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 (11956a - 8334a b - 1658a*b - 14980b - 4292a c - 14938a*b*c -
------------------------------------------------------------------------
2 2 2 3 2
1124b c - 13581a*c + 6243b*c - 14561c + 8900a d + 14260a*b*d -
------------------------------------------------------------------------
2 2 2 2
14481b d + 8937a*c*d + 10078b*c*d - 3133c d - 6931a*d + 1461b*d -
------------------------------------------------------------------------
2 3 2 2
6120c*d + 3177d - 10446a e + 7269a*b*e + 13265b e + 7387a*c*e -
------------------------------------------------------------------------
2 2
9210b*c*e - 1855c e + 7783a*d*e + 13054b*d*e - 14190c*d*e + 7746d e +
------------------------------------------------------------------------
2 2 2 2 3 3
12379a*e + 12687b*e - 7467c*e + 1868d*e + 12794e , - 11087a -
------------------------------------------------------------------------
2 2 3 2 2 2
3905a b - 7235a*b - 6167b + 522a c - 6816a*b*c + 14800b c - 10361a*c
------------------------------------------------------------------------
2 3 2 2
+ 9051b*c + 7444c + 11882a d + 10783a*b*d + 12344b d - 8691a*c*d -
------------------------------------------------------------------------
2 2 2 2 3 2
1228b*c*d - 7251c d - 2896a*d - 6562b*d + 6862c*d - 8241d + 5149a e
------------------------------------------------------------------------
2 2
+ 11498a*b*e - 2351b e - 1989a*c*e - 12479b*c*e - 6310c e + 13665a*d*e +
------------------------------------------------------------------------
2 2 2 2
11388b*d*e - 4608c*d*e + 9562d e - 6152a*e + 3298b*e - 10543c*e -
------------------------------------------------------------------------
2 3 3 2 2 3 2
603d*e + 6390e , 12452a + 9076a b + 5759a*b + 6229b - 6684a c +
------------------------------------------------------------------------
2 2 2 3 2
10228a*b*c - 4274b c + 9251a*c + 7418b*c + 5957c - 13762a d -
------------------------------------------------------------------------
2 2 2
4795a*b*d - 13532b d + 15301a*c*d + 6059b*c*d - 12710c d + 12708a*d +
------------------------------------------------------------------------
2 2 3 2 2
5420b*d - 15084c*d - 10241d + 5608a e + 592a*b*e + 4580b e -
------------------------------------------------------------------------
2
1270a*c*e + 13862b*c*e + 8309c e - 4608a*d*e - 380b*d*e - 8592c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3
10519d e + 5568a*e + 6494b*e + 14075c*e - 11780d*e + 13640e )
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+15617b3-9315a2c+2393abc+10391b2c+12850ac2-8459bc2+2779c3-14095a2d-
------------------------------------------------------------------------
648abd-7555b2d-9537acd+13653bcd+13106c2d+3483ad2+13747bd2-14381cd2+
------------------------------------------------------------------------
10817d3+11618a2e-15822abe+11527b2e+14292ace+1166bce-6430c2e+4652ade-
------------------------------------------------------------------------
5595bde-8185cde-12872d2e-1269ae2-13544be2+9778ce2+3053de2+9949e3
------------------------------------------------------------------------
a2b+10155b3+6188a2c-9323abc+8263b2c-6410ac2+2078bc2-1708c3+7332a2d+
------------------------------------------------------------------------
12967abd+692b2d+5370acd+5822bcd-5683c2d+12664ad2+547bd2-4321cd2+5801d3-
------------------------------------------------------------------------
7248a2e-1248abe-10736b2e+11341ace-11090bce+13954c2e-6967ade-7978bde+
------------------------------------------------------------------------
15466cde+15340d2e-3327ae2-10830be2+13359ce2-9339de2+12792e3
------------------------------------------------------------------------
a3-11689b3-2102a2c+3420abc+8357b2c+3595ac2-15225bc2+15792c3-371a2d-
------------------------------------------------------------------------
14557abd-6806b2d-7346acd-1521bcd-10525c2d-12128ad2-13256bd2+8409cd2+
------------------------------------------------------------------------
14958d3+8705a2e+3524abe+11662b2e-2401ace+12490bce+90c2e+13330ade-
------------------------------------------------------------------------
15137bde+12546cde-10894d2e-14981ae2-9975be2-13351ce2+5777de2-4371e3
------------------------------------------------------------------------
b3c-3748a2c2+7898abc2-378b2c2-2425ac3-13910bc3+9523c4+12041b3d-5973a2cd+
------------------------------------------------------------------------
5588abcd+7539b2cd+2056ac2d-13688bc2d-5761c3d-10664a2d2-3096abd2+1389b2d2
------------------------------------------------------------------------
+1491acd2-8210bcd2-7963c2d2+11874ad3+930bd3-1066cd3-9453d4+11537b3e-
------------------------------------------------------------------------
2208a2ce-12279abce+3767b2ce+5003ac2e-2643bc2e+4231c3e+9949a2de-8808abde+
------------------------------------------------------------------------
