27.8 Heilbronn matrix computation

Module: sage.modular.modsym.heilbronn

Module-level Functions

HeilbronnCremonaList( int p)

The Heilbronn matrices of determinant p, as defined by Cremona.

HeilbronnMerelList( int n)

Set of Heilbronn matrices of determinant n, as defined by Merel.

Class: Heilbronn

class Heilbronn

Functions: apply,$  $ to_list

apply( self, int u, int v, int N)

Return a list of pairs ((c,d),m), which is obtained as follows: 1) Compute the images (a,b) of the vector (u,v) (mod N) acted on by each of the HeilbronnCremona matrices in self. 2) Reduce each (a,b) to canonical form (c,d) using p1normalize 3) Sort. 4) Create the list ((c,d),m), where m is the number of times that (c,d) appears in the list created in steps 1-3 above. Note that the pairs ((c,d),m) are sorted lexicographically by (c,d).

Special Functions: __getitem__,$  $ __len__,$  $ _initialize_list

Class: HeilbronnCremona

class HeilbronnCremona

Functions: p

Special Functions: __getitem__,$  $ __repr__,$  $ _initialize_list

Class: HeilbronnMerel

class HeilbronnMerel

Functions: n

Special Functions: __repr__,$  $ _initialize_list

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