Ejemplo n.º 1
0
 def basis_of_subsp_annihilated_by(self, pol, a=2, parallel=False):
     '''
     Returns the basis of the subspace annihilated by pol(T(a)).
     '''
     S = PolynomialRing(QQ, names="x")
     pol = S(pol)
     A = self.hecke_matrix(a)
     B = polynomial_func(pol)(A.transpose())
     if parallel:
         with number_of_procs(1):
             res = pmap(self._to_form, B.kernel().basis())
     else:
         res = [self._to_form(v) for v in B.kernel().basis()]
     return res
Ejemplo n.º 2
0
    def test_ramanujan_conj_and_klingen(self):
        '''Test Ramanujan conjectures for eigenforms of determinant weights
        less than or equal to 29 and
        Hecke eigenvalues of Kligen-Eisenstein series.
        '''
        prec = 10

        @fork
        def _check(k, j):
            M = vvsmf(j, k, prec)
            if M.dimension() > 0:
                self.assertEqual(M.dimension(), len(M.basis()))
                _chply = M.hecke_charpoly(2)
                for cply, _ in _chply.factor():
                    K = NumberField(cply, names="a")
                    a = K.gens()[0]
                    f = M.eigenform_with_eigenvalue_t2(a)
                    self.assert_hecke_eigen_values(f)

        with number_of_procs(1):
            for k, j in CartesianProduct(range(4, 30), [2, 4, 10]):
                _check(k, j)