Coverage for local/lib/python2.7/site-packages/sage/modular/hecke/morphism.py : 50%

""" 

Morphisms of Hecke modules 

AUTHORS: 

- William Stein 

""" 

#***************************************************************************** 

# 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/ 

#***************************************************************************** 

import sage.misc.misc as misc 

from sage.modules.matrix_morphism import MatrixMorphism 

from sage.categories.morphism import Morphism 

# We also define other types of Hecke-module morphisms that aren't 

# specified by a matrix. E.g., Hecke operators, or maybe morphisms on 

# modular abelian varieties (which are specified by matrices, but on 

# integral homology). All morphisms derive from HeckeModuleMorphism. 

def is_HeckeModuleMorphism(x): 

r""" 

Return True if x is of type HeckeModuleMorphism. 

EXAMPLES:: 

sage: sage.modular.hecke.morphism.is_HeckeModuleMorphism(ModularSymbols(6).hecke_operator(7).hecke_module_morphism()) 

True 

""" 

return isinstance(x, HeckeModuleMorphism) 

def is_HeckeModuleMorphism_matrix(x): 

""" 

EXAMPLES:: 

sage: sage.modular.hecke.morphism.is_HeckeModuleMorphism_matrix(ModularSymbols(6).hecke_operator(7).matrix_form().hecke_module_morphism()) 

True 

""" 

return isinstance(x, HeckeModuleMorphism_matrix) 

class HeckeModuleMorphism(Morphism): 

r""" 

Abstract base class for morphisms of Hecke modules. 

""" 

pass 

class HeckeModuleMorphism_matrix(MatrixMorphism, HeckeModuleMorphism): 

""" 

Morphisms of Hecke modules when the morphism is given by a matrix. 

Note that care is needed when composing morphisms, because morphisms in 

Sage act on the left, but their matrices act on the right (!). So if F: A 

-> B and G : B -> C are morphisms, the composition A -> C is G*F, but its 

matrix is F.matrix() * G.matrix(). 

EXAMPLES:: 

sage: A = ModularForms(1, 4) 

sage: B = ModularForms(1, 16) 

sage: C = ModularForms(1, 28) 

sage: F = A.Hom(B)(matrix(QQ,1,2,srange(1, 3))) 

sage: G = B.Hom(C)(matrix(QQ,2,3,srange(1, 7))) 

sage: G * F 

Hecke module morphism defined by the matrix 

[ 9 12 15] 

Domain: Modular Forms space of dimension 1 for Modular Group SL(2,Z) ... 

Codomain: Modular Forms space of dimension 3 for Modular Group SL(2,Z) ... 

sage: F * G 

Traceback (most recent call last): 

... 

TypeError: Incompatible composition of morphisms: domain of left morphism must be codomain of right. 

""" 

def __init__(self, parent, A, name=''): 

""" 

INPUT: 

- ``parent`` - ModularSymbolsHomspace 

- ``A`` - Matrix 

- ``name`` - str (defaults to '') name of the morphism 

(used for printing) 

EXAMPLES:: 

sage: M = ModularSymbols(6) 

sage: t = M.Hom(M)(matrix(QQ,3,3,srange(9)), name="spam"); t 

Hecke module morphism spam defined by the matrix 

[0 1 2] 

[3 4 5] 

[6 7 8] 

Domain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ... 

Codomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ... 

sage: t == loads(dumps(t)) 

True 

""" 

if not isinstance(name, str): 

raise TypeError("name must be a string") 

self.__name = name 

MatrixMorphism.__init__(self, parent, A) 

def name(self, new=None): 

r""" 

Return the name of this operator, or set it to a new name. 

EXAMPLES:: 

sage: M = ModularSymbols(6) 

sage: t = M.Hom(M)(matrix(QQ,3,3,srange(9)), name="spam"); t 

Hecke module morphism spam defined by ... 

sage: t.name() 

'spam' 

sage: t.name("eggs"); t 

Hecke module morphism eggs defined by ... 

""" 

if new is None: 

return self.__name 

self.__name = new 

def _repr_(self): 

r""" 

String representation of self. 

EXAMPLES:: 

sage: M = ModularSymbols(6) 

sage: t = M.Hom(M)(matrix(QQ,3,3,srange(9))); t._repr_() 

'Hecke module morphism defined by the matrix\n[0 1 2]\n[3 4 5]\n[6 7 8]\nDomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...\nCodomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...' 

sage: t.name('spam'); t._repr_() 

'Hecke module morphism spam defined by the matrix\n[0 1 2]\n[3 4 5]\n[6 7 8]\nDomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...\nCodomain: Modular Symbols space of dimension 3 for Gamma_0(6) of weight ...' 

""" 

name = self.__name 

if name != '': 

name += ' ' 

return "Hecke module morphism %sdefined by the matrix\n%r\nDomain: %s\nCodomain: %s"%( 

name, self.matrix(), misc.strunc(self.domain()), misc.strunc(self.codomain())) 

# __mul__ method removed by David Loeffler 2009-04-14 as it is an exact duplicate of sage.modules.matrix_morphism.__mul__