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);