Snippets

Lilian Besson (Naereen) Small overload of the numpy.polynomial.Polynomial class to add a better printing (change the __str__ method only)

Created by Lilian Besson (Naereen) last modified Lilian Besson
# Note: For an example showing how to use this sort of technique to pretty print a polynomial object with LaTeX in a IPython console or notebook, see this tutorial:
# http://nbviewer.jupyter.org/github/Naereen/notebooks/blob/master/Demonstration%20of%20numpy.polynomial.Polynomial%20and%20nice%20display%20with%20LaTeX%20and%20MathJax%20%28python3%29.ipynb

Automatic test of all the docstrings:
Trying:
    P = MyPolynomial
Expecting nothing
ok
Trying:
    X = P([0, 1])  # We define the monome X, to work with it efficiently
Expecting nothing
ok
Trying:
    print(X)
Expecting:
    X
ok
Trying:
    Q1 = 1 + 2*X + 17*X**3
Expecting nothing
ok
Trying:
    print(Q1)
Expecting:
    1 + 2 * X + 17 * X**3
ok
Trying:
    Q2 = Q1 - 2*X
Expecting nothing
ok
Trying:
    print(Q2)
Expecting:
    1 + 17 * X**3
ok
Trying:
    Q3 = -1 - 2*X - 17*X**3
Expecting nothing
ok
Trying:
    print(Q3)
Expecting:
    (-1) + (-2) * X + (-17) * X**3
ok
Trying:
    print(-Q3)
Expecting:
    1 + 2 * X + 17 * X**3
ok
Trying:
    Q4 = (1 + 2*X + 17*X**3) ** 20
Expecting nothing
ok
Trying:
    print(Q4)  # doctest: +ELLIPSIS
Expecting:
    1 + 40 * X + 760 * X**2 + 9460 * X**3 + 90440 * X**4 + ... + 4064231406647572451819520 * X**60
ok
Trying:
    Q5 = (1 + 2*X + 17*X**3) ** 100
Expecting nothing
ok
Trying:
    print(Q5)  # doctest: +ELLIPSIS
Expecting:
    1 + 200 * X + 19800 * X**2 + 1295300 * X**3 + ... + 1108899372780782949283060780215564719143115314569706274981249422854766735454757111223455545827324114733078454801811428605952 * X**300
ok
3 items had no tests:
    __main__
    __main__.MyPolynomial
    __main__.MyPolynomial.__str__
1 items passed all tests:
  14 tests in __main__.test
14 tests in 4 items.
14 passed and 0 failed.
Test passed.

More details on these doctests can be found online in the official Python documentation:
https://docs.python.org/3/library/doctest.html
#! /usr/bin/env python3
# -*- coding: utf-8; mode: python -*-
""" A tiny modification of the method numpy.polynomial.Polynomial.__str__ to nicely display a polynomials.

Cf. https://docs.scipy.org/doc/numpy/reference/generated/numpy.polynomial.polynomial.Polynomial.html for more details about the original class.

For an example showing how to use this sort of technique to pretty print a polynomial object with LaTeX in a IPython console or notebook, see this tutorial: http://nbviewer.jupyter.org/github/Naereen/notebooks/blob/master/Demonstration%20of%20numpy.polynomial.Polynomial%20and%20nice%20display%20with%20LaTeX%20and%20MathJax%20%28python3%29.ipynb

- *Online:* https://bitbucket.org/snippets/lbesson/j6dpz#file-nicedisplay_numpy_polynomial_Polynomial.py
- *Author:* Lilian Besson, for http://perso.crans.org/besson/infoMP/oraux/solutions/PSI_Mat2_2015_25.html,
- *License:* MIT Licence (http://lbesson.mit-license.org).

"""

from __future__ import print_function, division  # Python 2 compatibility

from numpy.polynomial import Polynomial


class MyPolynomial(Polynomial):
    """ Small extension of the numpy.polynomial.Polynomial class to change its __str__ method.
    """
    def __str__(self):
        """ Improved __str__ method to print nicely the polynomial as we write it in maths."""
        coefs = self.coef
        res = ""
        for i, a in enumerate(coefs):
            if int(a) == a:  # Remove the trailing .0
                a = int(a)
            if i == 0:
                if a > 0:
                    res += "{a} + ".format(a=a)
                elif a < 0:
                    res += "({a}) + ".format(a=a)
            elif i == 1:
                if a == 1:
                    res += "X + "
                elif a > 0:
                    res += "{a} * X + ".format(a=a)
                elif a < 0:
                    res += "({a}) * X + ".format(a=a)
            else:
                if a == 1:
                    res += "X**{i} + ".format(i=i)
                elif a > 0:
                    res += "{a} * X**{i} + ".format(a=a, i=i)
                elif a < 0:
                    res += "({a}) * X**{i} + ".format(a=a, i=i)
        return res[:-3] if res else ""


P = MyPolynomial
X = P([0, 1])  # We define the monome X, to work with it efficiently
# eg. 1 + 2*X + 17*X**3


def test():
    """ Some tests of our improved ``__str__`` method.

