# coding: utf-8 # ## Exercise for the course [Python for MATLAB users](http://sese.nu/python-for-matlab-users-ht15/), by Olivier Verdier # In[ ]: import numpy as np import matplotlib.pyplot as plt get_ipython().run_line_magic('matplotlib', 'inline') # The goal of this exercise is to define a class `Polynomial`, which behaves like a polynomial. For instance # # ``` # p = Polynomial([1.,2.]) # ``` # should represent the polynomial \$1 + 2X\$. # # The object `p` should be callable # # ``` # p(.2) # value of the polynomial at 0.2 # ``` # # One should be able to add, multiply two polynomials. # # You will be guided through by the following detailed tasks. # In[ ]: class Polynomial: pass # implement here # Implement the `__init__` method, which stores a list of coefficients. Use the `array` function to copy the list, or array, of coefficiente which is passed. Store the coefficients in a property `coeffs`. # In[ ]: a = np.array([1.,2.]) p = Polynomial(a) assert not p.coeffs is a # Implement the method `__getitem__`, which allows to give acess to the coefficients. An out of bound index should return zero, like in mathematics. # In[ ]: assert np.allclose(p[0], 1.) assert np.allclose(p[3], 0.) # Implement the method `__add__`, which adds two polynomials. # In[ ]: q = Polynomial([1.,2.,3]) z = p+q assert np.allclose((p+q)[0], 2.) assert np.allclose((p+q)[2], 3.) # Implement the method `__repr__`, which returns a string such as `Polynomial(array([1.,2.]))`. # # **Hint**: use the function `repr` on the coefficient array of the polynomial. # In[ ]: assert repr(p) == "Polynomial(array([ 1., 2.]))" # Implement `differentiate` which returns the derivative of the polynomial. # In[ ]: assert np.allclose(p.differentiate().coeffs, array([2.])) # Implement the method `__call__`, which evaluates the polynomial at a given point. # # **Bonus** if the method works with array inputs, like `p(array([1.,2.,3.])`. # # **Hint**: Use the functions `reduce` and, possibly, the function `reversed`. # In[ ]: get_ipython().run_line_magic('pinfo', 'reduce') # In[ ]: assert allclose(p(0.), 1.)