Python element.ModuleElement类代码示例

    def __init__(self, parent, x=None):
        """
        INPUT:

        - ``parent`` -- a Hecke module

        - ``x`` -- element of the free module associated to parent

        EXAMPLES::

            sage: v = sage.modular.hecke.all.HeckeModuleElement(BrandtModule(37), vector(QQ,[1,2,3])); v
            (1, 2, 3)
            sage: type(v)
            <class 'sage.modular.hecke.element.HeckeModuleElement'>

        TESTS::

            sage: v = ModularSymbols(37).0
            sage: loads(dumps(v))
            (1,0)
            sage: loads(dumps(v)) == v
            True
        """
        ModuleElement.__init__(self, parent)
        if x is not None:
            self.__element = x

 def __init__(self, parent, data, check = True):
     V = parent.coefficient_module()
     if check:
         if isinstance(data,list):
             if data[0].parent() is V:
                 self._val = [V(o) for o in data]
             else:
                 dim = len(V.gens())
                 self._val = []
                 for i in range(0,dim * len(parent._G.coset_reps()),dim):
                     self._val.append(V(data[i:i+dim]))
         elif isinstance(data, self.__class__):
             self._val = [V(o) for o in data._val]
             if hasattr(self._val[0],'lift'):
                 prec = self._val[0].parent().precision_cap()
                 self._val = [o.lift(M = prec) for o in self._val]
         elif isinstance(data, Vector_integer_dense) or isinstance(data, Vector_rational_dense):
             data = list(data)
             dim = len(V.gens())
             self._val = []
             for i in range(0,dim * len(parent._G.coset_reps()),dim):
                 self._val.append(V(data[i:i+dim]))
         else:
             self._val = [V(data) for o in parent._G.coset_reps()]
         assert len(self._val) == len(parent._G.coset_reps())
     else:
         self._val = data
     ModuleElement.__init__(self,parent)

 def __init__(self, parent, element, check=True):
     """
     An element of a finite subgroup of a modular abelian variety.
     
     INPUT:
     
     
     -  ``parent`` - a finite subgroup of a modular abelian
        variety
     
     -  ``element`` - a QQ vector space element that
        represents this element in terms of the ambient rational homology
     
     -  ``check`` - bool (default: True) whether to check
        that element is in the appropriate vector space
     
     
     EXAMPLES: The following calls the TorsionPoint constructor
     implicitly::
     
         sage: J = J0(11)
         sage: G = J.finite_subgroup([[1/3,0], [0,1/5]]); G
         Finite subgroup with invariants [15] over QQbar of Abelian variety J0(11) of dimension 1
         sage: type(G.0)
         <class 'sage.modular.abvar.finite_subgroup.TorsionPoint'>
     """
     ModuleElement.__init__(self, parent)
     if check:
         if not element in parent.abelian_variety().vector_space():
             raise TypeError, "element must be a vector in the abelian variety's rational homology (embedded in the ambient Jacobian product)"
     if element.denominator() == 1:
         element = element.parent().zero_vector()
     self.__element = element

    def __init__(self, parent, data):
        r'''
        Define an element of `H^1(G,V)`

        INPUT:
            - G: a BigArithGroup
            - V: a CoeffModule
            - data: a list

        TESTS::

            sage: from darmonpoints.sarithgroup import BigArithGroup
            sage: from darmonpoints.cohomology_arithmetic import ArithCoh
            sage: G = BigArithGroup(5,6,1,use_shapiro=False,outfile='/tmp/darmonpoints.tmp') #  optional - magma
            sage: Coh = ArithCoh(G) #  optional - magma
            sage: 2 in Coh.hecke_matrix(13).eigenvalues() #  optional - magma
            True
            sage: -4 in Coh.hecke_matrix(7).eigenvalues() #  optional - magma
            True
            sage: PhiE = Coh.gen(1) #  optional - magma
        '''
        G = parent.group()
        V = parent.coefficient_module()
        if isinstance(data,list):
            self._val = [V(o) for o in data]
        else:
            self._val = [V(data.evaluate(b)) for b in parent.group().gens()]
        ModuleElement.__init__(self,parent)

 def __init__(self, parent, d):
     r"""Do not call directly!"""
     # This should be a dict 
     if not isinstance(d,dict):
         raise ValueError("RelativeHomologyClass.__init__ must be passed a dictionary.")
     self._d = d
     ModuleElement.__init__(self, parent=parent)

    def __init__(self, x, parent=None, check=True, reduce=True):
        """
        INPUT:
            - ``x`` -- object
            - ``parent`` -- FormalSums(R) module (default: FormalSums(ZZ))
            - ``check`` -- bool (default: True) if False, might not coerce
                           coefficients into base ring, which can speed
                           up constructing a formal sum.
            - ``reduce`` -- reduce (default: True) if False, do not
                            combine common terms

