hyperexpand.py 文件源码

def _compute_basis(self, closed_form):
        """
        Compute a set of functions B=(f1, ..., fn), a nxn matrix M
        and a 1xn matrix C such that:
           closed_form = C B
           z d/dz B = M B.
        """
        from sympy.matrices import Matrix, eye, zeros

        afactors = [_x + a for a in self.func.ap]
        bfactors = [_x + b - 1 for b in self.func.bq]
        expr = _x*Mul(*bfactors) - self.z*Mul(*afactors)
        poly = Poly(expr, _x)

        n = poly.degree() - 1
        b = [closed_form]
        for _ in xrange(n):
            b.append(self.z*b[-1].diff(self.z))

        self.B = Matrix(b)
        self.C = Matrix([[1] + [0]*n])

        m = eye(n)
        m = m.col_insert(0, zeros(n, 1))
        l = poly.all_coeffs()[1:]
        l.reverse()
        self.M = m.row_insert(n, -Matrix([l])/poly.all_coeffs()[0])