    First, let start by defining the monome X:

    >>> P = MyPolynomial
    >>> X = P([0, 1])  # We define the monome X, to work with it efficiently
    >>> print(X)
    X

    And then a few other polynomials:

    >>> Q1 = 1 + 2*X + 17*X**3
    >>> print(Q1)
    1 + 2 * X + 17 * X**3
    >>> Q2 = Q1 - 2*X
    >>> print(Q2)
    1 + 17 * X**3

    We can check that the negative signs work too:

    >>> Q3 = -1 - 2*X - 17*X**3
    >>> print(Q3)
    (-1) + (-2) * X + (-17) * X**3
    >>> print(-Q3)
    1 + 2 * X + 17 * X**3

    And with crazily long polynomials:

    >>> Q4 = (1 + 2*X + 17*X**3) ** 20
    >>> print(Q4)  # doctest: +ELLIPSIS
    1 + 40 * X + 760 * X**2 + 9460 * X**3 + 90440 * X**4 + ... + 4064231406647572451819520 * X**60
    >>> Q5 = (1 + 2*X + 17*X**3) ** 100
    >>> print(Q5)  # doctest: +ELLIPSIS
    1 + 200 * X + 19800 * X**2 + 1295300 * X**3 + ... + 1108899372780782949283060780215564719143115314569706274981249422854766735454757111223455545827324114733078454801811428605952 * X**300

    It works nicely !
    """
    pass


if __name__ == '__main__':
    from doctest import testmod
    print("Automatic test of all the docstrings:")
    testmod(verbose=True)
    print("\nMore details on these doctests can be found online in the official Python documentation:\nhttps://docs.python.org/3/library/doctest.html")
# End of the file
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Help on module nicedisplay_numpy_polynomial_Polynomial:

NAME
    nicedisplay_numpy_polynomial_Polynomial - A tiny modification of the method numpy.polynomial.Polynomial.__str__ to nicely display a polynomials.

FILE
    /home/lilian/publis/snippets/small-overload-of-the/nicedisplay_numpy_polynomial_Polynomial.py

DESCRIPTION
    Cf. https://docs.scipy.org/doc/numpy/reference/generated/numpy.polynomial.polynomial.Polynomial.html for more details about the original class.
    
    - *Online:* https://bitbucket.org/snippets/lbesson/j6dpz#file-nicedisplay_numpy_polynomial_Polynomial.py
    - *Author:* Lilian Besson, for http://perso.crans.org/besson/infoMP/oraux/solutions/PSI_Mat2_2015_25.html,
    - *License:* MIT Licence (http://lbesson.mit-license.org).

CLASSES
    numpy.polynomial.polynomial.Polynomial(numpy.polynomial._polybase.ABCPolyBase)
        MyPolynomial
    
