The python Method for Calculating the equation root, and the python Method for Calculating the equation

The python Method for Calculating the equation root, and the python Method for Calculating the equation

This article describes how to calculate the equation root in python. Share it with you for your reference. The specific implementation method is as follows:

''' 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")

I hope this article will help you with Python programming.