Merge branch 'pr-258' into devel

* pr-258:
  Added primitive collections for fans to Convex

Author: mohamed-barakat

Convex/examples/fans.g

@@ -35,8 +35,10 @@ RaysInMaximalCones( F );
 IsRegularFan( F );
 IsComplete( F );
 IsSmooth( F );
+PrimitiveCollections( F );
 F1 := MaximalCones( F )[ 1 ];
 DualCone( F1 );
 RayGenerators( F1 );
 F2 := StarSubdivisionOfIthMaximalCone( F, 1 );
-IsSmooth( F2 );
+IsSmooth( F2 );
+PrimitiveCollections( F2 );

Convex/gap/Fan.gd

@@ -84,6 +84,19 @@ DeclareAttribute( "MaximalCones",
 DeclareAttribute( "FVector",
                   IsFan );
 
+##  <#GAPDoc Label="PrimitiveCollections">
+##  <ManSection>
+##    <Attr Arg="fan" Name="PrimitiveCollections"/>
+##    <Returns>a list of lists</Returns>
+##    <Description>
+##      Returns the primitive collections of the fan <A>fan</A> as a list of lists.
+##    </Description>
+##  </ManSection>
+##  <#/GAPDoc>
+##
+DeclareAttribute( "PrimitiveCollections",
+                  IsFan );
+
 ####################################
 ##
 ## Properties

Convex/gap/Fan.gi

@@ -334,6 +334,60 @@ InstallMethod( FVector,
 
 end );
 
+##
+InstallMethod( PrimitiveCollections,
+               "for fans",
+               [ IsFan ],
+
+  function( fan )
+    local rays, max_cones, facets, all_points, d_max, primitive_collections, d, checked, facet,
+         I_minus_j, scanner, j, I;
+
+    # collect data of the fan
+    rays := RayGenerators( fan );
+    max_cones := MaximalCones( fan );
+    facets := List( [ 1 .. Length( max_cones ) ],
+                        i -> List( RayGenerators( max_cones[ i ] ), k -> Position( rays, k ) ) );
+    all_points := [ 1 .. Length( rays ) ];
+    d_max := Maximum( List( facets, i -> Length( i ) ) ) + 1;
+
+    # identify and return the primitive collections
+    primitive_collections := [];
+    for d in [ 1 .. d_max ] do
+        checked := [];
+        for facet in facets do
+            for I_minus_j in Combinations( facet, d ) do
+                scanner := Difference( all_points, Flat( I_minus_j ) );
+                for j in scanner do
+                    I := Concatenation( I_minus_j, [ j ] );
+
+                    if not I in checked then
+
+                        Add( checked, I );
+
+                        # (1) I is contained in the primitive collections iff it is not contained in any facet
+                        if ForAll( [ 1 .. Length( facets ) ],
+                                            i -> not IsSubsetSet( facets[ i ], I ) ) then
+
+                            # (2) I is generator of the primitive collections iff
+                            # primitive_collections does not contain a "smaller" generator
+                            if ForAll( [ 1 .. Length( primitive_collections ) ],
+                                            i -> not IsSubsetSet( I, primitive_collections[i] ) ) then
+
+                                # then add this new generator
+                                Append( primitive_collections, [ I ] );
+
+                            fi;
+                        fi;
+                    fi;
+                od;
+            od;
+        od;
+    od;
+    return primitive_collections;
+
+end );
+
 ####################################
 ##
 ## Properties