Python - Math - Solving Calculus Problems(Finding the Length of a Curve)

Doing Math with Python

開発環境

• OS X El Capitan - Apple (OS)
• Emacs (Text Editor)
• Python 3.5 (プログラミング言語)

Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More! (Amit Saha (著)、No Starch Press)のChapter 7.(Solving Calculus Problems)、Programming Challenges #4: Finding the Length of a Curve(No. 4953)を取り組んでみる。

Programming Challenges #4: Finding the Length of a Curve(No. 4953)

コード(Emacs)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import sympy

def finding_length(f, var, a, b):
    derivative = sympy.Derivative(f, var).doit()
    length = sympy.Integral(sympy.sqrt(1+derivative**2), (var, a, b))\
                  .doit().evalf()
    return length
    

if __name__ == '__main__':
    f = input('Enter a single variable function: ')
    try:
        f = sympy.sympify(f)
    except sympy.sympifyError as err:
        print('Invalid function entered: {0}'.format(err))
    else:
        var = sympy.Symbol('x')
        var = input('Enter the variable: ')
        var = sympy.Symbol(var)

        print('Enter two points')
        a = float(input())
        b = float(input())
        print('length: {0}'.format(finding_length(f, var, a, b)))

入出力結果(Terminal, IPython)

$ ./sample4.py
Enter a single variable function: 2*x**2 + 3 * x + 1
Enter the variable: x
Enter two points
-5
10
length: 268.372650946022
$