Quelle bound-test-08.xml Sprache: XML

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

SGrobnerTrunc
gap> F:=Rationals;;
gap> NPzero:=[[],[]];;
gap> NPone:=[[[]],[One(F)]];;

gap> SGrobnerTrunc([NPzero],5,[1,1])=[];
true
gap> SGrobnerTrunc([],5,[1,1])=[];
true
gap> SGrobnerTrunc([NPone],5,[1])=[NPone];
true

gap> F:=GF(2);;
gap> NPzero:=[[],[]];;
gap> NPone:=[[[]],[One(F)]];;

CheckHomogeneousNPs
gap> CheckHomogeneousNPs([],[1,1])=[];
true

gap> F:=Rationals;;
gap> NPzero:=[[],[]];;
gap> NPone:=[[[]],[One(F)]];;

gap> CheckHomogeneousNPs([NPone],[1,1])=[0];
true

XXX NPzero is Homogeneous but the degree can not be determined -> so false is
returned fail might be better here though
gap> CheckHomogeneousNPs([NPzero],[1,1])=false;
true

gap> F:=GF(2);;
gap> NPzero:=[[],[]];;
gap> NPone:=[[[]],[One(F)]];;

gap> CheckHomogeneousNPs([NPone],[1,1])=[0];
true

XXX NPzero is Homogeneous but the degree can not be determined -> so false is
returned fail might be better here though
gap> CheckHomogeneousNPs([NPzero],[1,1])=false;
true

BaseQATrunc
gap> BaseQATrunc([],1,[2,3])=[ [ [] ], [] ];
true
gap> BaseQATrunc([],2,[2,3])=[ [ [] ], [], [ [1] ]];
true
why GB instead of lterms (to check homogeneous-ness ?)
gap> BaseQATrunc([ [[[1]],[1]] ],2,[2,3])=[ [ [] ], [], [] ];
true
gap> BaseQATrunc([ [[[1]],[1]] ],3,[2,3])=[ [ [] ], [], [], [ [2] ] ];
true
gap> BaseQATrunc([ [[[]],[1]] ],3,[2,3])=[ [], [], [], [] ];
true
gap> BaseQATrunc([ [[[]],[One(GF(3))]] ],3,[2,3])=[ [], [], [], [] ];
true

DimsQATrunc
gap> DimsQATrunc([],1,[2,3])=[1,0];
true
gap> DimsQATrunc([],2,[2,3])=[1,0,1];
true
gap> DimsQATrunc([ [[[1]],[1]] ],2,[2,3])=[1,0,0];
true
gap> DimsQATrunc([ [[[1]],[1]] ],3,[2,3])=[1,0,0,1];
true
gap> DimsQATrunc([ [[[]],[1]] ],3,[2,3])=[0,0,0,0];
true
gap> DimsQATrunc([ [[[]],[One(GF(3))]] ],3,[2,3])=[0,0,0,0];
true

FreqsQATrunc
gap> FreqsQATrunc([],1,[2,3])=[ [ [ [  ], 1 ] ] ];
true
gap> FreqsQATrunc([],2,[2,3])=[ [ [ [  ], 1 ] ], [ [ [ 1, 0 ], 1 ] ] ];
true
gap> FreqsQATrunc([ [[[1]],[1]] ],2,[2,3])=[ [ [ [  ], 1 ] ] ];
true
gap> FreqsQATrunc([ [[[1]],[1]] ],3,[2,3])=[ [ [ [  ], 1 ] ], [ [ [ 0, 1 ], 1 ] ] ];
true
gap> FreqsQATrunc([ [[[]],[1]] ],3,[2,3])=[];
true
gap> FreqsQATrunc([ [[[]],[One(GF(3))]] ],3,[2,3])=[];
true

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