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#############################################################################
##
## oper.gd
## Copyright (C) 2014-19 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
# 1. Adding and removing vertices . . .
DeclareOperation("DigraphAddVertex", [IsDigraph]);
DeclareOperation("DigraphAddVertex", [IsDigraph, IsObject]);
DeclareOperation("DigraphAddVertices", [IsDigraph, IsInt]);
DeclareOperation("DigraphAddVertices", [IsDigraph, IsList]);
# 3-arg version of DigraphAddVertices is included for backwards compatibility.
DeclareOperation("DigraphAddVertices", [IsDigraph, IsInt, IsList]);
DeclareOperation("DigraphRemoveVertex", [IsDigraph, IsPosInt]);
DeclareOperation("DigraphRemoveVertices", [IsDigraph, IsList]);
DeclareOperation("DigraphRemoveVerticesNC", [IsDigraph, IsList]);
# 2. Adding, removing, and reversing edges . . .
DeclareOperation("DigraphAddEdge", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphAddEdge", [IsDigraph, IsList]);
DeclareOperation("DigraphAddEdges", [IsDigraph, IsList]);
DeclareOperation("DigraphRemoveEdge", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphRemoveEdge", [IsDigraph, IsList]);
DeclareOperation("DigraphRemoveEdges", [IsDigraph, IsList]);
DeclareOperation("DigraphReverseEdge", [IsDigraph, IsList]);
DeclareOperation("DigraphReverseEdge", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphReverseEdges", [IsDigraph, IsList]);
DeclareOperation("DigraphClosure", [IsDigraph, IsPosInt]);
DeclareOperation("DigraphContractEdge", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphContractEdge", [IsDigraph, IsDenseList]);
# 3. Ways of combining digraphs . . .
DeclareGlobalFunction("DigraphDisjointUnion");
DeclareGlobalFunction("DigraphJoin");
DeclareGlobalFunction("DigraphEdgeUnion");
DeclareGlobalFunction("DigraphCartesianProduct");
DeclareGlobalFunction("DigraphDirectProduct");
DeclareOperation("ModularProduct", [IsDigraph, IsDigraph]);
DeclareOperation("StrongProduct", [IsDigraph, IsDigraph]);
DeclareOperation("ConormalProduct", [IsDigraph, IsDigraph]);
DeclareOperation("HomomorphicProduct", [IsDigraph, IsDigraph]);
DeclareOperation("LexicographicProduct", [IsDigraph, IsDigraph]);
DeclareSynonym("DigraphModularProduct", ModularProduct);
DeclareSynonym("DigraphStrongProduct", StrongProduct);
DeclareSynonym("DigraphConormalProduct", ConormalProduct);
DeclareSynonym("DigraphHomomorphicProduct", HomomorphicProduct);
DeclareSynonym("DigraphLexicographicProduct", LexicographicProduct);
DeclareGlobalFunction("DIGRAPHS_CombinationOperProcessArgs");
DeclareOperation("DIGRAPHS_GraphProduct", [IsDigraph, IsDigraph, IsFunction]);
# 4. Actions . . .
DeclareOperation("OnDigraphs", [IsDigraph, IsPerm]);
DeclareOperation("OnDigraphs", [IsDigraph, IsTransformation]);
DeclareOperation("OnDigraphsNC", [IsDigraph, IsPerm]);
DeclareOperation("OnDigraphsNC", [IsDigraph, IsTransformation]);
DeclareOperation("OnTuplesDigraphs", [IsDigraphCollection, IsPerm]);
DeclareOperation("OnSetsDigraphs", [IsDigraphCollection, IsPerm]);
DeclareOperation("OnMultiDigraphs", [IsDigraph, IsPermCollection]);
DeclareOperation("OnMultiDigraphs", [IsDigraph, IsPerm, IsPerm]);
# 5. Substructures and quotients . . .
DeclareOperation("QuotientDigraph", [IsDigraph, IsList]);
DeclareOperation("InducedSubdigraph", [IsDigraph, IsList]);
