python计算方程式的根的代码，python计算方程式,''' roots =

python计算方程式的根的代码，python计算方程式,''' roots =

''' roots = polyRoots(a).    Uses Laguerre's method to compute all the roots of    a[0] + a[1]*x + a[2]*x^2 +...+ a[n]*x^n = 0.    The roots are returned in the array 'roots','''    from evalPoly import *from numpy import zeros,complexfrom cmath import sqrtfrom random import randomdef polyRoots(a,tol=1.0e-12):    def laguerre(a,tol):        x = random()   # Starting value (random number)        n = len(a) - 1        for i in range(30):            p,dp,ddp = evalPoly(a,x)            if abs(p) < tol: return x            g = dp/p            h = g*g - ddp/p            f = sqrt((n - 1)*(n*h - g*g))            if abs(g + f) > abs(g - f): dx = n/(g + f)            else: dx = n/(g - f)            x = x - dx            if abs(dx) < tol: return x        print 'Too many iterations'    def deflPoly(a,root):  # Deflates a polynomial        n = len(a)-1        b = [(0.0 + 0.0j)]*n        b[n-1] = a[n]        for i in range(n-2,-1,-1):            b[i] = a[i+1] + root*b[i+1]        return b    n = len(a) - 1    roots = zeros((n),dtype=complex)    for i in range(n):        x = laguerre(a,tol)        if abs(x.imag) < tol: x = x.real        roots[i] = x        a = deflPoly(a,x)    return roots    raw_input("\nPress return to exit")