------------------
14546b2e3+2175ace3+8877bce3+7233c2e3-4552ade3-9668bde3+4647cde3-9449d2e3
------------------------------------------------------------------------
+4106ae4-8847be4-13780ce4-783de4-7208e5
------------------------------------------------------------------------
a2c3+9253b2c3+8674ac4+15513bc4-636c5+12231a2c2d-10037abc2d-7808b2c2d+
------------------------------------------------------------------------
5149ac3d-11613bc3d+8847c4d+1553b3d2-13752a2cd2-591abcd2-9935b2cd2+
------------------------------------------------------------------------
11423ac2d2-1918bc2d2-12063c3d2-12752a2d3+11067abd3-9281b2d3-6531acd3-
------------------------------------------------------------------------
7635bcd3+3581c2d3+8969ad4+11488bd4-8075cd4-9020d5-2423a2c2e+10173abc2e+
------------------------------------------------------------------------
922b2c2e+11827ac3e+8630bc3e-1018c4e+8037b3de-2320a2cde-1693abcde+
------------------------------------------------------------------------
1035b2cde+7385ac2de+193bc2de+13788c3de+2017a2d2e+15710abd2e-9696b2d2e-
------------------------------------------------------------------------
15326acd2e+4703bcd2e+15021c2d2e-9290ad3e-11532bd3e-2271cd3e+44d4e+
------------------------------------------------------------------------
5159b3e2+1659a2ce2-12014abce2+4395b2ce2-5163ac2e2-323bc2e2-4688c3e2-
------------------------------------------------------------------------
10007a2de2-1984abde2-13183b2de2-7849acde2+10153bcde2-12385c2de2-
------------------------------------------------------------------------
9991ad2e2+5678bd2e2+2761cd2e2+7601d3e2+3515a2e3-3757abe3+231b2e3+
------------------------------------------------------------------------
12710ace3-1081bce3-11625c2e3+9602ade3-15797bde3+8107cde3+4611d2e3+
------------------------------------------------------------------------
10748ae4+1654be4-10834ce4-3791de4+5193e5 |
1 7
o6 : Matrix R <--- R
|
i7 : leadTerm gbSnapshot(I)
o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o7 : Matrix R <--- R
|