261 lines
6.2 KiB
Python
261 lines
6.2 KiB
Python
#! /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 .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):
|
|
""" 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)
|
|
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]))
|
|
>>> for s in P(2).explain():
|
|
... print(s)
|
|
3 * 2^2 + 2 * 2 + 1
|
|
3 * 4 + 4 + 1
|
|
12 + 5
|
|
17
|
|
"""
|
|
return Expression(self._mo.tree)(value)
|
|
|
|
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")
|
|
|
|
|
|
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)
|
|
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}")]
|
|
|
|
|
|
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)
|
|
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!")
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|