    class MyPolynomial(numpy.polynomial.polynomial.Polynomial)
     |  Small extension of the numpy.polynomial.Polynomial class to change its __str__ method.
     |  
     |  Method resolution order:
     |      MyPolynomial
     |      numpy.polynomial.polynomial.Polynomial
     |      numpy.polynomial._polybase.ABCPolyBase
     |      __builtin__.object
     |  
     |  Methods defined here:
     |  
     |  __str__(self)
     |      Improved __str__ method to print nicely the polynomial as we write it in maths.
     |  
     |  ----------------------------------------------------------------------
     |  Data and other attributes defined here:
     |  
     |  __abstractmethods__ = frozenset([])
     |  
     |  ----------------------------------------------------------------------
     |  Data and other attributes inherited from numpy.polynomial.polynomial.Polynomial:
     |  
     |  domain = array([-1,  1])
     |  
     |  nickname = 'poly'
     |  
     |  window = array([-1,  1])
     |  
     |  ----------------------------------------------------------------------
     |  Methods inherited from numpy.polynomial._polybase.ABCPolyBase:
     |  
     |  __add__(self, other)
     |  
     |  __call__(self, arg)
     |  
     |  __div__(self, other)
     |  
     |  __divmod__(self, other)
     |  
     |  __eq__(self, other)
     |  
     |  __floordiv__(self, other)
     |  
     |  __getstate__(self)
     |  
     |  __init__(self, coef, domain=None, window=None)
     |  
     |  __iter__(self)
     |  
     |  __len__(self)
     |  
     |  __mod__(self, other)
     |  
     |  __mul__(self, other)
     |  
     |  __ne__(self, other)
     |  
     |  __neg__(self)
     |  
     |  __pos__(self)
     |  
     |  __pow__(self, other)
     |  
     |  __radd__(self, other)
     |  
     |  __rdiv__(self, other)
     |  
     |  __rdivmod__(self, other)
     |  
     |  __repr__(self)
     |  
     |  __rfloordiv__(self, other)
     |  
     |  __rmod__(self, other)
     |  
     |  __rmul__(self, other)
     |  
     |  __rsub__(self, other)
     |  
     |  __rtruediv__(self, other)
     |  
     |  __setstate__(self, dict)
     |  
     |  __sub__(self, other)
     |  
     |  __truediv__(self, other)
     |  
     |  convert(self, domain=None, kind=None, window=None)
     |      Convert series to a different kind and/or domain and/or window.
     |      
     |      Parameters
     |      ----------
     |      domain : array_like, optional
     |          The domain of the converted series. If the value is None,
     |          the default domain of `kind` is used.
     |      kind : class, optional
     |          The polynomial series type class to which the current instance
     |          should be converted. If kind is None, then the class of the
     |          current instance is used.
     |      window : array_like, optional
     |          The window of the converted series. If the value is None,
     |          the default window of `kind` is used.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          The returned class can be of different type than the current
     |          instance and/or have a different domain and/or different
     |          window.
     |      
     |      Notes
     |      -----
     |      Conversion between domains and class types can result in
     |      numerically ill defined series.
     |      
     |      Examples
     |      --------
     |  
     |  copy(self)
     |      Return a copy.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          Copy of self.
     |  
     |  cutdeg(self, deg)
     |      Truncate series to the given degree.
     |      
     |      Reduce the degree of the series to `deg` by discarding the
     |      high order terms. If `deg` is greater than the current degree a
     |      copy of the current series is returned. This can be useful in least
     |      squares where the coefficients of the high degree terms may be very
     |      small.
     |      
     |      .. versionadded:: 1.5.0
     |      
     |      Parameters
     |      ----------
     |      deg : non-negative int
     |          The series is reduced to degree `deg` by discarding the high
     |          order terms. The value of `deg` must be a non-negative integer.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          New instance of series with reduced degree.
     |  
     |  degree(self)
     |      The degree of the series.
     |      
     |      .. versionadded:: 1.5.0
     |      
     |      Returns
     |      -------
     |      degree : int
     |          Degree of the series, one less than the number of coefficients.
     |  
     |  deriv(self, m=1)
     |      Differentiate.
     |      
     |      Return a series instance of that is the derivative of the current
     |      series.
     |      
     |      Parameters
     |      ----------
     |      m : non-negative int
     |          Find the derivative of order `m`.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A new series representing the derivative. The domain is the same
     |          as the domain of the differentiated series.
     |  
     |  has_samecoef(self, other)
     |      Check if coefficients match.
     |      
     |      .. versionadded:: 1.6.0
     |      
     |      Parameters
     |      ----------
     |      other : class instance
     |          The other class must have the ``coef`` attribute.
     |      
     |      Returns
     |      -------
     |      bool : boolean
     |          True if the coefficients are the same, False otherwise.
     |  
     |  has_samedomain(self, other)
     |      Check if domains match.
     |      
     |      .. versionadded:: 1.6.0
     |      
     |      Parameters
     |      ----------
     |      other : class instance
     |          The other class must have the ``domain`` attribute.
     |      
     |      Returns
     |      -------
     |      bool : boolean
     |          True if the domains are the same, False otherwise.
     |  
     |  has_sametype(self, other)
     |      Check if types match.
     |      
     |      .. versionadded:: 1.7.0
     |      
     |      Parameters
     |      ----------
     |      other : object
     |          Class instance.
     |      
     |      Returns
     |      -------
     |      bool : boolean
     |          True if other is same class as self
     |  
     |  has_samewindow(self, other)
     |      Check if windows match.
     |      
     |      .. versionadded:: 1.6.0
     |      
     |      Parameters
     |      ----------
     |      other : class instance
     |          The other class must have the ``window`` attribute.
     |      
     |      Returns
     |      -------
     |      bool : boolean
     |          True if the windows are the same, False otherwise.
     |  
     |  integ(self, m=1, k=[], lbnd=None)
     |      Integrate.
     |      
     |      Return a series instance that is the definite integral of the
     |      current series.
     |      
     |      Parameters
     |      ----------
     |      m : non-negative int
     |          The number of integrations to perform.
     |      k : array_like
     |          Integration constants. The first constant is applied to the
     |          first integration, the second to the second, and so on. The
     |          list of values must less than or equal to `m` in length and any
     |          missing values are set to zero.
     |      lbnd : Scalar
     |          The lower bound of the definite integral.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A new series representing the integral. The domain is the same
     |          as the domain of the integrated series.
     |  
     |  linspace(self, n=100, domain=None)
     |      Return x, y values at equally spaced points in domain.
     |      
     |      Returns the x, y values at `n` linearly spaced points across the
     |      domain.  Here y is the value of the polynomial at the points x. By
     |      default the domain is the same as that of the series instance.
     |      This method is intended mostly as a plotting aid.
     |      
     |      .. versionadded:: 1.5.0
     |      
     |      Parameters
     |      ----------
     |      n : int, optional
     |          Number of point pairs to return. The default value is 100.
     |      domain : {None, array_like}, optional
     |          If not None, the specified domain is used instead of that of
     |          the calling instance. It should be of the form ``[beg,end]``.
     |          The default is None which case the class domain is used.
     |      
     |      Returns
     |      -------
     |      x, y : ndarray
     |          x is equal to linspace(self.domain[0], self.domain[1], n) and
     |          y is the series evaluated at element of x.
     |  
     |  mapparms(self)
     |      Return the mapping parameters.
     |      
     |      The returned values define a linear map ``off + scl*x`` that is
     |      applied to the input arguments before the series is evaluated. The
     |      map depends on the ``domain`` and ``window``; if the current
     |      ``domain`` is equal to the ``window`` the resulting map is the
     |      identity.  If the coefficients of the series instance are to be
     |      used by themselves outside this class, then the linear function
     |      must be substituted for the ``x`` in the standard representation of
     |      the base polynomials.
     |      
     |      Returns
     |      -------
     |      off, scl : float or complex
     |          The mapping function is defined by ``off + scl*x``.
     |      
     |      Notes
     |      -----
     |      If the current domain is the interval ``[l1, r1]`` and the window
     |      is ``[l2, r2]``, then the linear mapping function ``L`` is
     |      defined by the equations::
     |      
     |          L(l1) = l2
     |          L(r1) = r2
     |  
     |  roots(self)
     |      Return the roots of the series polynomial.
     |      
     |      Compute the roots for the series. Note that the accuracy of the
     |      roots decrease the further outside the domain they lie.
     |      
     |      Returns
     |      -------
     |      roots : ndarray
     |          Array containing the roots of the series.
     |  
     |  trim(self, tol=0)
     |      Remove trailing coefficients
     |      
     |      Remove trailing coefficients until a coefficient is reached whose
