Coverage for local/lib/python2.7/site-packages/sage/modular/hecke/degenmap.py : 62%
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""" Degeneracy maps """ from __future__ import absolute_import
#***************************************************************************** # Sage: System for Algebra and Geometry Experimentation # # Copyright (C) 2005 William Stein <wstein@gmail.com> # # Distributed under the terms of the GNU General Public License (GPL) # # This code is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # General Public License for more details. # # The full text of the GPL is available at: # # http://www.gnu.org/licenses/ #*****************************************************************************
from . import morphism
class DegeneracyMap(morphism.HeckeModuleMorphism_matrix): """ A degeneracy map between Hecke modules of different levels.
EXAMPLES:
We construct a number of degeneracy maps::
sage: M = ModularSymbols(33) sage: d = M.degeneracy_map(11) sage: d Hecke module morphism degeneracy map corresponding to f(q) |--> f(q) defined by the matrix [ 1 0 0] [ 0 0 1] [ 0 0 -1] [ 0 1 -1] [ 0 0 1] [ 0 -1 1] [-1 0 0] [-1 0 0] [-1 0 0] Domain: Modular Symbols space of dimension 9 for Gamma_0(33) of weight ... Codomain: Modular Symbols space of dimension 3 for Gamma_0(11) of weight ... sage: d.t() 1 sage: d = M.degeneracy_map(11,3) sage: d.t() 3
The parameter d must be a divisor of the quotient of the two levels::
sage: d = M.degeneracy_map(11,2) Traceback (most recent call last): ... ValueError: The level of self (=33) must be a divisor or multiple of level (=11), and t (=2) must be a divisor of the quotient.
Degeneracy maps can also go from lower level to higher level::
sage: M.degeneracy_map(66,2) Hecke module morphism degeneracy map corresponding to f(q) |--> f(q^2) defined by the matrix [ 2 0 0 0 0 0 1 0 0 0 1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 -1] [ 0 0 1 -1 0 -1 1 0 -1 2 0 0 0 -1 0 0 -1 1 2 -2 0 0 0 -1 1] [ 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 -1 1 0 0 -1 1 0 0 0] [ 0 0 0 0 0 0 0 0 0 2 -1 0 0 1 0 0 -1 1 0 0 1 0 -1 -1 1] [ 0 -1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 -1 0 0 -1 0 0 0 0 0] [ 0 0 0 0 0 0 0 1 -1 0 0 2 -1 0 0 1 0 0 0 -1 0 -1 1 -1 1] [ 0 0 0 0 1 -1 0 1 -1 0 0 0 0 0 -1 2 0 0 0 0 1 0 1 0 0] [ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0] [ 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 1 1 0 0 0] Domain: Modular Symbols space of dimension 9 for Gamma_0(33) of weight ... Codomain: Modular Symbols space of dimension 25 for Gamma_0(66) of weight ... """ def __init__(self, matrix, domain, codomain, t): r""" Initialise a degeneracy map.
EXAMPLES::
sage: D = ModularSymbols(Gamma0(100)).degeneracy_map(2,5); D Hecke module morphism degeneracy map corresponding to f(q) |--> f(q^5) defined by the matrix 31 x 1 dense matrix over Rational Field Domain: Modular Symbols space of dimension 31 for Gamma_0(100) of weight ... Codomain: Modular Symbols space of dimension 1 for Gamma_0(2) of weight ... sage: D == loads(dumps(D)) True """ else:
def t(self): """ Return the divisor of the quotient of the two levels associated to the degeneracy map.
EXAMPLES::
sage: M = ModularSymbols(33) sage: d = M.degeneracy_map(11,3) sage: d.t() 3 sage: d = M.degeneracy_map(11,1) sage: d.t() 1 """ |