This file contains the code 
examples in Exercises 1, separated out here to make it easier to cut and paste into a gap window.

LoadPackage("GBNP");
SetInfoLevel(InfoGBNP,0);
SetInfoLevel(InfoGBNPTime,0);

A:=FreeAssociativeAlgebraWithOne(Rationals, "x", "y", "z");
x:=A.x;; y:=A.y;; z:=A.z;; o:=One(A);;
uerels:=[y*x - 2*x*y, z*y - 3*y*z, z*x - 5*x*z];
uerelsNP:=GP2NPList(uerels);;
PrintNPList(uerelsNP);
GBNP.ConfigPrint(A);
GB:=SGrobnerTrunc(uerelsNP, 12, [1,1,1]);;
PrintNPList(GB);

A:=FreeAssociativeAlgebraWithOne(Rationals, "x", "y");
x:=A.x;; y:=A.y;; o:=One(A);;
uerels:=[y*x - x*y - x*x];
uerelsNP:=GP2NPList(uerels);;
PrintNPList(uerelsNP);
GBNP.ConfigPrint(A);
GB:=SGrobnerTrunc(uerelsNP, 12, [1,1,1]);;
PrintNPList(GB);


A:=FreeAssociativeAlgebraWithOne(Rationals, "x", "y");
x:=A.x;; y:=A.y;; o:=One(A);;
uerels:=[x*y - y*x - y*y];
uerelsNP:=GP2NPList(uerels);;
PrintNPList(uerelsNP);
GBNP.ConfigPrint(A);
GB:=SGrobnerTrunc(uerelsNP, 12, [1,1,1]);;
PrintNPList(GB);

A:=FreeAssociativeAlgebraWithOne(Rationals, "x", "y", "z");
x:=A.x;; y:=A.y;; z:=A.z;; o:=One(A);;
a:=2; 
b:=3;
c:=5;
uerels:=[a*y*x + b*x*y + c*z*z, a*x*z + b*z*x + c*y*y, a*z*y + b*y*z + c*x*x];
uerelsNP:=GP2NPList(uerels);;
PrintNPList(uerelsNP);
GBNP.ConfigPrint(A);
GB:=SGrobnerTrunc(uerelsNP, 8, [1,1,1]);;
PrintNPList(GB);

A:=FreeAssociativeAlgebraWithOne(Rationals, "x", "y", "z");
x:=A.x;; y:=A.y;; z:=A.z;; o:=One(A);;
uerels:=[z*x  + x*z, y*z  + z*y, z*z - x*x - y*y];
uerelsNP:=GP2NPList(uerels);;
PrintNPList(uerelsNP);
GBNP.ConfigPrint(A);
GB:=SGrobnerTrunc(uerelsNP, 12, [1,1,1]);;
PrintNPList(GB);