Home | Trees | Index | Help |
|
---|
Package sage :: Package modular :: Package modsym :: Module manin_symbols :: Class ManinSymbolList_character |
|
ManinSymbolList
--+
|
ManinSymbolList_character
List of Manin Symbols with character. ManinSymbolList_character(character, weight): INPUT: character -- a dirichlet character weight -- integer weight >= 2 EXAMPLE: >>> from sage.modular.dirichlet import * >>> eps = DirichletGroup(4).gen(0) >>> m = ManinSymbolList_character(eps,2); m Manin Symbol List of weight 2 for Gamma1(4) with character [-1] >>> m.list() [(0, 0, 1), (0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 1, 3), (0, 2, 1)]
Method Summary | |
---|---|
__init__(self,
character,
weight)
| |
__repr__(self)
| |
Apply the matrix m=[a,b,c,d] to the j-th Manin symbol. | |
apply_I(self,
j)
| |
apply_S(self,
j)
| |
apply_T(self,
j)
| |
apply_TT(self,
j)
| |
character(self)
| |
Return the index into the list of Manin symbols of x. | |
level(self)
| |
manin_symbol(self,
i)
| |
normalize(self,
x)
| |
Inherited from ManinSymbolList | |
| |
| |
| |
|
Method Details |
---|
apply(self, j, m)Apply the matrix m=[a,b,c,d] to the j-th Manin symbol. INPUT: j -- integer m = [a, b, c, d] a list of 4 integers. OUTPUT: a list of pairs (j, alpha_i), where each alpha_i is an integer, j is an integer (the j-th sage symbol), and the sum alpha_i*x_i is the image of self under the right action of the matrix [a,b;c,d]. Here the right action of g=[a,b;c,d] on a Manin symbol [P(X,Y),(u,v)] is [P(aX+bY,cX+dY),(u,v)*g]. EXAMPLES: >>> from sage.modular.dirichlet import * >>> eps = DirichletGroup(4).gen(0) >>> m = ManinSymbolList_character(eps,4) >>> m[6] (1, 0, 1) >>> m.apply(4, [1,0,0,1]) [(4, 1)] >>> m.apply(1, [-1,0,0,1]) [(1, -1)] |
index(self, x)Return the index into the list of Manin symbols of x. If x is not in the list, then this function returns -1. INPUT: x -- element of sage symbols list, which need not be normalized OUTPUT: int -- the index of the Manin symbol equivalent to (i,u,v). |
Home | Trees | Index | Help |
|
---|
Generated by Epydoc 2.1 on Mon May 9 17:57:02 2005 | http://epydoc.sf.net |