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#############################################################################
##
#W reesmat.gd GAP library J. D. Mitchell
##
#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file contains the declarations for Rees Matrix semigroups
# Elements...
DeclareCategory( "IsReesMatrixSemigroupElement", IsAssociativeElement);
DeclareCategory( "IsReesZeroMatrixSemigroupElement", IsAssociativeElement);
DeclareCategoryCollections( "IsReesMatrixSemigroupElement");
DeclareCategoryCollections( "IsReesZeroMatrixSemigroupElement");
DeclareGlobalFunction( "RMSElement" );
DeclareSynonym( "ReesMatrixSemigroupElement", RMSElement);
DeclareSynonym( "ReesZeroMatrixSemigroupElement", RMSElement);
DeclareOperation("ELM_LIST", [IsReesMatrixSemigroupElement, IsPosInt]);
DeclareOperation("ELM_LIST", [IsReesZeroMatrixSemigroupElement, IsPosInt]);
DeclareProperty("IsOne", IsReesMatrixSemigroupElement);
DeclareProperty("IsOne", IsReesZeroMatrixSemigroupElement);
# for backwards compatibility...
DeclareOperation("RowOfReesMatrixSemigroupElement",
[IsReesMatrixSemigroupElement]);
DeclareOperation("RowOfReesZeroMatrixSemigroupElement",
[IsReesZeroMatrixSemigroupElement]);
DeclareOperation("ColumnOfReesMatrixSemigroupElement",
[IsReesMatrixSemigroupElement]);
DeclareOperation("ColumnOfReesZeroMatrixSemigroupElement",
[IsReesZeroMatrixSemigroupElement]);
DeclareOperation("UnderlyingElementOfReesMatrixSemigroupElement",
[IsReesMatrixSemigroupElement]);
DeclareOperation("UnderlyingElementOfReesZeroMatrixSemigroupElement",
[IsReesZeroMatrixSemigroupElement]);
# Semigroups...
DeclareSynonymAttr("IsReesMatrixSubsemigroup",
IsSemigroup and IsReesMatrixSemigroupElementCollection);
DeclareSynonymAttr("IsReesZeroMatrixSubsemigroup",
IsSemigroup and IsReesZeroMatrixSemigroupElementCollection);
DeclareProperty("IsReesMatrixSemigroup", IsSemigroup);
DeclareProperty("IsReesZeroMatrixSemigroup", IsSemigroup);
InstallTrueMethod(IsReesMatrixSemigroup,
IsReesMatrixSubsemigroup and IsWholeFamily);
InstallTrueMethod(IsReesZeroMatrixSemigroup,
IsReesZeroMatrixSubsemigroup and IsWholeFamily);
DeclareOperation("ReesMatrixSemigroup", [IsSemigroup, IsRectangularTable]);
DeclareOperation("ReesZeroMatrixSemigroup", [IsSemigroup, IsDenseList]);
DeclareOperation( "GeneratorsOfReesMatrixSemigroup",
[IsReesMatrixSubsemigroup, IsList, IsSemigroup, IsList]);
DeclareGlobalFunction( "GeneratorsOfReesMatrixSemigroupNC");
DeclareOperation( "ReesMatrixSubsemigroup",
[IsReesMatrixSubsemigroup, IsList, IsSemigroup, IsList]);
DeclareGlobalFunction("ReesMatrixSubsemigroupNC");
DeclareOperation( "GeneratorsOfReesZeroMatrixSemigroup",
[IsReesZeroMatrixSubsemigroup, IsList, IsSemigroup, IsList]);
DeclareGlobalFunction( "GeneratorsOfReesZeroMatrixSemigroupNC");
DeclareOperation( "ReesZeroMatrixSubsemigroup",
[IsReesZeroMatrixSubsemigroup, IsList, IsSemigroup, IsList]);
DeclareGlobalFunction("ReesZeroMatrixSubsemigroupNC");
DeclareAttribute("Matrix", IsReesMatrixSubsemigroup);
DeclareAttribute("Matrix", IsReesZeroMatrixSubsemigroup);
DeclareSynonymAttr("MatrixOfReesMatrixSemigroup", Matrix);
DeclareSynonymAttr("MatrixOfReesZeroMatrixSemigroup", Matrix);
DeclareAttribute("Rows", IsReesMatrixSubsemigroup);
DeclareAttribute("Rows", IsReesZeroMatrixSubsemigroup);
DeclareSynonymAttr("RowsOfReesMatrixSemigroup", Rows);
DeclareSynonymAttr("RowsOfReesZeroMatrixSemigroup", Rows);
DeclareAttribute("Columns", IsReesMatrixSubsemigroup);
DeclareAttribute("Columns", IsReesZeroMatrixSubsemigroup);
DeclareSynonymAttr("ColumnsOfReesMatrixSemigroup", Columns);
DeclareSynonymAttr("ColumnsOfReesZeroMatrixSemigroup", Columns);
DeclareAttribute("UnderlyingSemigroup", IsReesMatrixSubsemigroup);
DeclareAttribute("UnderlyingSemigroup", IsReesZeroMatrixSubsemigroup);
DeclareSynonym("UnderlyingSemigroupOfReesMatrixSemigroup",
UnderlyingSemigroup);
DeclareSynonym("UnderlyingSemigroupOfReesZeroMatrixSemigroup",
UnderlyingSemigroup);
# Other
DeclareAttribute("AssociatedReesMatrixSemigroupOfDClass", IsGreensDClass);
DeclareAttribute("IsomorphismReesMatrixSemigroup", IsSemigroup);
# undocumented
DeclareAttribute("ReesMatrixSemigroupOfFamily", IsFamily);
DeclareAttribute("TypeReesMatrixSemigroupElements",
IsReesMatrixSubsemigroup);
DeclareAttribute("TypeReesMatrixSemigroupElements",
IsReesZeroMatrixSubsemigroup);
DeclareOperation("ZeroOp", [IsReesMatrixSemigroupElement]);
DeclareOperation("ZeroOp", [IsReesZeroMatrixSemigroupElement]);
DeclareOperation("MultiplicativeZeroOp", [IsReesMatrixSemigroup]);
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