OKlibrary  0.2.1.6
Homomorphisms.mac
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```00001 /* Oliver Kullmann, 6.8.2012 (Swansea) */
00002 /* Copyright 2012 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/Hypergraphs/Lisp/Homomorphisms.mac")\$
00024 oklib_include("OKlib/ComputerAlgebra/Hypergraphs/Lisp/Generators/Ramsey.mac")\$
00025 oklib_include("OKlib/ComputerAlgebra/Hypergraphs/Lisp/Generators/Schur.mac")\$
00026 oklib_include("OKlib/ComputerAlgebra/Algebra/Lisp/Groupoids/Groups/CyclicGroups.mac")\$
00027 oklib_include("OKlib/ComputerAlgebra/Algebra/Lisp/Groupoids/Groups/SymmetricGroups.mac")\$
00028
00029 kill(f)\$
00030
00031
00032 /* ***********************************
00033    * Relations to Ramsey-hypergraphs *
00034    ***********************************
00035 */
00036
00037 okltest_hom_ramsey_schur(f) := (
00038   for n : 0 thru cokltl(5,20) do
00039     assert(homomorphism_bydef_hg(f(n), ramsey_hg(3,2,n+1), schurtriples_hg(n)) = true),
00040   for n : 0 thru cokltl(5,20) do
00041     assert(suphomomorphism_bydef_hg(f(n), ramsey_hg(4,2,n+1), wschurtriples_hg(n)) = true),
00042   true)\$
00043
00044 okltest_hom_ramsey_group_ugrpi(f) := (
00045 for n : 1 thru cokltl(5,20) do (
00046   assert(homomorphism_bydef_hg(f(cyclic_ugrpi(n)), ramsey_hg(3,2,n), grouptriples_ugrp2hg(cyclic_ugrp(n))) = true),
00047   assert(suphomomorphism_bydef_hg(f(cyclic_ugrpi(n)), ramsey_hg(4,2,n), wgrouptriples_ugrp2hg(cyclic_ugrp(n))) = true)
00048   ),
00049   for n : 0 thru cokltl(3,4,5) do (
00050   assert(homomorphism_bydef_hg(f(sym_l_ugrpi(n)), ramsey_hg(3,2,n!), grouptriples_ugrp2hg(sym_l_ugrp(n))) = true),
00051   assert(suphomomorphism_bydef_hg(f(sym_l_ugrpi(n)), ramsey_hg(4,2,n!), wgrouptriples_ugrp2hg(sym_l_ugrp(n))) = true)
00052   ),
00053   true)\$
00054
00055
00056 /* *****************
00057    * Automorphisms *
00058    *****************
00059 */
00060
00061 okltest_auto_pdschur(f) := (
00062   for n : 0 thru cokltl(5,16) do
00063    for x in inv_residues(n+1) do
00064     assert(automorphism_bydef_hg(f(n,x), schurtriples_pd_hg(n)) = true),
00065   true)\$
00066
00067 okltest_auto_pdwschur(f) := (
00068   for n : 0 thru cokltl(5,16) do
00069    for x in inv_residues(n+1) do
00070     assert(automorphism_bydef_hg(f(n,x), wschurtriples_pd_hg(n)) = true),
00071   true)\$
00072
00073
```