     |      absolute value greater than `tol` or the beginning of the series is
     |      reached. If all the coefficients would be removed the series is set
     |      to ``[0]``. A new series instance is returned with the new
     |      coefficients.  The current instance remains unchanged.
     |      
     |      Parameters
     |      ----------
     |      tol : non-negative number.
     |          All trailing coefficients less than `tol` will be removed.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          Contains the new set of coefficients.
     |  
     |  truncate(self, size)
     |      Truncate series to length `size`.
     |      
     |      Reduce the series to length `size` by discarding the high
     |      degree terms. The value of `size` must be a positive integer. This
     |      can be useful in least squares where the coefficients of the
     |      high degree terms may be very small.
     |      
     |      Parameters
     |      ----------
     |      size : positive int
     |          The series is reduced to length `size` by discarding the high
     |          degree terms. The value of `size` must be a positive integer.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          New instance of series with truncated coefficients.
     |  
     |  ----------------------------------------------------------------------
     |  Class methods inherited from numpy.polynomial._polybase.ABCPolyBase:
     |  
     |  basis(cls, deg, domain=None, window=None) from abc.ABCMeta
     |      Series basis polynomial of degree `deg`.
     |      
     |      Returns the series representing the basis polynomial of degree `deg`.
     |      
     |      .. versionadded:: 1.7.0
     |      
     |      Parameters
     |      ----------
     |      deg : int
     |          Degree of the basis polynomial for the series. Must be >= 0.
     |      domain : {None, array_like}, optional
     |          If given, the array must be of the form ``[beg, end]``, where
     |          ``beg`` and ``end`` are the endpoints of the domain. If None is
     |          given then the class domain is used. The default is None.
     |      window : {None, array_like}, optional
     |          If given, the resulting array must be if the form
     |          ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of
     |          the window. If None is given then the class window is used. The
     |          default is None.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A series with the coefficient of the `deg` term set to one and
     |          all others zero.
     |  
     |  cast(cls, series, domain=None, window=None) from abc.ABCMeta
     |      Convert series to series of this class.
     |      
     |      The `series` is expected to be an instance of some polynomial
     |      series of one of the types supported by by the numpy.polynomial
     |      module, but could be some other class that supports the convert
     |      method.
     |      
     |      .. versionadded:: 1.7.0
     |      
     |      Parameters
     |      ----------
     |      series : series
     |          The series instance to be converted.
     |      domain : {None, array_like}, optional
     |          If given, the array must be of the form ``[beg, end]``, where
     |          ``beg`` and ``end`` are the endpoints of the domain. If None is
     |          given then the class domain is used. The default is None.
     |      window : {None, array_like}, optional
     |          If given, the resulting array must be if the form
     |          ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of
     |          the window. If None is given then the class window is used. The
     |          default is None.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A series of the same kind as the calling class and equal to
     |          `series` when evaluated.
     |      
     |      See Also
     |      --------
     |      convert : similar instance method
     |  
     |  fit(cls, x, y, deg, domain=None, rcond=None, full=False, w=None, window=None) from abc.ABCMeta
     |      Least squares fit to data.
     |      
     |      Return a series instance that is the least squares fit to the data
     |      `y` sampled at `x`. The domain of the returned instance can be
     |      specified and this will often result in a superior fit with less
     |      chance of ill conditioning.
     |      
     |      Parameters
     |      ----------
     |      x : array_like, shape (M,)
     |          x-coordinates of the M sample points ``(x[i], y[i])``.
     |      y : array_like, shape (M,) or (M, K)
     |          y-coordinates of the sample points. Several data sets of sample
     |          points sharing the same x-coordinates can be fitted at once by
     |          passing in a 2D-array that contains one dataset per column.
     |      deg : int
     |          Degree of the fitting polynomial.
     |      domain : {None, [beg, end], []}, optional
     |          Domain to use for the returned series. If ``None``,
     |          then a minimal domain that covers the points `x` is chosen.  If
     |          ``[]`` the class domain is used. The default value was the
     |          class domain in NumPy 1.4 and ``None`` in later versions.
     |          The ``[]`` option was added in numpy 1.5.0.
     |      rcond : float, optional
     |          Relative condition number of the fit. Singular values smaller
     |          than this relative to the largest singular value will be
     |          ignored. The default value is len(x)*eps, where eps is the
     |          relative precision of the float type, about 2e-16 in most
     |          cases.
     |      full : bool, optional
     |          Switch determining nature of return value. When it is False
     |          (the default) just the coefficients are returned, when True
     |          diagnostic information from the singular value decomposition is
     |          also returned.
     |      w : array_like, shape (M,), optional
     |          Weights. If not None the contribution of each point
     |          ``(x[i],y[i])`` to the fit is weighted by `w[i]`. Ideally the
     |          weights are chosen so that the errors of the products
     |          ``w[i]*y[i]`` all have the same variance.  The default value is
     |          None.
     |      
     |          .. versionadded:: 1.5.0
     |      window : {[beg, end]}, optional
     |          Window to use for the returned series. The default
     |          value is the default class domain
     |      
     |          .. versionadded:: 1.6.0
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A series that represents the least squares fit to the data and
     |          has the domain specified in the call.
     |      
     |      [resid, rank, sv, rcond] : list
     |          These values are only returned if `full` = True
     |      
     |          resid -- sum of squared residuals of the least squares fit
     |          rank -- the numerical rank of the scaled Vandermonde matrix
     |          sv -- singular values of the scaled Vandermonde matrix
     |          rcond -- value of `rcond`.
     |      
     |          For more details, see `linalg.lstsq`.
     |  
     |  fromroots(cls, roots, domain=[], window=None) from abc.ABCMeta
     |      Return series instance that has the specified roots.
     |      
     |      Returns a series representing the product
     |      ``(x - r[0])*(x - r[1])*...*(x - r[n-1])``, where ``r`` is a
     |      list of roots.
     |      
     |      Parameters
     |      ----------
     |      roots : array_like
     |          List of roots.
     |      domain : {[], None, array_like}, optional
     |          Domain for the resulting series. If None the domain is the
     |          interval from the smallest root to the largest. If [] the
     |          domain is the class domain. The default is [].
     |      window : {None, array_like}, optional
     |          Window for the returned series. If None the class window is
     |          used. The default is None.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          Series with the specified roots.
     |  
     |  identity(cls, domain=None, window=None) from abc.ABCMeta
     |      Identity function.
     |      
     |      If ``p`` is the returned series, then ``p(x) == x`` for all
     |      values of x.
     |      
     |      Parameters
     |      ----------
     |      domain : {None, array_like}, optional
     |          If given, the array must be of the form ``[beg, end]``, where
     |          ``beg`` and ``end`` are the endpoints of the domain. If None is
     |          given then the class domain is used. The default is None.
     |      window : {None, array_like}, optional
     |          If given, the resulting array must be if the form
     |          ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of
     |          the window. If None is given then the class window is used. The
     |          default is None.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |           Series of representing the identity.
     |  
     |  ----------------------------------------------------------------------
     |  Data descriptors inherited from numpy.polynomial._polybase.ABCPolyBase:
     |  
     |  __dict__
     |      dictionary for instance variables (if defined)
     |  
     |  __weakref__
     |      list of weak references to the object (if defined)
     |  
     |  ----------------------------------------------------------------------
     |  Data and other attributes inherited from numpy.polynomial._polybase.ABCPolyBase:
     |  
     |  __array_priority__ = 1000
     |  
     |  __hash__ = None
     |  
     |  __metaclass__ = <class 'abc.ABCMeta'>
     |      Metaclass for defining Abstract Base Classes (ABCs).
     |      
     |      Use this metaclass to create an ABC.  An ABC can be subclassed
     |      directly, and then acts as a mix-in class.  You can also register
     |      unrelated concrete classes (even built-in classes) and unrelated
     |      ABCs as 'virtual subclasses' -- these and their descendants will
     |      be considered subclasses of the registering ABC by the built-in
     |      issubclass() function, but the registering ABC won't show up in
     |      their MRO (Method Resolution Order) nor will method
     |      implementations defined by the registering ABC be callable (not
     |      even via super()).
     |  
     |  maxpower = 100
    
