12.6.1.1 P1List Objects

class P1List
Instances of class P1List have the following methods (in addition to inherited methods and special methods):

apply_I,$  $ apply_S,$  $ apply_T,$  $ index,$  $ index_and_scalar,$  $ index_of_normalized_pair,$  $ list,$  $ N,$  $ normalize,$  $ normalize_with_scalar

Further documentation:

index( )

Returns the index of the class of $ (u,v)$ in the fixed list of representatives of $ \mathbf{P}^1(\mathbf{Z}/N\mathbf{Z})$ .

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 $ PP^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 $ \mathbf{P}^1(\mathbf{Z}/N\mathbf{Z})$ .

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

Instances of class P1List also have the following special methods:

__getitem__,$  $ __getslice__,$  $ __len__,$  $ __repr__

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