        EXAMPLES::

            sage: FormalSum([(1,2/3), (3,2/3), (-5, 7)])
            4*2/3 - 5*7
            sage: a = FormalSum([(1,2/3), (3,2/3), (-5, 7)], reduce=False); a
            2/3 + 3*2/3 - 5*7
            sage: a.reduce()
            sage: a
            4*2/3 - 5*7
            sage: FormalSum([(1,2/3), (3,2/3), (-5, 7)], parent=FormalSums(GF(5)))
            4*2/3

        Notice below that the coefficient 5 doesn't get reduced modulo 5::

            sage: FormalSum([(1,2/3), (3,2/3), (-5, 7)], parent=FormalSums(GF(5)), check=False)
            4*2/3 - 5*7

        Make sure we first reduce before checking coefficient types::

            sage: x,y = var('x, y')
            sage: FormalSum([(1/2,x), (2,y)], FormalSums(QQ))
            1/2*x + 2*y
            sage: FormalSum([(1/2,x), (2,y)], FormalSums(ZZ))
            Traceback (most recent call last):
            ...
            TypeError: no conversion of this rational to integer
            sage: FormalSum([(1/2,x), (1/2,x), (2,y)], FormalSums(ZZ))
            x + 2*y
        """
        if x == 0:
            x = []
        self._data = x
        if parent is None:
            parent = formal_sums
        ModuleElement.__init__(self, parent)
        assert isinstance(parent, parent.category().parent_class)
        if reduce:  # first reduce
            self.reduce()
        if check:   # then check
            k = parent.base_ring()
            try:
                self._data = [(k(t[0]), t[1]) for t in self._data]
            except (IndexError, KeyError) as msg:
                raise TypeError("%s\nInvalid formal sum"%msg)

        def __init__(self, parent, vectors):
            """
            Initialize ``self``.

            EXAMPLES::

                sage: F.<x,y> = FreeAlgebra(ZZ)
                sage: H = F.hochschild_complex(F)
                sage: a = H({0: x-y, 2: H.module(2).basis().an_element()})
                sage: TestSuite(a).run()
            """
            self._vec = vectors
            ModuleElement.__init__(self, parent)

    def __init__(self,_parent,vec,quick=False):
        ModuleElement.__init__(self,_parent)
        self._parent=_parent
        self._nE=2*len(_parent._E) # We record the values at the opposite edges
        self._cached_values=dict()
        self._R=Qp(_parent._X._p,prec=_parent._prec)
        if(quick):
                self._F=[v for v in vec]
        else:
            if(isinstance(vec,pAutomorphicForm)):
                self._F=[self._parent._U(vec._F[ii]) for ii in range(self._nE)]
                self._make_invariant()

            elif(isinstance(vec,HarmonicCocycleElement)):
                assert(_parent._U.weight()==vec._wt-2)
                self._F=[]
                assert(2*len(vec._F)==self._nE)
                assert(isinstance(_parent._U,OCVn))
                E=self._parent._E


                MMM=vec._parent._U.element_class
                tmp=[]
                for ii in range(len(vec._F)):
                    newtmp=MMM(vec._parent._U,vec._F[ii]).l_act_by(E[ii].rep.inverse())
                    tmp.append(newtmp)
                    self._F.append(_parent._U(newtmp))
                A=Matrix(QQ,2,2,[0,-1/_parent._X._p,-1,0])
                for ii in range(len(vec._F)):
                    self._F.append(_parent._U(-1*tmp[ii].r_act_by(A)))
                self._make_invariant()

