Add Jan's files

_data/participants.yml

@@ -7,6 +7,11 @@
 
 - name: Jan De Beule
   affiliation: Ghent University
+  links:
+    "slides": ../talks/jdebeule_gapdays_fall2015.pdf
+    "demo 1": ../talks/demo1.g
+    "demo 2": ../talks/demo2.g
+    "demo 3": ../talks/demo3.g
 
 - name: Martin Bies
   affiliation: Institute for Theoretical Physics, Heidelberg

talks/demo1.g

@@ -0,0 +1,50 @@
+q := 25;
+pg := PG(2,q);
+pts := Points(pg);
+List(pts);
+p := Random(pts);
+lines := List(Lines(pg));
+l := Random(lines);
+p * l;
+Lines(p);
+List(last);
+Points(l);
+List(last);
+
+conic := ParabolicQuadric(2,q);
+EquationForPolarSpace(conic);
+pts := Points(conic);
+pts := List(pts);
+
+group := CollineationGroup(pg);
+g := Random(group);
+p^g;
+OnProjSubspaces(l,g);
+
+Stabilizer(group,pts[1],\^);
+time;
+FiningStabiliser(group,pts[1]);
+time;
+
+stab := FiningSetwiseStabiliser(group,pts);
+CollineationGroup(conic);
+
+mat := IdentityMat(3,GF(q));
+form := QuadraticFormByMatrix(mat,GF(q));
+conic2 := PolarSpace(form);
+
+EquationForPolarSpace(conic2);
+pts := List(Points(conic2));
+p := Random(pts);
+
+stab := FiningSetwiseStabiliser(group,pts);
+CollineationGroup(conic2);
+
+ppts := List(Points(pg));;
+orbs := FiningOrbits(stab,ppts);
+o1 := orbs[1];
+p := Random(o1);
+List(Lines(p),x->Number(pts,y->y in x));
+Collected(last);
+
+

talks/demo2.g

@@ -0,0 +1,20 @@
+q := 2;
+ps := HermitianPolarSpace(4,q^2);
+EquationForPolarSpace(ps);
+CategoriesOfObject(ps);
+group := CollineationGroup(ps);
+graph := IncidenceGraph(ps);;
+Diameter(graph);
+Girth(graph);
+
+adj := function(x,y)
+return ProjectiveDimension(Meet(x,y))=-1;
+end;
+
+lines := AsList(Lines(ps));;
+
+graph := Graph(group,lines,\^,adj,true);;
+
+size := q^5+1;
+cliques := CompleteSubgraphs(graph,size);
+

talks/demo3.g

@@ -0,0 +1,14 @@
+LoadPackage( "AtlasRep" );
+titsgroup:=AtlasGroup("2F4(2)'");
+g1:=AtlasSubgroup(titsgroup,3);
+g2:=AtlasSubgroup(titsgroup,5);
+conj:=ConjugacyClassSubgroups(titsgroup,g1);;
+ # Now look for the conjugate of g1 with maximal intersection
+g1:=First(conj, sg -> Size(Intersection(sg,g2))=2048);
+cg:=CosetGeometry(titsgroup,[g1,g2]);;
+Rank2Parameters(cg);
+[ [ 8, 8, 8 ], [ 2, 1755 ], [ 4, 2925 ] ]
+pts := Set(ElementsOfIncidenceStructure(cg,1));;
+lines := Set(ElementsOfIncidenceStructure(cg,2));;
+gp := GeneralisedPolygonByElements(pts,lines,\*,titsgroup,OnCosetGeometryElement);
+