1075b2de-6558acde-6808bcde-7738c2de+12453ad2e-5848bd2e+14562cd2e-1293d3e
------------------------------------------------------------------------
+12722a2e2-7595abe2-15256b2e2-9487ace2+1702bce2+1970c2e2-13194ade2-
------------------------------------------------------------------------
1354bde2-12962cde2-4112d2e2-588ae3-6801be3+10618ce3+6863de3+14146e4
------------------------------------------------------------------------
b4-187a2c2+14312abc2+3109b2c2-8554ac3+4653bc3-10112c4-8517b3d-12363a2cd-
------------------------------------------------------------------------
2967abcd+12626b2cd-14603ac2d+8905bc2d+15536c3d+3618a2d2+828abd2-
------------------------------------------------------------------------
11521b2d2-1298acd2-6997bcd2-6258c2d2-10448ad3-3773bd3+7721cd3+15516d4-
------------------------------------------------------------------------
11658b3e+15522a2ce+4156abce-15428b2ce-15145ac2e-14170bc2e-15912c3e-
------------------------------------------------------------------------
14917a2de+3041abde-723b2de+2410acde-2753bcde+13899c2de-7005ad2e+5438bd2e
------------------------------------------------------------------------
+4299cd2e-14540d3e+166a2e2-14593abe2+14961b2e2-11046ace2-9341bce2-
------------------------------------------------------------------------
14472c2e2+8553ade2-5255bde2-11782cde2+12483d2e2+764ae3-1740be3-10383ce3+
------------------------------------------------------------------------
3938de3-273e4 abc3-8320b2c3+2575ac4-7182bc4-7063c5-10998a2c2d+8382abc2d+
------------------------------------------------------------------------
12543b2c2d+2884ac3d+10598bc3d+2026c4d+2975b3d2-6173a2cd2+5505abcd2+
------------------------------------------------------------------------
6899b2cd2-12858ac2d2-11571bc2d2+10280c3d2+11770a2d3-1426abd3-11497b2d3-
------------------------------------------------------------------------
2236acd3+13951bcd3-2204c2d3+14000ad4+5795bd4-15107cd4+10171d5-4527a2c2e+
------------------------------------------------------------------------
9516abc2e-10621b2c2e-1204ac3e+6242bc3e-15900c4e+12361b3de-4418a2cde+
------------------------------------------------------------------------
15878abcde-6613b2cde+6216ac2de+9691bc2de+3404c3de+10538a2d2e-6866abd2e-
------------------------------------------------------------------------
4051b2d2e-380acd2e-12735bcd2e+9639c2d2e+12698ad3e-1937bd3e-167cd3e+
------------------------------------------------------------------------
15263d4e-15714b3e2+10118a2ce2+2963abce2+10932b2ce2+11699ac2e2-10121bc2e2
------------------------------------------------------------------------
+8986c3e2-3749a2de2-10915abde2+8788b2de2-3475acde2-523bcde2-1666c2de2+
------------------------------------------------------------------------
5962ad2e2+499bd2e2+11416cd2e2-15739d3e2+15189a2e3-13020abe3+6263b2e3+
------------------------------------------------------------------------
15450ace3+11086bce3+2905c2e3+9720ade3-10327bde3+2146cde3-10867d2e3+
------------------------------------------------------------------------
11742ae4+15179be4+8389ce4+1096de4+4240e5
------------------------------------------------------------------------
a2c3-6674b2c3-12231ac4-9941bc4-1089c5+10492a2c2d-6571abc2d+11036b2c2d+
------------------------------------------------------------------------
11826ac3d-14485bc3d+6268c4d+9889b3d2+6715a2cd2+12800abcd2-4541b2cd2-
------------------------------------------------------------------------
5255ac2d2+5938bc2d2-12702c3d2+6782a2d3-9793abd3-5894b2d3-9341acd3+
------------------------------------------------------------------------
10474bcd3-12805c2d3-4562ad4-483bd4+15669cd4+13882d5-8996a2c2e-1717abc2e+
------------------------------------------------------------------------
14073b2c2e+10889ac3e-12445bc3e-2714c4e+6011b3de+3329a2cde-242abcde-
------------------------------------------------------------------------
9037b2cde+13275ac2de-14753bc2de-13537c3de-11226a2d2e-597abd2e-4268b2d2e+
------------------------------------------------------------------------
11155acd2e-9769bcd2e+6247c2d2e-6503ad3e-10049bd3e-2671cd3e+2161d4e-
------------------------------------------------------------------------
10243b3e2+15615a2ce2-703abce2+5683b2ce2-2210ac2e2+1220bc2e2-12627c3e2+
------------------------------------------------------------------------
1238a2de2+4515abde2+7011b2de2+10554acde2-10292bcde2+3726c2de2-13350ad2e2
------------------------------------------------------------------------
-4421bd2e2-1948cd2e2+8420d3e2-9796a2e3+12919abe3-3694b2e3+6251ace3-
------------------------------------------------------------------------
9806bce3-9947c2e3-7787ade3+3890bde3+3230cde3+4964d2e3+8764ae4-8238be4+
------------------------------------------------------------------------
5850ce4-3363de4+6830e5 |
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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