            elif(isinstance(vec,list) and len(vec)==self._nE):
                try:
                    self._F=[self._parent._U(v) for v in vec]
                except:
                    try:
                        veczp=_parent._U._R(vec)
                        self._parent=_parent
                        self._F=[self._parent._U(veczp) for ii in range(self._nE)]
                    except:
                        print vec
                        assert(0)
            else:
                try:
                    veczp=_parent._U._R(vec)
                    self._parent=_parent
                    self._F=[self._parent._U(veczp) for ii in range(self._nE)]
                except:
                    raise ValueError,"Cannot initialize a p-adic automorphic form with the given input="+str(vec)

    def __init__(self,parent,vec,quick = False):
        ModuleElement.__init__(self,parent)
        self._num_generators = len(parent._list)
        self._cached_values = dict()
        self._R = Qp(parent.prime(),prec = parent._prec)
        if quick:
            # assert vec[0].parent() == parent._U
            self._value = [ parent._U(v) for v in vec ]
        else:
            if isinstance(vec,pAutomorphicFormElement):
                self._value = parent._make_invariant([parent._U(vec._value[ii]) for ii in range(self._num_generators)])

            elif isinstance(vec,HarmonicCocycleElement):
                assert(parent._U.weight() == vec._wt-2)
                F = []
                assert(2*len(vec._F) == self._num_generators)
                assert(isinstance(parent._U,OCVn))
                E = parent._list

                MMM = vec.parent()._U.element_class
                tmp = []
                for ii in range(len(vec._F)):
                    newtmp = MMM(vec.parent()._U,vec._F[ii]).l_act_by(E[ii].rep.inverse())
                    tmp.append(newtmp)
                    F.append(parent._U(newtmp))
                A = Matrix(QQ,2,2,[0,-1/parent.prime(),-1,0])
                for ii in range(len(vec._F)):
                    F.append(parent._U(-1*tmp[ii].r_act_by(A)))
                self._value = parent._make_invariant(F)

            elif isinstance(vec,list) and len(vec) == self._num_generators:
                try:
                    self._value = [parent._U(v) for v in vec]
                except:
                    try:
                        veczp = parent._U._R(vec)

                        self._value = [parent._U(veczp) for ii in range(self._num_generators)]
                    except:
                        print vec
                        assert(0)
            else:
                try:
                    veczp = parent._U._R(vec)
                    self._value = [parent._U(veczp) for ii in range(self._num_generators)]
                except:
                    raise ValueError,"Cannot initialize a p-adic automorphic form with the given input = "+str(vec)

    def __init__(self, parent, element, check=True):
        """
        Initialize ``self``.

        EXAMPLES::

            sage: J = J0(11)
            sage: G = J.finite_subgroup([[1/2,0], [0,1/2]])
            sage: TestSuite(G).run() # long time
        """
        ModuleElement.__init__(self, parent)
        if check:
            if element not in parent.abelian_variety().vector_space():
                raise TypeError("element must be a vector in the abelian variety's rational homology (embedded in the ambient Jacobian product)")
        if element.denominator() == 1:
            element = element.parent().zero_vector()
        self.__element = element

 def __init__(self, parent, val=0, check=False):
     ModuleElement.__init__(self, parent)
     self._parent = parent
     self._n = self._parent._n
     self._nhalf = Integer(self._n / 2)
     self._depth = self._parent._depth
     if check:
         if isinstance(val, self.__class__):
             d = min([val._parent._depth, parent._depth])
             assert val._parent.weight() == parent.weight()
             self._val = Matrix(self._parent._R, self._depth, 1, 0)
             for ii in range(d):
                 self._val[ii, 0] = val._val[ii, 0]
         else:
             try:
                 self._val = MatrixSpace(self._parent._R, self._depth, 1)(val)
             except:
                 self._val = val * ones_matrix(self._parent._R, self._depth, 1)
     self._val = copy(val)

 def __init__(self, parent, precision, coefficient_function, components, bounding_precision ) :
     r"""
     INPUT:
         - ``parent``       -- An instance of :class:~`fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ambient.MonoidPowerSeriesAmbient_abstract`.
         - ``precision``    -- A filter for the parent's action.
         - ``coefficient_function`` -- A function returning for each pair of characters and
                                       monoid element a Fourier coefficients.
         - ``components``   -- ``None`` or a list of characters. A list of components that do not
                               vanish. If ``None`` no component is assumed to be zero.
     