    P = class MyPolynomial(numpy.polynomial.polynomial.Polynomial)
     |  Small extension of the numpy.polynomial.Polynomial class to change its __str__ method.
     |  
     |  Method resolution order:
     |      MyPolynomial
     |      numpy.polynomial.polynomial.Polynomial
     |      numpy.polynomial._polybase.ABCPolyBase
     |      __builtin__.object
     |  
     |  Methods defined here:
     |  
     |  __str__(self)
     |      Improved __str__ method to print nicely the polynomial as we write it in maths.
     |  
     |  ----------------------------------------------------------------------
     |  Data and other attributes defined here:
     |  
     |  __abstractmethods__ = frozenset([])
     |  
     |  ----------------------------------------------------------------------
     |  Data and other attributes inherited from numpy.polynomial.polynomial.Polynomial:
     |  
     |  domain = array([-1,  1])
     |  
     |  nickname = 'poly'
     |  
     |  window = array([-1,  1])
     |  
     |  ----------------------------------------------------------------------
     |  Methods inherited from numpy.polynomial._polybase.ABCPolyBase:
     |  
     |  __add__(self, other)
     |  
     |  __call__(self, arg)
     |  
     |  __div__(self, other)
     |  
     |  __divmod__(self, other)
     |  
     |  __eq__(self, other)
     |  
     |  __floordiv__(self, other)
     |  
     |  __getstate__(self)
     |  
     |  __init__(self, coef, domain=None, window=None)
     |  
     |  __iter__(self)
     |  
     |  __len__(self)
     |  
     |  __mod__(self, other)
     |  
     |  __mul__(self, other)
     |  
     |  __ne__(self, other)
     |  
     |  __neg__(self)
     |  
     |  __pos__(self)
     |  
     |  __pow__(self, other)
     |  
     |  __radd__(self, other)
     |  
     |  __rdiv__(self, other)
     |  
     |  __rdivmod__(self, other)
     |  
     |  __repr__(self)
     |  
     |  __rfloordiv__(self, other)
     |  
     |  __rmod__(self, other)
     |  
     |  __rmul__(self, other)
     |  
     |  __rsub__(self, other)
     |  
     |  __rtruediv__(self, other)
     |  
     |  __setstate__(self, dict)
     |  
     |  __sub__(self, other)
     |  
     |  __truediv__(self, other)
     |  
     |  convert(self, domain=None, kind=None, window=None)
     |      Convert series to a different kind and/or domain and/or window.
     |      
     |      Parameters
     |      ----------
     |      domain : array_like, optional
     |          The domain of the converted series. If the value is None,
     |          the default domain of `kind` is used.
     |      kind : class, optional
     |          The polynomial series type class to which the current instance
     |          should be converted. If kind is None, then the class of the
     |          current instance is used.
     |      window : array_like, optional
     |          The window of the converted series. If the value is None,
     |          the default window of `kind` is used.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          The returned class can be of different type than the current
     |          instance and/or have a different domain and/or different
     |          window.
     |      
     |      Notes
     |      -----
     |      Conversion between domains and class types can result in
     |      numerically ill defined series.
     |      
     |      Examples
     |      --------
     |  
     |  copy(self)
     |      Return a copy.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          Copy of self.
     |  
     |  cutdeg(self, deg)
     |      Truncate series to the given degree.
     |      
     |      Reduce the degree of the series to `deg` by discarding the
     |      high order terms. If `deg` is greater than the current degree a
     |      copy of the current series is returned. This can be useful in least
     |      squares where the coefficients of the high degree terms may be very
     |      small.
     |      
     |      .. versionadded:: 1.5.0
     |      
     |      Parameters
     |      ----------
     |      deg : non-negative int
     |          The series is reduced to degree `deg` by discarding the high
     |          order terms. The value of `deg` must be a non-negative integer.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          New instance of series with reduced degree.
     |  
     |  degree(self)
     |      The degree of the series.
     |      
     |      .. versionadded:: 1.5.0
     |      
     |      Returns
     |      -------
     |      degree : int
     |          Degree of the series, one less than the number of coefficients.
     |  
     |  deriv(self, m=1)
     |      Differentiate.
     |      
     |      Return a series instance of that is the derivative of the current
     |      series.
     |      
     |      Parameters
     |      ----------
     |      m : non-negative int
     |          Find the derivative of order `m`.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A new series representing the derivative. The domain is the same
     |          as the domain of the differentiated series.
     |  
     |  has_samecoef(self, other)
     |      Check if coefficients match.
     |      
     |      .. versionadded:: 1.6.0
     |      
     |      Parameters
     |      ----------
     |      other : class instance
     |          The other class must have the ``coef`` attribute.
     |      
     |      Returns
     |      -------
     |      bool : boolean
     |          True if the coefficients are the same, False otherwise.
     |  
     |  has_samedomain(self, other)
     |      Check if domains match.
     |      
     |      .. versionadded:: 1.6.0
     |      
     |      Parameters
     |      ----------
     |      other : class instance
     |          The other class must have the ``domain`` attribute.
     |      
     |      Returns
     |      -------
     |      bool : boolean
     |          True if the domains are the same, False otherwise.
     |  
     |  has_sametype(self, other)
     |      Check if types match.
     |      
     |      .. versionadded:: 1.7.0
     |      
     |      Parameters
     |      ----------
     |      other : object
     |          Class instance.
     |      
     |      Returns
     |      -------
     |      bool : boolean
     |          True if other is same class as self
     |  
     |  has_samewindow(self, other)
     |      Check if windows match.
     |      
     |      .. versionadded:: 1.6.0
     |      
     |      Parameters
     |      ----------
     |      other : class instance
     |          The other class must have the ``window`` attribute.
     |      
     |      Returns
     |      -------
     |      bool : boolean
     |          True if the windows are the same, False otherwise.
     |  
     |  integ(self, m=1, k=[], lbnd=None)
     |      Integrate.
     |      
     |      Return a series instance that is the definite integral of the
     |      current series.
     |      
