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

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#! /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
"""
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from ..expression import Expression
from functools import partial
from .token import Token
from ...core.MO import MO
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from ...core.MO.atoms import moify
__all__ = ["Polynomial", "Quadratic", "Linear"]
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class Polynomial(Token):
""" Token representing a polynomial
:examples:
>>> from ...core.MO.polynomial import MOpolynomial
>>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
>>> P
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<Polynomial 3x^2 + 2x + 1>
"""
def __init__(self, a, name="", ancestor=None):
""" Initiate Polynomial with a MO"""
if not isinstance(a, MO):
if isinstance(a, str):
raise TypeError
else:
raise TypeError
else:
mo = a
Token.__init__(self, mo, name, ancestor)
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self._mathtype = "polynome"
@classmethod
def from_mo(cls, mo, name="", ancestor=None):
return cls(mo, name, ancestor)
@classmethod
def from_coefficients(cls, coefficients):
""" Initiate polynomial from list of coefficients """
pass
@classmethod
def random(cls):
raise NotImplementedError
def __setitem__(self, key, item):
""" Use Polynomial like if they were a dictionnary to set coefficients """
raise NotImplementedError("Can't set coefficient of a polynomial")
def __getitem__(self, key):
""" Use Polynomial like if they were a dictionnary to get coefficients
:examples:
>>> from ...core.MO.polynomial import MOpolynomial
>>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
>>> P[0]
<MOnumber 1>
>>> P[1]
<MOnumber 2>
>>> P[2]
<MOnumber 3>
>>> P[3]
Traceback (most recent call last):
...
KeyError: 3
"""
return self._mo.coefficients[key]
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]))
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>>> for s in P(2).explain():
... print(s)
3 * 2^2 + 2 * 2 + 1
3 * 4 + 4 + 1
12 + 5
17
"""
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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()
def differentiate(self):
""" Differentiate a polynome
:example:
>>> from ...core.MO.polynomial import MOpolynomial
>>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
>>> P
<Polynomial 3x^2 + 2x + 1>
>>> P.differentiate()
<Linear 2 + 6x>
>>> for s in P.differentiate().explain():
... print(s)
0 + 2 + 3 * 2x
2 + 3 * 2 * x
2 + 6x
"""
return Expression(self._mo.differentiate()).simplify()
@property
def roots(self):
""" Get roots of the Polynomial """
raise NotImplementedError("Can't compute roots not specific polynomial")
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class Linear(Polynomial):
""" Token representing a linear ax + b
:examples:
>>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
>>> P = Linear(MOpolynomial('x', [1, 2]))
>>> P
<Linear 2x + 1>
>>> P.a
<MOnumber 2>
>>> P.b
<MOnumber 1>
>>> P.differentiate()
<Integer 2>
>>> P.roots
[<Fraction - 2 / 1>]
"""
def __init__(self, mo, name="", ancestor=None):
""" Initiate Linear with MO
:examples:
>>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
>>> P = Linear(MOpolynomial('x', [1, 2]))
>>> P
<Linear 2x + 1>
>>> Q = Linear(MOMonomial(3, 'x', 1))
>>> Q
<Linear 3x>
"""
Polynomial.__init__(self, mo, name, ancestor)
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self._mathtype = "affine"
@classmethod
def random(cls):
raise NotImplementedError
@property
def a(self):
return self[1]
@property
def b(self):
return self[0]
@property
def roots(self):
""" Get the root of the polynomial
:examples:
>>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
>>> P = Linear(MOpolynomial('x', [1, 2]))
>>> P.roots
[<Fraction - 2 / 1>]
>>> #P = Linear(MOpolynomial('x', [1, -2]))
>>> #P.roots
"""
try:
return [Expression.from_str(f"-{self.a}/{self.b}").simplify()]
except AttributeError:
return [Expression.from_str(f"-{self.a}/{self.b}")]
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class Quadratic(Polynomial):
""" Token representing a quadratic ax^2 + bx + c
:examples:
>>> from ...core.MO.polynomial import MOpolynomial
>>> P = Quadratic(MOpolynomial('x', [1, 2, 3]))
>>> P
<Quadratic 3x^2 + 2x + 1>
>>> P.a
<MOnumber 3>
>>> P.b
<MOnumber 2>
>>> P.c
<MOnumber 1>
>>> P.delta
<Integer - 8>
>>> for s in P.delta.explain():
... print(s)
2^2 - 4 * 3 * 1
4 - 12 * 1
4 - 12
- 8
>>> P.differentiate()
<Linear 2 + 6x>
>>> P.roots
[]
"""
def __init__(self, mo, name="", ancestor=None):
""" Initiate Quadratic from MO
>>> from ...core.MO.polynomial import MOpolynomial
>>> P = Quadratic(MOpolynomial('x', [1, 2, 3]))
>>> P
<Quadratic 3x^2 + 2x + 1>
"""
Polynomial.__init__(self, mo, name, ancestor)
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self._mathtype = "polynome du 2nd degré"
@classmethod
def random(cls):
raise NotImplementedError
@property
def a(self):
return self[2]
@property
def b(self):
return self[1]
@property
def c(self):
return self[0]
@property
def delta(self):
return Expression.from_str(f"{self.b}^2-4*{self.a}*{self.c}").simplify()
@property
def roots(self):
if self.delta._mo < 0:
return []
elif self.delta._mo == 0:
return [Expression.from_str(f"-{self.b}/(2*{self.a})").simplify()]
else:
raise NotImplementedError("Todo!")
def extract_variable(leaf):
try:
return leaf.variable
except AttributeError:
return None
def replace(leaf, origin, dest):
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""" 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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