Package sage :: Package modular :: Package modsym :: Module p1list :: Class P1List
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Type P1List

object --+
         |
        P1List


Method Summary
  __init__(...)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature
  __getitem__(x, y)
x.__getitem__(y) <==> x[y]
  __getslice__(x, i, j)
Use of negative indices is not supported.
  __len__(x)
x.__len__() <==> len(x)
  __new__(T, S, ...)
T.__new__(S, ...) -> a new object with type S, a subtype of T
  __repr__(x)
x.__repr__() <==> repr(x)
  apply_I(...)
  apply_S(...)
  apply_T(...)
  index(...)
Returns the index of the class of (u,v) in the fixed list of representatives of P^1(Z/NZ).
  index_and_scalar(...)
Returns the index of the class of (u,v) in the fixed list of representatives of P^1(Z/NZ).
  index_of_normalized_pair(...)
Returns the index of the class of (u,v) in the fixed list of representatives of P^1(Z/NZ).
  list(...)
  N(...)
  normalize(...)
  normalize_with_scalar(...)
normalize_with_scalar(self, int u, int v) INPUT: u, v -- integers, with GCD(u,v,N)=1.
    Inherited from object
  __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
  __setattr__(...)
x.__setattr__('name', value) <==> x.name = value
  __str__(x)
x.__str__() <==> str(x)

Method Details

__init__(...)
(Constructor)

x.__init__(...) initializes x; see x.__class__.__doc__ for signature
Overrides:
__builtin__.object.__init__

__getitem__(x, y)
(Indexing operator)

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

__getslice__(x, i, j)
(Slicling operator)

Use of negative indices is not supported.
Returns:
x[i:j]

__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__

__repr__(x)
(Representation operator)

x.__repr__() <==> repr(x)
Returns:
repr(x)
Overrides:
__builtin__.object.__repr__

index(...)

Returns the index of the class of (u,v) in the fixed list of
representatives of P^1(Z/NZ).
INPUT:
    u, v -- integers, with GCD(u,v,N)=1.
OUTPUT:
    i -- the index of u, v, in the P^1 list.

index_and_scalar(...)

Returns the index of the class of (u,v) in the fixed list of
representatives of P^1(Z/NZ).
INPUT:
    u, v -- integers, with GCD(u,v,N)=1.
OUTPUT:
    i -- the index of u, v, in the P^1 list.
    s -- scalar that transforms normalized form to u,v

index_of_normalized_pair(...)

Returns the index of the class of (u,v) in the fixed list of
representatives of P^1(Z/NZ).
INPUT:
    u, v -- integers, with GCD(u,v,N)=1 normalized so they lie in the list.
OUTPUT:
    i -- the index of u, v, in the P^1 list.

normalize_with_scalar(...)

normalize_with_scalar(self, int u, int v)

INPUT:
    u, v -- integers, with GCD(u,v,N)=1.
OUTPUT:
    uu, vv -- integers of *normalized* rep
    ss -- scalar such that (ss*uu, ss*vv) = (u,v) mod N

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