     |      Parameters
     |      ----------
     |      m : non-negative int
     |          The number of integrations to perform.
     |      k : array_like
     |          Integration constants. The first constant is applied to the
     |          first integration, the second to the second, and so on. The
     |          list of values must less than or equal to `m` in length and any
     |          missing values are set to zero.
     |      lbnd : Scalar
     |          The lower bound of the definite integral.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A new series representing the integral. The domain is the same
     |          as the domain of the integrated series.
     |  
     |  linspace(self, n=100, domain=None)
     |      Return x, y values at equally spaced points in domain.
     |      
     |      Returns the x, y values at `n` linearly spaced points across the
     |      domain.  Here y is the value of the polynomial at the points x. By
     |      default the domain is the same as that of the series instance.
     |      This method is intended mostly as a plotting aid.
     |      
     |      .. versionadded:: 1.5.0
     |      
     |      Parameters
     |      ----------
     |      n : int, optional
     |          Number of point pairs to return. The default value is 100.
     |      domain : {None, array_like}, optional
     |          If not None, the specified domain is used instead of that of
     |          the calling instance. It should be of the form ``[beg,end]``.
     |          The default is None which case the class domain is used.
     |      
     |      Returns
     |      -------
     |      x, y : ndarray
     |          x is equal to linspace(self.domain[0], self.domain[1], n) and
     |          y is the series evaluated at element of x.
     |  
     |  mapparms(self)
     |      Return the mapping parameters.
     |      
     |      The returned values define a linear map ``off + scl*x`` that is
     |      applied to the input arguments before the series is evaluated. The
     |      map depends on the ``domain`` and ``window``; if the current
     |      ``domain`` is equal to the ``window`` the resulting map is the
     |      identity.  If the coefficients of the series instance are to be
     |      used by themselves outside this class, then the linear function
     |      must be substituted for the ``x`` in the standard representation of
     |      the base polynomials.
     |      
     |      Returns
     |      -------
     |      off, scl : float or complex
     |          The mapping function is defined by ``off + scl*x``.
     |      
     |      Notes
     |      -----
     |      If the current domain is the interval ``[l1, r1]`` and the window
     |      is ``[l2, r2]``, then the linear mapping function ``L`` is
     |      defined by the equations::
     |      
     |          L(l1) = l2
     |          L(r1) = r2
     |  
     |  roots(self)
     |      Return the roots of the series polynomial.
     |      
     |      Compute the roots for the series. Note that the accuracy of the
     |      roots decrease the further outside the domain they lie.
     |      
     |      Returns
     |      -------
     |      roots : ndarray
     |          Array containing the roots of the series.
     |  
     |  trim(self, tol=0)
     |      Remove trailing coefficients
     |      
     |      Remove trailing coefficients until a coefficient is reached whose
     |      absolute value greater than `tol` or the beginning of the series is
     |      reached. If all the coefficients would be removed the series is set
     |      to ``[0]``. A new series instance is returned with the new
     |      coefficients.  The current instance remains unchanged.
     |      
     |      Parameters
     |      ----------
     |      tol : non-negative number.
     |          All trailing coefficients less than `tol` will be removed.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          Contains the new set of coefficients.
     |  
     |  truncate(self, size)
     |      Truncate series to length `size`.
     |      
     |      Reduce the series to length `size` by discarding the high
     |      degree terms. The value of `size` must be a positive integer. This
     |      can be useful in least squares where the coefficients of the
     |      high degree terms may be very small.
     |      
     |      Parameters
     |      ----------
     |      size : positive int
     |          The series is reduced to length `size` by discarding the high
     |          degree terms. The value of `size` must be a positive integer.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          New instance of series with truncated coefficients.
     |  
     |  ----------------------------------------------------------------------
     |  Class methods inherited from numpy.polynomial._polybase.ABCPolyBase:
     |  
     |  basis(cls, deg, domain=None, window=None) from abc.ABCMeta
     |      Series basis polynomial of degree `deg`.
     |      
     |      Returns the series representing the basis polynomial of degree `deg`.
     |      
     |      .. versionadded:: 1.7.0
     |      
     |      Parameters
     |      ----------
     |      deg : int
     |          Degree of the basis polynomial for the series. Must be >= 0.
     |      domain : {None, array_like}, optional
     |          If given, the array must be of the form ``[beg, end]``, where
     |          ``beg`` and ``end`` are the endpoints of the domain. If None is
     |          given then the class domain is used. The default is None.
     |      window : {None, array_like}, optional
     |          If given, the resulting array must be if the form
     |          ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of
     |          the window. If None is given then the class window is used. The
     |          default is None.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A series with the coefficient of the `deg` term set to one and
     |          all others zero.
     |  
     |  cast(cls, series, domain=None, window=None) from abc.ABCMeta
     |      Convert series to series of this class.
     |      
     |      The `series` is expected to be an instance of some polynomial
     |      series of one of the types supported by by the numpy.polynomial
     |      module, but could be some other class that supports the convert
     |      method.
     |      
     |      .. versionadded:: 1.7.0
     |      
     |      Parameters
     |      ----------
     |      series : series
     |          The series instance to be converted.
     |      domain : {None, array_like}, optional
     |          If given, the array must be of the form ``[beg, end]``, where
     |          ``beg`` and ``end`` are the endpoints of the domain. If None is
     |          given then the class domain is used. The default is None.
     |      window : {None, array_like}, optional
     |          If given, the resulting array must be if the form
