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: http://www.gnu.org/licenses/lgpl.html gap> ########################## END COPYRIGHT MESSAGE ##########################

gap> LoadPackage("gbnp"); ───────────────────────────────────────────────────────────────────────────── Loading GBNP 1.0.3 (Non-commutative Gröbner bases) by A.M. Cohen (http://www.win.tue.nl/~amc) and J.W. Knopper (J.W.Knopper@tue.nl). Homepage: http://mathdox.org/products/gbnp/ ───────────────────────────────────────────────────────────────────────────── true

gap> check:=function (l, i) > # exact answer matches > if IsInt(l) and l=i then > return true; > fi; > # no exact answer, but correct answer is in interval > if IsList(l) and l[1]<=i and i<=l[2] then > return true; > fi; > # not a correct answer > return false; > end; function( l, i ) ... end

DetermineGrowthQA gap> DetermineGrowthQA([],2,true)="exponential growth"; true gap> DetermineGrowthQA([[1]],2,true)=1; true gap> DetermineGrowthQA([[1,2]],2,true)=2; true gap> DetermineGrowthQA([[2,1]],2,true)=2; true gap> DetermineGrowthQA([[1,2,1],[2,2,1]],2,true)=2; # correct true gap> DetermineGrowthQA([[1],[2]],2,true)=0; # correct true

gap> DetermineGrowthQA([],2,false)="exponential growth"; true gap> DetermineGrowthQA([[1]],2,false)=1; true gap> check(DetermineGrowthQA([[1,2]],2,false),2); true gap> DetermineGrowthQA([[2,1]],2,false)=2; true gap> DetermineGrowthQA([[1,2,1],[2,2,1]],2,false)=2; # correct true gap> DetermineGrowthQA([[1],[2]],2,false)=0; # correct true

FinCheckQA gap> FinCheckQA([],2)=false; true gap> FinCheckQA([[]],2); true gap> FinCheckQA([[1],[2]],2); true gap> FinCheckQA([[1],[2]],2); true gap> FinCheckQA([[2]],2)=false; true

HilbertSeriesQA gap> HilbertSeriesQA([],2,10)=[1,2,4,8,16,32,64,128,256,512,1024]; true gap> HilbertSeriesQA([[]],2,10)=[]; true gap> HilbertSeriesQA([[1,2]],2,10)=[1,2,3,4,5,6,7,8,9,10,11]; true gap> HilbertSeriesQA([[2,1]],2,10)=[1,2,3,4,5,6,7,8,9,10,11]; true gap> HilbertSeriesQA([[1]],2,10)=[1,1,1,1,1,1,1,1,1,1,1]; true gap> HilbertSeriesQA([[1,2,1],[2,2,1]],2,10)=[ 1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ]; true

PreprocessAnalysisQA

gap> PreprocessAnalysisQA([],2,10)=[]; true gap> PreprocessAnalysisQA([[]],2,10)=[[]]; true

now for some not completely trivial ones, that tested true when I wrote them gap> PreprocessAnalysisQA([[1,2],[1,1],[2,2]],2,1)=[[1,1],[2]]; true gap> PreprocessAnalysisQA([[1,2],[1,1],[2,2]],2,2)=[[1],[2]]; true