     TESTS::
         sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_lazyelement import *
         sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import *
         sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
         sage: m = FreeModule(QQ, 3)
         sage: emps = EquivariantMonoidPowerSeriesModule( NNMonoid(), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", m) )
         sage: h = EquivariantMonoidPowerSeries_moduleelement_lazy(emps, emps.action().filter(3), lambda (ch, k) : m([1,2,3]), None, None)
     """
     ModuleElement.__init__(self, parent)
     EquivariantMonoidPowerSeries_abstract_lazy.__init__(self, parent, precision,
              coefficient_function, components, bounding_precision)

 def __init__(self, parent, polynomial) :
     r"""
     INPUT:
         - ``parent``     -- An instance of :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_module.GradedExpansionModule_class`.
         - ``polynomial`` -- A polynomial in the polynomial ring underlying the parent.
     
     TESTS::
         sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
         sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import *
         sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_element import *
         sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_grading import DegreeGrading
         sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_module import *
         sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_element import *
         sage: m = FreeModule(QQ, 3)
         sage: mpsm = MonoidPowerSeriesModule(m, NNMonoid(False))
         sage: mps = mpsm.base_ring()
         sage: P.<a,b> = QQ[]
         sage: ger = GradedExpansionModule_class(Sequence([MonoidPowerSeries(mps, {1: 1}, mps.monoid().filter(4))]), Sequence([MonoidPowerSeries(mpsm, {1: m([1,1,1]), 2: m([1,3,-3])}, mpsm.monoid().filter(4))]), P.ideal(0), DegreeGrading((1,2)))
         sage: h = GradedExpansionVector_class(ger, a)
     """
     ModuleElement.__init__(self, parent)
     GradedExpansion_abstract.__init__(self, parent, polynomial)

    def __init__(self, parent, terms):
        """
        Kontsevich graph sum.

        A formal sum of Kontsevich graphs, modulo the relation that
        swapping two edges (L and R) originating from an internal vertex
        introduces a minus sign.

        INPUT:

        - ``parent`` -- a ``KontsevichGraphSums`` module.
        - ``terms`` -- list of ``(coefficient, graph)`` tuples,
          where ``coefficient`` is in ``parent.base_ring()``,
          and ``graph`` is an immutable KontsevichGraph.

        OUTPUT:

        A formal sum of Kontsevich graphs.

        EXAMPLES::

            sage: K = KontsevichGraphSums(QQ)
            sage: KG = KontsevichGraph(ground_vertices=(), immutable=True)
            sage: KontsevichGraphSum(K, [(1/2, KG)])
            1/2*(Kontsevich graph with 0 vertices on 0 ground vertices)
        """
        if terms == 0:
            terms = []
        if not isinstance(terms, list):
            raise TypeError('Input must be a list of terms.')
        if not all(isinstance(t, tuple) and len(t) == 2 for t in terms):
            raise TypeError('Terms must be (coefficient, graph) tuples.')
        if not all(c in parent.base_ring() and isinstance(g, KontsevichGraph)
                   and getattr(g, '_immutable', False) for (c,g) in terms):
            raise TypeError('Coefficients must be in base ring, and ' +
                            'graphs must be immutable KontsevichGraphs.')
        self._terms = terms
        ModuleElement.__init__(self, parent=parent)

    def __init__(self, parent, x, check=DEBUG):
        """
        INPUT:

        - ``parent`` -- parent module M

        - ``x`` -- element of M.V()

        - ``check`` -- (default: True) if True, verify that x in M.V()

        EXAMPLES::

            sage: V = span([[1/2,1,1],[3/2,2,1],[0,0,1]],ZZ); W = V.span([2*V.0+4*V.1, 9*V.0+12*V.1, 4*V.2])
            sage: Q = V/W
            sage: x = Q(V.0-V.1); type(x)
            <class 'sage.modules.fg_pid.fgp_element.FGP_Module_class_with_category.element_class'>
            sage: isinstance(x,sage.modules.fg_pid.fgp_element.FGP_Element)
            True

        For full documentation, see :class:`FGP_Element`.
        """
        if check: assert x in parent.V(), 'The argument x='+str(x)+' is not in the covering module!'
        ModuleElement.__init__(self, parent)
        self._x = x