     |          ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of
     |          the window. If None is given then the class window is used. The
     |          default is None.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A series of the same kind as the calling class and equal to
     |          `series` when evaluated.
     |      
     |      See Also
     |      --------
     |      convert : similar instance method
     |  
     |  fit(cls, x, y, deg, domain=None, rcond=None, full=False, w=None, window=None) from abc.ABCMeta
     |      Least squares fit to data.
     |      
     |      Return a series instance that is the least squares fit to the data
     |      `y` sampled at `x`. The domain of the returned instance can be
     |      specified and this will often result in a superior fit with less
     |      chance of ill conditioning.
     |      
     |      Parameters
     |      ----------
     |      x : array_like, shape (M,)
     |          x-coordinates of the M sample points ``(x[i], y[i])``.
     |      y : array_like, shape (M,) or (M, K)
     |          y-coordinates of the sample points. Several data sets of sample
     |          points sharing the same x-coordinates can be fitted at once by
     |          passing in a 2D-array that contains one dataset per column.
     |      deg : int
     |          Degree of the fitting polynomial.
     |      domain : {None, [beg, end], []}, optional
     |          Domain to use for the returned series. If ``None``,
     |          then a minimal domain that covers the points `x` is chosen.  If
     |          ``[]`` the class domain is used. The default value was the
     |          class domain in NumPy 1.4 and ``None`` in later versions.
     |          The ``[]`` option was added in numpy 1.5.0.
     |      rcond : float, optional
     |          Relative condition number of the fit. Singular values smaller
     |          than this relative to the largest singular value will be
     |          ignored. The default value is len(x)*eps, where eps is the
     |          relative precision of the float type, about 2e-16 in most
     |          cases.
     |      full : bool, optional
     |          Switch determining nature of return value. When it is False
     |          (the default) just the coefficients are returned, when True
     |          diagnostic information from the singular value decomposition is
     |          also returned.
     |      w : array_like, shape (M,), optional
     |          Weights. If not None the contribution of each point
     |          ``(x[i],y[i])`` to the fit is weighted by `w[i]`. Ideally the
     |          weights are chosen so that the errors of the products
     |          ``w[i]*y[i]`` all have the same variance.  The default value is
     |          None.
     |      
     |          .. versionadded:: 1.5.0
     |      window : {[beg, end]}, optional
     |          Window to use for the returned series. The default
     |          value is the default class domain
     |      
     |          .. versionadded:: 1.6.0
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          A series that represents the least squares fit to the data and
     |          has the domain specified in the call.
     |      
     |      [resid, rank, sv, rcond] : list
     |          These values are only returned if `full` = True
     |      
     |          resid -- sum of squared residuals of the least squares fit
     |          rank -- the numerical rank of the scaled Vandermonde matrix
     |          sv -- singular values of the scaled Vandermonde matrix
     |          rcond -- value of `rcond`.
     |      
     |          For more details, see `linalg.lstsq`.
     |  
     |  fromroots(cls, roots, domain=[], window=None) from abc.ABCMeta
     |      Return series instance that has the specified roots.
     |      
     |      Returns a series representing the product
     |      ``(x - r[0])*(x - r[1])*...*(x - r[n-1])``, where ``r`` is a
     |      list of roots.
     |      
     |      Parameters
     |      ----------
     |      roots : array_like
     |          List of roots.
     |      domain : {[], None, array_like}, optional
     |          Domain for the resulting series. If None the domain is the
     |          interval from the smallest root to the largest. If [] the
     |          domain is the class domain. The default is [].
     |      window : {None, array_like}, optional
     |          Window for the returned series. If None the class window is
     |          used. The default is None.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |          Series with the specified roots.
     |  
     |  identity(cls, domain=None, window=None) from abc.ABCMeta
     |      Identity function.
     |      
     |      If ``p`` is the returned series, then ``p(x) == x`` for all
     |      values of x.
     |      
     |      Parameters
     |      ----------
     |      domain : {None, array_like}, optional
     |          If given, the array must be of the form ``[beg, end]``, where
     |          ``beg`` and ``end`` are the endpoints of the domain. If None is
     |          given then the class domain is used. The default is None.
     |      window : {None, array_like}, optional
     |          If given, the resulting array must be if the form
     |          ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of
     |          the window. If None is given then the class window is used. The
     |          default is None.
     |      
     |      Returns
     |      -------
     |      new_series : series
     |           Series of representing the identity.
     |  
     |  ----------------------------------------------------------------------
     |  Data descriptors inherited from numpy.polynomial._polybase.ABCPolyBase:
     |  
     |  __dict__
     |      dictionary for instance variables (if defined)
     |  
     |  __weakref__
     |      list of weak references to the object (if defined)
     |  
     |  ----------------------------------------------------------------------
     |  Data and other attributes inherited from numpy.polynomial._polybase.ABCPolyBase:
     |  
     |  __array_priority__ = 1000
     |  
     |  __hash__ = None
     |  
     |  __metaclass__ = <class 'abc.ABCMeta'>
     |      Metaclass for defining Abstract Base Classes (ABCs).
     |      
     |      Use this metaclass to create an ABC.  An ABC can be subclassed
     |      directly, and then acts as a mix-in class.  You can also register
     |      unrelated concrete classes (even built-in classes) and unrelated
     |      ABCs as 'virtual subclasses' -- these and their descendants will
     |      be considered subclasses of the registering ABC by the built-in
     |      issubclass() function, but the registering ABC won't show up in
     |      their MRO (Method Resolution Order) nor will method
     |      implementations defined by the registering ABC be callable (not
     |      even via super()).
     |  
     |  maxpower = 100