# 6. In and out degrees, neighbours, and edges of vertices . . .
DeclareOperation("InDegreeOfVertex", [IsDigraph, IsPosInt]);
DeclareOperation("InDegreeOfVertexNC", [IsDigraph, IsPosInt]);
DeclareOperation("OutDegreeOfVertex", [IsDigraph, IsPosInt]);
DeclareOperation("OutDegreeOfVertexNC", [IsDigraph, IsPosInt]);
DeclareOperation("InNeighboursOfVertex", [IsDigraph, IsPosInt]);
DeclareOperation("InNeighboursOfVertexNC", [IsDigraph, IsPosInt]);
DeclareOperation("OutNeighboursOfVertex", [IsDigraph, IsPosInt]);
DeclareOperation("OutNeighboursOfVertexNC", [IsDigraph, IsPosInt]);
DeclareSynonym("InNeighborsOfVertex", InNeighboursOfVertex);
DeclareSynonym("OutNeighborsOfVertex", OutNeighboursOfVertex);
DeclareOperation("DigraphInEdges", [IsDigraph, IsPosInt]);
DeclareOperation("DigraphOutEdges", [IsDigraph, IsPosInt]);
# 7. Copies of out/in-neighbours
DeclareOperation("OutNeighboursMutableCopy", [IsDigraph]);
DeclareOperation("InNeighboursMutableCopy", [IsDigraph]);
DeclareOperation("AdjacencyMatrixMutableCopy", [IsDigraph]);
DeclareOperation("BooleanAdjacencyMatrixMutableCopy", [IsDigraph]);
DeclareSynonym("OutNeighborsMutableCopy", OutNeighboursMutableCopy);
DeclareSynonym("InNeighborsMutableCopy", InNeighboursMutableCopy);
# 8. IsSomething . . .
DeclareOperation("IsDigraphEdge", [IsDigraph, IsList]);
DeclareOperation("IsDigraphEdge", [IsDigraph, IsInt, IsInt]);
DeclareOperation("IsSubdigraph", [IsDigraph, IsDigraph]);
DeclareOperation("IsUndirectedSpanningTree", [IsDigraph, IsDigraph]);
DeclareOperation("IsUndirectedSpanningForest", [IsDigraph, IsDigraph]);
DeclareOperation("IsMatching", [IsDigraph, IsHomogeneousList]);
DeclareOperation("IsMaximalMatching", [IsDigraph, IsHomogeneousList]);
DeclareOperation("IsMaximumMatching", [IsDigraph, IsHomogeneousList]);
DeclareOperation("IsPerfectMatching", [IsDigraph, IsHomogeneousList]);
DeclareOperation("IsDigraphPath",
[IsDigraph, IsHomogeneousList, IsHomogeneousList]);
DeclareOperation("IsDigraphPath", [IsDigraph, IsList]);
# 9. Connectivity . . .
DeclareOperation("DigraphIsKing", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphKings", [IsDigraph, IsPosInt]);
DeclareOperation("DigraphFloydWarshall",
[IsDigraph, IsFunction, IsObject, IsObject]);
DeclareOperation("DigraphDijkstra",
[IsDigraph, IsPosInt]);
DeclareOperation("DigraphDijkstra",
[IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphConnectedComponent", [IsDigraph, IsPosInt]);
DeclareOperation("DigraphStronglyConnectedComponent", [IsDigraph, IsPosInt]);
DeclareOperation("DigraphPath", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("IteratorOfPaths", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("IteratorOfPaths", [IsList, IsPosInt, IsPosInt]);
DeclareOperation("IteratorOfPathsNC", [IsList, IsPosInt, IsPosInt]);
DeclareOperation("IsReachable", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphLongestDistanceFromVertex", [IsDigraph, IsPosInt]);
DeclareOperation("DigraphRandomWalk", [IsDigraph, IsPosInt, IsInt]);
DeclareOperation("DigraphLayers", [IsDigraph, IsPosInt]);
DeclareAttribute("DIGRAPHS_Layers", IsDigraph, "mutable");
DeclareOperation("DigraphDistanceSet", [IsDigraph, IsPosInt, IsInt]);
DeclareOperation("DigraphDistanceSet", [IsDigraph, IsPosInt, IsList]);
DeclareOperation("DigraphShortestDistance", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphShortestDistance", [IsDigraph, IsList, IsList]);
DeclareOperation("DigraphShortestDistance", [IsDigraph, IsList]);
DeclareOperation("DigraphShortestPath", [IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("DigraphShortestPathSpanningTree", [IsDigraph, IsPosInt]);
DeclareOperation("VerticesReachableFrom", [IsDigraph, IsPosInt]);
DeclareOperation("VerticesReachableFrom", [IsDigraph, IsList]);
DeclareOperation("IsOrderIdeal", [IsDigraph, IsList]);
DeclareOperation("IsOrderFilter", [IsDigraph, IsList]);
DeclareOperation("Dominators", [IsDigraph, IsPosInt]);
DeclareOperation("DominatorTree", [IsDigraph, IsPosInt]);
DeclareOperation("DigraphCycleBasis", [IsDigraph]);
# 10. Operations for vertices . . .
DeclareOperation("PartialOrderDigraphJoinOfVertices",
[IsDigraph, IsPosInt, IsPosInt]);
DeclareOperation("PartialOrderDigraphMeetOfVertices",
[IsDigraph, IsPosInt, IsPosInt]);
[ Dauer der Verarbeitung: 0.20 Sekunden
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