我目前正在为我的大学学习做蟒蛇练习。我非常坚持这个任务：
指数函数e ^ x的度数N的泰勒多项式由下式给出：
N
p(x) = Sigma x^k/k!
k = 0
创建一个程序，（i）导入类多项式（在下面找到），（ii）从命令行读取x和一系列N值，（iii）创建表示泰勒多项式的多项式实例，以及（iv）打印给定N值的p（x）值以及精确值e ^ x。尝试使用x = 0.5,3,10和N = 2,5,10,15,25的程序。
Polynomial.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！我应该把我的代码写在一个单独的文件中。我正在考虑创建一个Polynomial类的实例，并在argv [2：]的列表中发送，但这似乎不起作用。在将数据发送到多项式类之前，我是否必须使用def计算不同N值的泰勒多项式？
任何帮助都很棒，提前谢谢：）
答案 0 :(得分：2)
还没完成，但这回答了我相信的主要问题。将类Polynomial放在poly.p中并导入它。
from poly import Polynomial as p
from math import exp,factorial
def get_input(n):
''' get n numbers from stdin '''
entered = list()
for i in range(n):
print 'input number '
entered.append(raw_input())
return entered
def some_input():
return [[2,3,4],[4,3,2]]
get input from cmd line
n = 3
a = get_input(n)
b = get_input(n)
#a,b = some_input()
ap = p(a)
bp = p(b)
print 'entered : ',a,b
c = ap+bp
print 'a + b = ',c
print exp(3)
x = ap
print x
sum = p([0])
for k in range(1,5):
el = x
for j in range(1,k):
el el * x
print 'el: ',el
if el!=None and sum!=None:
sum = sum + el
print 'sum ',sum
输出
entered : [2, 3, 4] [4, 3, 2]
a + b = 6*1 + 6*x + 6*x^2
20.0855369232
2*1 + 3*x + 4*x^2
sum 2*1 + 3*x + 4*x^2
el: 4*1 + 12*x + 25*x^2 + 24*x^3 + 16*x^4
sum 6*1 + 15*x + 29*x^2 + 24*x^3 + 16*x^4
el: 4*1 + 12*x + 25*x^2 + 24*x^3 + 16*x^4
el: 8*1 + 36*x + 102*x^2 + 171*x^3 + 204*x^4 + 144*x^5 + 64*x^6
sum 14*1 + 51*x + 131*x^2 + 195*x^3 + 220*x^4 + 144*x^5 + 64*x^6
el: 4*1 + 12*x + 25*x^2 + 24*x^3 + 16*x^4
el: 8*1 + 36*x + 102*x^2 + 171*x^3 + 204*x^4 + 144*x^5 + 64*x^6
el: 16*1 + 96*x + 344*x^2 + 792*x^3 + 1329*x^4 + 1584*x^5 + 1376*x^6 + 768*x^7 + 256*x^8
sum 30*1 + 147*x + 475*x^2 + 987*x^3 + 1549*x^4 + 1728*x^5 + 1440*x^6 + 768*x^7 + 256*x^8
答案 1 :(得分：1)
我用以下方式解决了这个问题，虽然我不确定它是否回答问题（iv）。 输出只是将e ** x的精确值与模块Polynomial的计算值进行比较。
from math import factorial, exp
from Polynomial import *
from sys import *
#Reads x and N from the command line on the form [filename.py, x-value, N-value]
x = eval(argv[1])
N = eval(argv[2])
#Creating list of coefficients on the form [1 / i!]
list_coeff = [1./factorial(i) for i in range(N)]
print list_coeff
#Creating an instance of class Polynomial
p1 = Polynomial(list_coeff)
print 'Calculated value of e**%f = %f ' %(x, p1.__call__(x))
print 'Exact value of e**%f = %f'% (x, exp(x))
"""Test Execution
Terminal > python Polynomial_exp.py 0.5 5
[1.0, 1.0, 0.5, 0.16666666666666666, 0.041666666666666664]
Calculated value of e**0.500000 = 1.648438
Exact value of e**0.500000 = 1.648721
"""