FUNCTIONS
    test()
        Some tests of our improved ``__str__`` method.
        
        First, let start by defining the monome X:
        
        >>> P = MyPolynomial
        >>> X = P([0, 1])  # We define the monome X, to work with it efficiently
        >>> print(X)
        X
        
        And then a few other polynomials:
        
        >>> Q1 = 1 + 2*X + 17*X**3
        >>> print(Q1)
        1 + 2 * X + 17 * X**3
        >>> Q2 = Q1 - 2*X
        >>> print(Q2)
        1 + 17 * X**3
        
        We can check that the negative signs work too:
        
        >>> Q3 = -1 - 2*X - 17*X**3
        >>> print(Q3)
        (-1) + (-2) * X + (-17) * X**3
        >>> print(-Q3)
        1 + 2 * X + 17 * X**3
        
        And with crazily long polynomials:
        
        >>> Q4 = (1 + 2*X + 17*X**3) ** 20
        >>> print(Q4)  # doctest: +ELLIPSIS
        1 + 40 * X + 760 * X**2 + 9460 * X**3 + 90440 * X**4 + ... + 4064231406647572451819520 * X**60
        >>> Q5 = (1 + 2*X + 17*X**3) ** 100
        >>> print(Q5)  # doctest: +ELLIPSIS
        1 + 200 * X + 19800 * X**2 + 1295300 * X**3 + ... + 1108899372780782949283060780215564719143115314569706274981249422854766735454757111223455545827324114733078454801811428605952 * X**300
        
        It works nicely !

DATA
    X = MyPolynomial([ 0.,  1.], [-1,  1], [-1,  1])
    division = _Feature((2, 2, 0, 'alpha', 2), (3, 0, 0, 'alpha', 0), 8192...
    print_function = _Feature((2, 6, 0, 'alpha', 2), (3, 0, 0, 'alpha', 0)...




Report
======
38 statements analysed.

Statistics by type
------------------

+---------+-------+-----------+-----------+------------+---------+
|type     |number |old number |difference |%documented |%badname |
+=========+=======+===========+===========+============+=========+
|module   |1      |1          |=          |100.00      |100.00   |
+---------+-------+-----------+-----------+------------+---------+
|class    |1      |1          |=          |100.00      |100.00   |
+---------+-------+-----------+-----------+------------+---------+
|method   |1      |1          |=          |100.00      |0.00     |
+---------+-------+-----------+-----------+------------+---------+
|function |1      |1          |=          |100.00      |0.00     |
+---------+-------+-----------+-----------+------------+---------+



External dependencies
---------------------
::

    numpy 
      \-polynomial (nicedisplay_numpy_polynomial_Polynomial)



Raw metrics
-----------

+----------+-------+------+---------+-----------+
|type      |number |%     |previous |difference |
+==========+=======+======+=========+===========+
|code      |39     |38.61 |39       |=          |
+----------+-------+------+---------+-----------+
|docstring |49     |48.51 |49       |=          |
+----------+-------+------+---------+-----------+
|comment   |2      |1.98  |2        |=          |
+----------+-------+------+---------+-----------+
|empty     |11     |10.89 |11       |=          |
+----------+-------+------+---------+-----------+



Duplication
-----------

+-------------------------+------+---------+-----------+
|                         |now   |previous |difference |
+=========================+======+=========+===========+
|nb duplicated lines      |0     |0        |=          |
+-------------------------+------+---------+-----------+
|percent duplicated lines |0.000 |0.000    |=          |
+-------------------------+------+---------+-----------+



Messages by category
--------------------

+-----------+-------+---------+-----------+
|type       |number |previous |difference |
+===========+=======+=========+===========+
|convention |0      |0        |=          |
+-----------+-------+---------+-----------+
|refactor   |0      |0        |=          |
+-----------+-------+---------+-----------+
|warning    |0      |0        |=          |
+-----------+-------+---------+-----------+
|error      |0      |0        |=          |
+-----------+-------+---------+-----------+



Global evaluation
-----------------
Your code has been rated at 10.00/10 (previous run: 10.00/10, +0.00)
Wow ! Now this deserves our uttermost respect.
Please send your code to python-projects@logilab.org

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