Home | Trees | Index | Help |
|
---|
Package sage :: Package modular :: Package modsym :: Module manin_symbols :: Class ManinSymbolList_gamma1 |
|
ManinSymbolList
--+
|
ManinSymbolList_gamma1
List of Manin symbols for Gamma0(N).
EXAMPLE:>>> m = ManinSymbolList_gamma0(5,2); m Manin Symbol List of weight 2 for Gamma0(5) >>> m.list() [(0, 0, 1), (0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 1, 3), (0, 1, 4)] >>> m = ManinSymbolList_gamma0(6,4); m Manin Symbol List of weight 4 for Gamma0(6) >>> len(m) 36
Method Summary | |
---|---|
__init__(self,
level,
weight)
| |
__repr__(self)
| |
Apply the matrix m=[a,b,c,d] to the j-th Manin symbol. | |
apply_I(self,
j)
| |
Apply 2x2 matrix J = [-1,0,0,-1]. | |
apply_S(self,
j)
| |
apply_T(self,
j)
| |
apply_TT(self,
j)
| |
level(self)
| |
manin_symbol(self,
i)
| |
normalize(self,
x)
| |
Inherited from ManinSymbolList | |
| |
| |
Return the index into the list of Manin symbols of x. | |
| |
|
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]. |
apply_J(self, j)Apply 2x2 matrix J = [-1,0,0,-1]. |
Home | Trees | Index | Help |
|
---|
Generated by Epydoc 2.1 on Mon Jun 20 15:43:22 2005 | http://epydoc.sf.net |