Package sage :: Package modular :: Package modsym :: Module heilbronn :: Class Heilbronn
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Type Heilbronn

object --+
         |
        Heilbronn

Known Subclasses:
HeilbronnCremona, HeilbronnMerel

Method Summary
  __getitem__(x, y)
x.__getitem__(y) <==> x[y]
  __len__(x)
x.__len__() <==> len(x)
  __new__(T, S, ...)
T.__new__(S, ...) -> a new object with type S, a subtype of T
  apply(...)
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.
  to_list(...)
    Inherited from object
  __init__(...)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature
  __delattr__(...)
x.__delattr__('name') <==> del x.name
  __getattribute__(...)
x.__getattribute__('name') <==> x.name
  __hash__(x)
x.__hash__() <==> hash(x)
  __reduce__(...)
helper for pickle
  __reduce_ex__(...)
helper for pickle
  __repr__(x)
x.__repr__() <==> repr(x)
  __setattr__(...)
x.__setattr__('name', value) <==> x.name = value
  __str__(x)
x.__str__() <==> str(x)

Method Details

__getitem__(x, y)
(Indexing operator)

x.__getitem__(y) <==> x[y]
Returns:
x[y]

__len__(x)
(Length operator)

x.__len__() <==> len(x)
Returns:
len(x)

__new__(T, S, ...)

T.__new__(S, ...) -> a new object with type S, a subtype of T
Returns:
a new object with type S, a subtype of T
Overrides:
__builtin__.object.__new__

apply(...)

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).

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