【发布时间】：2012-10-22 12:22:20
【问题描述】：
我目前正在为我的大学学习做一个 Python 练习。我非常坚持这项任务：
指数函数 e^x 的 N 次泰勒多项式由下式给出：
N
p(x) = Sigma x^k/k!
k = 0
制作一个程序，(i) 导入类 Polynomial（可在下面找到），(ii) 从命令行读取 x 和一系列 N 值，(iii) 创建一个表示泰勒多项式的 Polynomial 实例，以及 (iv)打印给定 N 值的 p(x) 值以及精确值 e^x。试试 x = 0.5, 3, 10 和 N = 2, 5, 10, 15, 25 的程序。
多项式.py
import numpy
class Polynomial:
def __init__(self, coefficients):
self.coeff = coefficients
def __call__(self, x):
"""Evaluate the polynomial."""
s = 0
for i in range(len(self.coeff)):
s += self.coeff[i]*x**i
return s
def __add__(self, other):
# Start with the longest list and add in the other
if len(self.coeff) > len(other.coeff):
result_coeff = self.coeff[:] # copy!
for i in range(len(other.coeff)):
result_coeff[i] += other.coeff[i]
else:
result_coeff = other.coeff[:] # copy!
for i in range(len(self.coeff)):
result_coeff[i] += self.coeff[i]
return Polynomial(result_coeff)
def __mul__(self, other):
c = self.coeff
d = other.coeff
M = len(c) - 1
N = len(d) - 1
result_coeff = numpy.zeros(M+N+1)
for i in range(0, M+1):
for j in range(0, N+1):
result_coeff[i+j] += c[i]*d[j]
return Polynomial(result_coeff)
def differentiate(self):
"""Differentiate this polynomial in-place."""
for i in range(1, len(self.coeff)):
self.coeff[i-1] = i*self.coeff[i]
del self.coeff[-1]
def derivative(self):
"""Copy this polynomial and return its derivative."""
dpdx = Polynomial(self.coeff[:]) # make a copy
dpdx.differentiate()
return dpdx
def __str__(self):
s = ''
for i in range(0, len(self.coeff)):
if self.coeff[i] != 0:
s += ' + %g*x^%d' % (self.coeff[i], i)
# Fix layout
s = s.replace('+ -', '- ')
s = s.replace('x^0', '1')
s = s.replace(' 1*', ' ')
s = s.replace('x^1 ', 'x ')
#s = s.replace('x^1', 'x') # will replace x^100 by x^00
if s[0:3] == ' + ': # remove initial +
s = s[3:]
if s[0:3] == ' - ': # fix spaces for initial -
s = '-' + s[3:]
return s
def simplestr(self):
s = ''
for i in range(0, len(self.coeff)):
s += ' + %g*x^%d' % (self.coeff[i], i)
return s
def _test():
p1 = Polynomial([1, -1])
p2 = Polynomial([0, 1, 0, 0, -6, -1])
p3 = p1 + p2
print p1, ' + ', p2, ' = ', p3
p4 = p1*p2
print p1, ' * ', p2, ' = ', p4
print 'p2(3) =', p2(3)
p5 = p2.derivative()
print 'd/dx', p2, ' = ', p5
print 'd/dx', p2,
p2.differentiate()
print ' = ', p5
p4 = p2.derivative()
print 'd/dx', p2, ' = ', p4
if __name__ == '__main__':
_test()
现在我真的陷入了困境，我很想得到解释！我应该将我的代码写在一个单独的文件中。我正在考虑创建多项式类的实例，并在 argv[2:] 中发送列表，但这似乎不起作用。在将 N 的不同值发送到 Polynomial 类之前，我是否必须创建一个 def 来计算泰勒多项式？
任何帮助都很好，在此先感谢:)
【问题讨论】：