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#############################################################################
##
#W workspaces/load-workspace.tst
#Y Copyright (C) 2016 Michael Young
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
## This file, together with save-workspace.tst, tests the ability to save
## and load workspaces which include Semigroups objects. Objects should be
## created and stored in save-workspace.tst, and then loaded and tested in
## load-workspace.tst to ensure that they work correctly after being saved.
##
#############################################################################
# DO NOT USE LOCAL VARIABLES @local in this file!
# Set up testing environment
gap> START_TEST("Semigroups package: workspaces/load-workspace.tst");
gap> SEMIGROUPS.StartTest();
#############################################################################
## Test objects that were created in save-workspace.tst, using the same
## variable names. Give the test blocks the same headers as in the previous
## file.
#############################################################################
# Congruences from libsemigroups
gap> NrEquivalenceClasses(cong);
4
gap> [Matrix(IsBooleanMat, [[0, 1], [1, 0]]),
> Matrix(IsBooleanMat, [[0, 1], [1, 0]])] in cong;
true
gap> [Matrix(IsBooleanMat, [[0, 1], [1, 1]]),
> Matrix(IsBooleanMat, [[0, 1], [1, 0]])] in cong;
true
gap> [Matrix(IsBooleanMat, [[0, 0], [0, 0]]),
> Matrix(IsBooleanMat, [[0, 1], [1, 0]])] in cong;
false
gap> EquivalenceRelationCanonicalLookup(cong);
[ 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 4, 3 ]
# Semigroups from libsemigroups
gap> Size(T);
9
gap> NrIdempotents(T);
8
gap> Factorization(T, x);
[ 4 ]
gap> D := DClass(T, x);;
gap> id := Idempotents(D);
[ Matrix(IsBooleanMat, [[0, 1], [0, 1]]),
Matrix(IsBooleanMat, [[1, 1], [0, 0]]),
Matrix(IsBooleanMat, [[1, 1], [1, 1]]),
Matrix(IsBooleanMat, [[1, 0], [0, 0]]),
Matrix(IsBooleanMat, [[1, 0], [1, 0]]) ]
gap> ForAll(id, x -> x in T);
true
gap> Size(U);
9
gap> NrIdempotents(U);
8
gap> xx := U.1 * U.2 * U.3 ^ 5 * U.2 * U.3;
Transformation( [ 2, 2, 4, 4 ] )
gap> Factorization(U, xx);
[ 4 ]
gap> DD := DClass(U, xx);;
gap> idd := Idempotents(DD);
[ Transformation( [ 1, 1, 4, 4 ] ), Transformation( [ 2, 2, 4, 4 ] ),
Transformation( [ 3, 3, 3 ] ), Transformation( [ 1, 1, 1 ] ),
Transformation( [ 2, 2, 2 ] ) ]
gap> ForAll(idd, x -> x in U);
true
# Bipartitions
gap> y;
<bipartition: [ 1, 3 ], [ 2, 4, -1 ], [ 5, 6, -2, -3 ], [ -4, -5 ], [ -6 ]>
gap> IsBipartition(y);
true
gap> DegreeOfBipartition(y);
6
gap> RankOfBipartition(y);
2
gap> NrTransverseBlocks(y);
2
gap> NrLeftBlocks(y);
3
gap> NrRightBlocks(y);
4
gap> NrBlocks(y);
5
gap> LeftBlocks(y);
<blocks: [ 1, 3 ], [ 2*, 4* ], [ 5*, 6* ]>
gap> RightBlocks(y);
<blocks: [ 1* ], [ 2*, 3* ], [ 4, 5 ], [ 6 ]>
gap> IntRepOfBipartition(y);
[ 1, 2, 1, 2, 3, 3, 2, 3, 3, 4, 4, 5 ]
gap> LeftProjection(y);
<bipartition: [ 1, 3 ], [ 2, 4, -2, -4 ], [ 5, 6, -5, -6 ], [ -1, -3 ]>
gap> RightProjection(y);
<bipartition: [ 1, -1 ], [ 2, 3, -2, -3 ], [ 4, 5 ], [ 6 ], [ -4, -5 ],
[ -6 ]>
gap> One(y);
<block bijection: [ 1, -1 ], [ 2, -2 ], [ 3, -3 ], [ 4, -4 ], [ 5, -5 ],
[ 6, -6 ]>
gap> IsBlockBijection(y);
false
gap> IsUniformBlockBijection(y);
false
gap> IsTransBipartition(y);
false
gap> IsDualTransBipartition(y);
false
gap> IsPermBipartition(y);
false
gap> IsPartialPermBipartition(y);
false
# Blocks
gap> b;
<blocks: [ 1*, 3* ], [ 2, 4, 7 ], [ 5*, 6*, 8*, 9* ], [ 10* ]>
gap> ProjectionFromBlocks(b);
<bipartition: [ 1, 3, -1, -3 ], [ 2, 4, 7 ], [ 5, 6, 8, 9, -5, -6, -8, -9 ],
[ 10, -10 ], [ -2, -4, -7 ]>
gap> NrBlocks(b);
4
gap> RankOfBlocks(b);
3
gap> NrTransverseBlocks(b);
3
gap> DegreeOfBlocks(b);
10
gap> AsDigraph(b);
<immutable digraph with 10 vertices, 23 edges>
gap> CanonicalBlocks(b);
<blocks: [ 1* ], [ 2*, 3* ], [ 4*, 5*, 6*, 7* ], [ 8, 9, 10 ]>
# No point unbinding local variables, since this will only ever be run in a
# workspace
gap> SEMIGROUPS.StopTest();
gap> STOP_TEST("Semigroups package: workspaces/load-workspace.tst");
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