Module: sage.modular.modsym.p1list
Module-level Functions
n) |
N, u, v) |
N, u, v) |
p1_normalize_int(N, u, v):
Computes the canonical representative of
equivalent
to
along with a transforming scalar.
INPUT: N -- an integer u -- an integer v -- an integer OUTPUT: If gcd(u,v,N) = 1, then returns uu -- an integer vv -- an integer ss -- an integer such that (ss*uu, ss*vv) is equivalent to (u,v) mod N and if gcd(u,v,N) != 1, returns 0, 0, 0
N, u, v) |
p1_normalize_llong(N, u, v):
Computes the canonical representative of
equivalent
to
along with a transforming scalar.
INPUT: N -- an integer u -- an integer v -- an integer OUTPUT: If gcd(u,v,N) = 1, then returns uu -- an integer vv -- an integer ss -- an integer such that (ss*uu, ss*vv) is equivalent to (u,v) mod N and if gcd(u,v,N) != 1, returns 0, 0, 0
int N) |
int N) |
p1list_int(int N):
Make a list of the normalized elements of
.
int N) |
p1list_llong(int N):
Make a list of the normalized elements of
.
) |
Return (True,i) where i is such that v[i] == x if there is such an i, or (False,j) otherwise, where j is the position that a should be inserted so that v remains sorted.
INPUT: v -- a list, which is assumed sorted x -- Python object OUTPUT: bool, int
Class: export
Class: P1List
Functions: apply_I,
apply_S,
apply_T,
index,
index_and_scalar,
index_of_normalized_pair,
list,
N,
normalize,
normalize_with_scalar
self, int u, int v) |
Returns the index of the class of
in the fixed list of
representatives of
.
INPUT: u, v -- integers, with GCD(u,v,N)=1. OUTPUT: i -- the index of u, v, in the P^1 list.
self, int u, int v) |
Returns the index of the class of
in the fixed list of
representatives of
.
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
self, int u, int v) |
Returns the index of the class of
in the fixed list of
representatives of
.
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.
self, int u, int v) |
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
Special Functions: __getitem__,
__getslice__,
__len__,
__reduce__,
__repr__
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