gap> ######################### BEGIN COPYRIGHT MESSAGE #########################
GBNP - computing Gröbner bases of noncommutative polynomials
Copyright
2001-
2010 by Arjeh M. Cohen, Dié A.H. Gijsbers, Jan Willem
Knopper, Chris Krook. Address: Discrete Algebra and Geometry (DAM) group
at the Department of Mathematics and Computer Science of Eindhoven
University of Technology.
For acknowledgements see the manual. The manual can be found in several
formats in the doc subdirectory of the GBNP distribution. The
acknowledgements formatted as text can be found in the file chap0.txt.
GBNP is free software; you can redistribute it and/or modify it under
the terms of the Lesser GNU General
Public License as published by the
Free Software Foundation (FSF); either
version 2.
1 of the License, or
(at your option) any later
version. For details, see the file
'LGPL' in
the doc subdirectory of the GBNP distribution or see the FSF
's own site:
https://www.gnu.org/licenses/lgpl.html
gap> ########################## END COPYRIGHT MESSAGE ##########################
gap> LoadPackage(
"gbnp", false);
true
gap> NPzero:=[[],[]];;
gap> NPone:=[[[]],[
1]];;
gap> NPone_2:=[[[]],[One(GF(
2))]];;
gap> NPMone1:=[[[-
1,]],[
1]];;
gap> NPMone2:=[[[-
2,]],[
1]];;
gap> NPMone1_2:=[[[-
1,]],[One(GF(
2))]];;
gap> NPMone2_2:=[[[-
2,]],[One(GF(
2))]];;
gap> GBRempty:=SGrobnerModule([],[]);;
gap> GBRone:=SGrobnerModule([],[NPone]);;
gap> GBRone_12:=SGrobnerModule([NPMone1,NPMone2],[]);;
gap> GBRone_1:=SGrobnerModule([NPMone1],[]);;
BaseQM
gap> BaseQM(GBRempty,
1,
1,
2);
"infinite"
gap> BaseQM(GBRone,
0,
0,
0)=[];
true
gap> BaseQM(GBRone_12,
0,
0,
0)=[];
true
gap> BaseQM(GBRone_12,
0,
2,
0)=[];
true
DimQM
gap> DimQM(GBRone,
0,
0)=
0;
true
gap> DimQM(GBRone_12,
0,
0)=
0;
true
gap> DimQM(GBRone_12,
0,
2)=
0;
true
MulQM
gap> MulQM(NPone,NPone,GBRempty)=NPone;
true
gap> MulQM(NPone,NPzero,GBRempty)=NPzero;
true
gap> MulQM(NPzero,NPone,GBRempty)=NPzero;
true
gap> MulQM(NPzero,NPzero,GBRempty)=NPzero;
true
gap> MulQM(NPone,NPone,GBRone)=NPzero;
true
gap> MulQM(NPMone1,NPone,GBRone_1)=NPzero;
true
gap> MulQM(NPMone2,NPone,GBRone_1)=NPMone2;
true
SGrobnerModule
check function
gap> check:=function(r, p, ts)
> return (r.p = p) and (r.ts = ts);
> end;;
first some standard checks
gap> check(SGrobnerModule([],[]), [], []);
true
gap> check(SGrobnerModule([],[NPzero]), [], []);
true
gap> check(SGrobnerModule([],[NPone]), [], [NPone]);
true
gap> check(SGrobnerModule([],[NPone_2]), [], [NPone_2]);
true
now some prefix checks
gap> check(SGrobnerModule([NPMone1],[]),[NPMone1],[]);
true
gap> check(SGrobnerModule([NPMone1],[NPone]),[],[NPone]);
true
gap> check(SGrobnerModule([NPMone1_2],[NPone_2]),[],[NPone_2]);
true
gap> check(SGrobnerModule([NPMone1_2,NPMone2_2],[NPone_2]),[],[NPone_2]);
true
gap> check(SGrobnerModule([NPMone1_2,NPMone2_2],[]),[NPMone2_2,NPMone1_2],[]);
true
StrongNormalFormNPM
gap> StrongNormalFormNPM(NPzero,GBRempty)=NPzero;
true
gap> StrongNormalFormNPM(NPone,GBRempty)=NPone;
true
gap> StrongNormalFormNPM(NPMone1,GBRempty)=NPMone1;
true
gap> StrongNormalFormNPM(NPMone1,GBRone)=NPzero;
true
gap> StrongNormalFormNPM(NPone,GBRone)=NPzero;
true
gap> StrongNormalFormNPM(NPone,GBRone_12)=NPone;
true
gap> StrongNormalFormNPM(NPMone1,GBRone_12)=NPzero;
true
