PolyClass.ipynb

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