Mapytex/mapytex/calculus/API/tokens/polynomial.py

#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright © 2017 lafrite <lafrite@Poivre>
#
# Distributed under terms of the MIT license.

"""
Tokens representing polynomials functions 

"""
from ..expression import Expression
from functools import partial
from .token import Token
from ...core.MO import MO
from ...core.MO.atoms import moify

__all__ = ["Polynomial", "Quadratic", "Linear"]


class Polynomial(Token):

    """ Token representing a polynomial 

    :examples:
    >>> from ...core.MO.polynomial import MOpolynomial
    >>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
    >>> P
    <Polynomial 3x^2 + 2x + 1>
    """

    def __init__(self, a, name="", ancestor=None):
        if not isinstance(a, MO):
            if isinstance(a, str):
                raise TypeError
            else:
                raise TypeError
        else:
            mo = a

        Token.__init__(self, mo, name, ancestor)
        self._mathtype = "polynome"

    @classmethod
    def from_mo(cls, mo, name="", ancestor=None):

        return cls(mo, name, ancestor)

    @classmethod
    def random(cls):
        raise NotImplemented

    def __setitem__(self, key, item):
        """ Use Polynomial like if they were a dictionnary to set coefficients """
        pass

    def __getitem__(self, key):
        """ Use Polynomial like if they were a dictionnary to get coefficients """
        pass

    def __call__(self, value):
        """ Call a Polynomial to evaluate itself on value 

        :examples:
        >>> from ...core.MO.polynomial import MOpolynomial
        >>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
        >>> for s in P(2).explain():
        ...     print(s)
        3 * 2^2 + 2 * 2 + 1
        3 * 4 + 4 + 1
        12 + 5
        17
        """
        tree = self._mo.tree
        variable = (set(tree.get_leafs(extract_variable)) - {None}).pop()

        dest = moify(value)
        replace_var = partial(replace, origin=variable, dest=dest)
        tree = tree.map_on_leaf(replace_var)

        return Expression(tree).simplify()


class Linear(Polynomial):

    """ Token representing a linear """

    def __init__(self, mo, name="", ancestor=None):

        Polynomial.__init__(self, mo, name, ancestor)
        self._mathtype = "affine"

    @classmethod
    def random(cls):
        raise NotImplemented


class Quadratic(Polynomial):

    """ Token representing a quadratic """

    def __init__(self, mo, name="", ancestor=None):

        Polynomial.__init__(self, mo, name, ancestor)
        self._mathtype = "polynome du 2nd degré"

    @classmethod
    def random(cls):
        raise NotImplemented


def extract_variable(leaf):
    try:
        return leaf.variable
    except AttributeError:
        return None

def replace(leaf, origin, dest):
    """ Recursively replace origin to dest in leaf """
    try:
        leaf.tree
    except AttributeError:
        if leaf == origin:
            return dest
        return leaf

    replace_var = partial(replace, origin=origin, dest=dest)
    return leaf.tree.map_on_leaf(replace_var)
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