高阶导数

Question

我正在尝试写一个Python程序，让用户输入一个多项式，然后计算它的导数。我的代码是：

print ("Derviatives: ")
k5 = raw.input("Enter 5th degree + coefficent:     ")
k4 = raw.input("Enter 4th degree + coefficent:     ")
k3 = raw.input("Enter 3rd degree + coefficent:     ")
k2 = raw.input("Enter 2nd degree + coefficent:     ")
k1 = raw.input("Enter 1st degree + coefficent:     ")
k0 = raw.input("Enter constant:    ")
int(k5)
int(k4)
int(k3)
int(k2)
int(k1)
int(k0)
print (k5, "  ", k4, "  ", k3, "  ", k2, "   ", k1, "  ", k0)
1in =  raw.input("Correct Y/N?")
if (1in != Y)
    k5 = raw.input("Enter 5th degree + coefficent:     ")
    k4 = raw.input("Enter 4th degree + coefficent:     ")
    k3 = raw.input("Enter 3rd degree + coefficent:     ")
    k2 = raw.input("Enter 2nd degree + coefficent:     ")
    k1 = raw.input("Enter 1st degree + coefficent:     ")
    k0 = raw.input("Enter constant:    ")   

else
    """CODE GOES HERE"""

我还是个刚入门的Python程序员，所以对一些基本的语法问题还不是很清楚。有没有什么库是我应该导入的呢？

Answer 1

我看到你的代码有以下几个问题：

1. 变量名不能以数字开头，比如 1in。
2. 你有一个未定义的变量 Y。我猜你是想和一个字符串比较，所以应该写成 "Y"。
3. 在Python的 if 语句中，括号不是必须的，但结尾的冒号是必须的。else 也是一样。
4. 用一个系数列表会比用一堆变量更好。
5. 应该是 raw_input，而不是 raw.input。
6. 虽然直接用 int(k5) 可以验证值（如果字符串不是整数就会报错），但这不会改变变量的内容，所以 k5 仍然会是一个字符串。

我想展示一点代码，虽然我不是在帮你完成任务（实现算法），而只是展示语言的特性。所以...我会这样做：

# There are no do...while-style loops in Python, so we'll do it this way
# loop forever, and break when confirmation prompt gets "y"
while True:
    k = []  # That's an empty list.

    # I'm assuming Python 2.x here. Add parentheses for Python 3.x.
    print "Derivatives:"

    # This range will work like a list [5, 4, 3, 2, 1].
    for n in range(5, 1, -1):
        k.append(int(raw_input("Enter {0}th degree + coefficient:  ".format(n)))

    ## Or you could do it this way:
    #for num in ["5th", "4th", "3rd", "2nd", "1st"]:
    #    k.append(int(raw_input("Enter {0} degree + coefficient:  ".format(num)))

    k.append(int(raw_input("Enter constant:  ".format(n)))

    # Here's a bit tricky part - a list comprehension.
    # Read on those, they're useful.
    # We need the comprehension, because our list is full of ints,
    # and join experts a list of strings.
    print " ".join(str(x) for x in k)

    ## If you didn't get the previous line - that's fine,
    ## it's fairly advanced subject. Just do like you're used to:
    #print k[0], " ", k[1], " ", k[2], " ", k[3], " ", k[4], " ", k[5]

    # Oh, and did you notice 5th coeff. is at k[0]?
    # That's because we appended them to the list in reverse order.
    # Let's reverse the list in-place, so the constant will be k[0] and so on.
    k.reverse()

    # You don't always need an intermediate variable for single-use values,
    # like when asking for confirmation. Just put raw_input call directly
    # in if statement condition - it would work just fine.
    #
    # And let's be case-insensitive here and accept both "Y" and "y"
    if raw_input("Correct [Y/N]? ").lower() == "y":
        break

Answer 2

好的，使用 raw_input 而不是 raw.input。它是内置的，和 int 一样，所以不需要导入任何东西。当你想把输入转换成整数（int）时，记得要把结果赋值给一个变量，不然什么都不会改变。你可以把这些功能连在一起使用，比如 k5 = int(raw_input("提示.. "))。另外，正如 Evert 提到的，变量名不能以数字开头，所以 1in 需要改一下。这个代码应该可以正常工作：

print("Derviatives: ")
k5 = raw_input("Enter 5th degree + coefficent:     ")
k4 = raw_input("Enter 4th degree + coefficent:     ")
k3 = raw_input("Enter 3rd degree + coefficent:     ")
k2 = raw_input("Enter 2nd degree + coefficent:     ")
k1 = raw_input("Enter 1st degree + coefficent:     ")
k0 = raw_input("Enter constant:    ")
k5 = int(k5)
k4 = int(k4)
k3 = int(k3)
k2 = int(k2)
k1 = int(k1)
k0 = int(k0)
print(k5, "  ", k4, "  ", k3, "  ", k2, "   ", k1, "  ", k0)
in1 = raw_input("Correct Y/N?")
if in1 != "Y":
    k5 = raw_input("Enter 5th degree + coefficent:     ")
    k4 = raw_input("Enter 4th degree + coefficent:     ")
    k3 = raw_input("Enter 3rd degree + coefficent:     ")
    k2 = raw_input("Enter 2nd degree + coefficent:     ")
    k1 = raw_input("Enter 1st degree + coefficent:     ")
    k0 = raw_input("Enter constant:    ")   

else:
    """CODE GOES HERE"""

还有，检查一下你使用的 Python 版本。如果是 Python 3，你需要把 raw_input 改成 input。如果你用的是 Python 2，打印语句就不需要括号。例如，print("Derviatives: ") 应该改成 print "Derviatives: "。

Answer 3

使用Sympy库：

在代码的最上面加上这两行：

from sympy import *
import numpy as np

然后在"""代码在这里"""的地方加上这些：

x = Symbol('x')
y = k5*x**5  + k4*x**4 + k3*x**3  + k2*x**2  + k1*x  +constant
yprime = y.diff(x)
yprime