OKlibrary  0.2.1.6
BasicNotions.mac
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00001 /* Oliver Kullmann, 19.9.2009 (Swansea) */
00002 /* Copyright 2009 Oliver Kullmann
00003 This file is part of the OKlibrary. OKlibrary is free software; you can redistribute
00004 it and/or modify it under the terms of the GNU General Public License as published by
00005 the Free Software Foundation and included in this library; either version 3 of the
00006 License, or any later version. */
00007 
00022 oklib_include("OKlib/ComputerAlgebra/TestSystem/Lisp/Asserts.mac")$
00023 oklib_include("OKlib/ComputerAlgebra/Algebra/Lisp/Groupoids/Semigroups/BasicExamples.mac")$
00024 oklib_include("OKlib/ComputerAlgebra/Algebra/Lisp/Groupoids/Groups/CyclicGroups.mac")$
00025 oklib_include("OKlib/ComputerAlgebra/Algebra/Lisp/Ringframes/Rings/ResidueClasses.mac")$
00026 
00027 kill(f)$
00028 
00029 
00030 /* *****************
00031    * Basic notions *
00032    *****************
00033 */
00034 
00035 okltest_ecompo_p(f) := (
00036 
00037   /* XXX */
00038   true)$
00039 
00040 okltest_recompo_p(f) := (
00041 
00042   /* XXX */
00043   true)$
00044 
00045 okltest_act_set_p(f) := block([LG],
00046   LG : [empty_sgr, singleton_mon, cyclic_ugrp(2)],
00047   for G in LG do
00048     assert(f(G[2], G[1], G[1]) = true),
00049   /* XXX */
00050   true)$
00051 
00052 okltest_ract_set_p(f) := (
00053   assert(okltest_act_set_p(buildq([f], lambda([act2_,A,X], f(lambda([x,a],act2_(a,x)),X,A)))) = true),
00054   true)$
00055 
00056 okltest_act_grd_p(f) := block([G],
00057   assert(f(empty_sgr[2], empty_sgr[1], empty_sgr) = true),
00058   assert(f(singleton_mon[2], singleton_mon[1], singleton_mon) = true),
00059   G : cyclic_ugrp(2),
00060   assert(f(G[2], G[1], G) = false),
00061   assert(f(residues_rng(2)[3],G[1],G) = true),
00062   /* XXX */
00063   true)$
00064 
00065 okltest_ract_grd_p(f) := (
00066   assert(okltest_act_grd_p(buildq([f], lambda([act2_,A,V], f(lambda([x,a],act2_(a,x)),V,A)))) = true),
00067   true)$
00068 
00069 okltest_act_ugrd_p(f) := block([G],
00070   assert(f(singleton_mon[2], singleton_mon[1], singleton_mon) = true),
00071   G : cyclic_ugrp(2),
00072   assert(f(G[2], G[1], G) = false),
00073   assert(f(residues_rng(2)[3],G[1],G) = true),
00074   /* XXX */
00075   true)$
00076 
00077 okltest_ract_ugrd_p(f) := (
00078   assert(okltest_act_ugrd_p(buildq([f], lambda([act2_,A,V], f(lambda([x,a],act2_(a,x)),V,A)))) = true),
00079   true)$
00080 
00081 
00082 /* ***************
00083    * Conversions *
00084    ***************
00085 */
00086 
00087 
00088 
00089 /* ********************
00090    * Basic operations *
00091    ********************
00092 */
00093 
00094 
00095 
00096