This is a short description of the magma code that imports the database of all rotary maps (orientable reflexible, non-orientable reflexible and chiral) of genus between 2 and 1501 (for the orienatble maps) and 3 and 1502 (for non-orientable maps).
load "ImportOrientableReflexibleMapsGenus1501.mgm";
Requires also: OrientableReflexibleGenus1501-rels.txt, OrientableReflexibleGenus1501-data.csv
Loads the the reflexible (regular) maps on orientable surfaces of genus \(g, 2\le g \le 1501\). For now, only the following commands are available.
OrientableReflexibleMapOfName(ID)
For ID being one of the names of an orientable reflexible maps (such as "R14.12"), constructs a finitely presented group on 3 generators: R,S and T with T inverting R and S. Here R is intepretated as a rotation around a face and S as a rotation around an incident vertex. If "*" is added to the ID, then the dual is returned.
IDsOfReflexibleOrientableMapsOfGenus(g)
For a positive integer g > 2, returns IDs for all non-orientable regular maps up to genus g, including the IDs that end with "*". When these IDs are passed to NonOrientableMapOfName(ID), all maps of that genus are returned (including the duals). The IDs have the form "R<g>.<k>" where g is the genus of the map and k is the index of that map within all of that genus (up to duals). The ID of the dual of the map "R<g>.<k>" is denoted by "R<g>.<k>*".
NumberOfReflexibleOrientableMapsOfGenus(g)
Returns the number of relfexible orientable of genus g, for 2 \le g \le 1501.
GenusOfReflexibleOrientableMap(ID)
For ID being one of the names of an orientable reflexible maps (such as "R14.12"), returns the genus of that map.
TypeOfReflexibleOrientableMap(ID)
Returns the triple [p,q,r] where p is the face-length, q is the valence and r is the lingth of the Petrie walk.
NumberOfVerticesOfReflexibleOrientableMap(ID)
Returns the number of vertices of the map with the name ID.
NumberOfEdgesOfReflexibleOrientableMap(ID)
Returns the number of edges of the map with the name ID.
NumberOfFacesOfReflexibleOrientableMap(ID)
Returns the number of faces of the map with the name ID.
MultiplicityOfReflexibleOrientableMap(ID)
Returns the pair [mV,mF] where mV is the vertex-multiplicity (i.e. the number of edges between two adjacent vertices) and mF is mV in the dual (that is, the number of edges shared by two adjacent faces).
WilsonInvarianceOfReflexibleOrientableMap(ID)
Returns one of the strings "I", "I+D", "I+P", "I+DPD", "I+DP+PD", "All", meaining that the map with the name being ID is invariant under identiti only, duality, Petrie duality, Opposite, PetrieDual or all of the Wilson operations on the maps.
SizeOfHoleClassOfReflexibleOrientableMap(ID)
Given the name ID of a reflexible orientable map M of valence q, returns the number of multipliers t in Z_q^* such that the t-hole-map of M is isomorphic to M.
load "ImportNonOrientableMapsGenus1502.mgm";
Requires also: NonorientableGenus1502-rels.txt, NonorientableGenus1502-data.csv
Loads the regular (rotary) maps on non-orientable surfaces of genus \(g, 3\le g \le 1502\). The following commands become available after loading:
NonOrientableMapOfName(ID)
For ID being one of the names of a non-orientable reflexible maps (such as "N64.4"), constructs a finitely presented group on 3 generators: R,S and T with T inverting R and S, R rotating around a face and S rotatin around a vertex. If "*" is added to the ID, then the dual is returned.
IDsOfNonOrientableMapsOfGenus(g)
For a positive integer g > 2, returns IDs for all non-orientable regular maps up to genus g, including the IDs that end with "*". When these IDs are passed to NonOrientableMapOfName(ID), all maps on that genus are returned (including the duals).
NumberOfNonOrientableMapsOfGenus(g)
Returns the number of non-orientable regular maps of genus g.
GenusOfNonOrientableMap(ID)
Returns the genus of the non-orientable regular map with the name ID.
TypeOfNonOrientableMap(ID)
Returns the triple [p,q,r] where p is the face-length, q is the valence and r is the lingth of the Petrie walk.
NumberOfVerticesOfNonOrientableMap(ID)
Returns the number of vertices of the non-orientable regular map with the name ID.
NumberOfEdgesOfNonOrientableMap(ID)
Returns the number of edges of the non-orientable regular map with the name ID.
NumberOfFacesOfNonOrientableMap(ID)
Returns the number of faces of the non-orientable regular map with the name ID.
MultiplicityOfNonOrientableMap(ID)
Returns the pair [mV,mF] where mV is the vertex-multiplicity (i.e. the number of edges between two adjacent vertices) and mF is mV in the dual.
WilsonInvarianceOfNonOrientableMap(ID)
Returns one of the strings "I", "I+D", "I+P", "I+DPD", "I+DP+PD", "All", meaining that the map with the name being ID is invariant under identiti only, duality, Petrie duality, Opposite, PetrieDual or all of the Wilson operations on the maps.
SizeOfHoleClassOfNonOrientableMap(ID)
The number of the maps that are a j-hole of the map with ID for some j coprime to the valence.
load "ImportChiralMapsGenus1501.mgm";
Requires also files: ChiralGenus1501-rels.txt, ChiralGenus1501-data.csv
Loads chiral rotary maps on orientable surfaces of genus \(g, 2\le g \le 1501\). The following commands become available upon loading:
ChiralMapOfName(ID)
Given an ID of a chiral map (say "C10.2" or "C10.2*"), returns a FPgroup G generated by two generators R:=G.1 and S:=G.2, where R is a rotation about the centre of a face and S is a rotation around a vertex. The symbol "*" in the ID indicates that the map is the dual of the one whose ID has no "*".
IDsOfChiralMapsOfGenus(g)
For a given genus g, returns all the IDs of the chiral maps of genus g.
NumberOfChiralMapsOfGenus(g)
Returns the number of chiral maps of genus g.
GenusOfChiralMap(ID)
Returns the genus of the map with the name being ID.
TypeOfChiralMap(ID)
Returns [p,q,r] of the map with the name being ID.
NumberOfVerticesOfChiralMap(ID)
Returns the number of vertices of the map with the name being ID.
NumberOfEdgesOfChiralMap(ID)
Returns the edges of vertices of the map with the name being ID.
NumberOfFacesOfChiralMap(ID)
Returns the number of faces of the map with the name being ID.
MultiplicityOfChiralMap(ID)
Returns the pair [mV,mF] where mV is the vertex-multiplicity (i.e. the number of edges between two adjacent vertices) and mF is mV in the dual.
WilsonInvarianceOfChiralMap(ID)
Returns one of the strings: Four (invariant under none), SD, MSD. depending on which "Wilson operations" it is invariant under.
SizeOfHoleClassOfChiralMap(ID)
The number of the maps that are a j-hole of the map with ID for some j coprime to the valence.