319 lines
7.9 KiB
Python
319 lines
7.9 KiB
Python
#! /usr/bin/env python
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# -*- coding: utf-8 -*-
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# vim:fenc=utf-8
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#
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# Copyright © 2017 lafrite <lafrite@Poivre>
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#
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# Distributed under terms of the MIT license.
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"""
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Tokens representing polynomials functions
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"""
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from ..expression import Expression
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from .token import Token
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from . import to_be_token
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from ...core.MO import MO
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from ...core.MO.atoms import moify
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from ...core.MO.polynomial import MOpolynomial
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__all__ = ["Polynomial", "Quadratic", "Linear"]
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class Polynomial(Token):
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""" Token representing a polynomial
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:examples:
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>>> from ...core.MO.polynomial import MOpolynomial
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>>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
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>>> P
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<Polynomial 3x^2 + 2x + 1>
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"""
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def __init__(self, a, name="", ancestor=None):
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""" Initiate Polynomial with a MO"""
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if not isinstance(a, MO):
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raise TypeError
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Token.__init__(self, a, name, ancestor)
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self._mathtype = "polynome"
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@classmethod
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def from_mo(cls, mo, name="", ancestor=None):
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return cls(mo, name, ancestor)
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@classmethod
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def from_coefficients(cls, coefficients, variable_name="x", name=""):
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""" Initiate polynomial from list of coefficients
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:examples:
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>>> P = Polynomial.from_coefficients([1, 2, 3])
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>>> P
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<Polynomial 3x^2 + 2x + 1>
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>>> P = Polynomial.from_coefficients([1, 2, -3])
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>>> P
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<Polynomial - 3x^2 + 2x + 1>
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>>> P = Polynomial.from_coefficients([1, 2, 3], "y")
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>>> P
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<Polynomial 3y^2 + 2y + 1>
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"""
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return cls(MOpolynomial(variable_name, coefficients), name)
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@property
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def raw(self):
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raise NotImplementedError("Polynomial does not exists in python")
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def __setitem__(self, key, item):
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""" Use Polynomial like if they were a dictionnary to set coefficients """
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raise NotImplementedError("Can't set coefficient of a polynomial")
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@to_be_token
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def __getitem__(self, key):
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""" Use Polynomial like if they were a dictionnary to get coefficients
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:examples:
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>>> from ...core.MO.polynomial import MOpolynomial
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>>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
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>>> P[0]
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<Integer 1>
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>>> P[1]
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<Integer 2>
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>>> P[2]
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<Integer 3>
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>>> P[3]
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Traceback (most recent call last):
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...
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KeyError: 3
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"""
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return self._mo.coefficients[key]
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def __call__(self, value):
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""" Call a Polynomial to evaluate itself on value
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:examples:
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>>> from ...core.MO.polynomial import MOpolynomial
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>>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
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>>> for s in P(2).explain():
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... print(s)
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3 * 2^2 + 2 * 2 + 1
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3 * 4 + 4 + 1
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12 + 5
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17
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"""
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return Expression(self._mo.tree)(value)
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def differentiate(self):
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""" Differentiate a polynome
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:example:
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>>> from ...core.MO.polynomial import MOpolynomial
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>>> P = Polynomial(MOpolynomial('x', [1, 2, 3]))
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>>> P
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<Polynomial 3x^2 + 2x + 1>
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>>> P.differentiate()
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<Linear 6x + 2>
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>>> for s in P.differentiate().explain():
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... print(s)
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0 + 2 + 3 * 2x
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2 + 3 * 2 * x
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6x + 2
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"""
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return Expression(self._mo.differentiate()).simplify()
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@property
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def roots(self):
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""" Get roots of the Polynomial """
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raise NotImplementedError("Can't compute roots not specific polynomial")
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class Linear(Polynomial):
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""" Token representing a linear ax + b
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:examples:
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>>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
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>>> P = Linear(MOpolynomial('x', [1, 2]))
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>>> P
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<Linear 2x + 1>
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>>> P.a
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<Integer 2>
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>>> P.b
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<Integer 1>
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>>> P.differentiate()
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<Integer 2>
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>>> P.roots
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[<Integer - 2>]
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>>> for i in P.roots[0].explain():
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... print(i)
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- 2 / 1
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- 2
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"""
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def __init__(self, mo, name="", ancestor=None):
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""" Initiate Linear with MO
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:examples:
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>>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
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>>> P = Linear(MOpolynomial('x', [1, 2]))
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>>> P
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<Linear 2x + 1>
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>>> Q = Linear(MOMonomial(3, 'x', 1))
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>>> Q
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<Linear 3x>
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"""
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Polynomial.__init__(self, mo, name, ancestor)
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self._mathtype = "affine"
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@property
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@to_be_token
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def a(self):
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return self[1]
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@property
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@to_be_token
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def b(self):
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return self[0]
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@property
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@to_be_token
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def roots(self):
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""" Get the root of the polynomial
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:examples:
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>>> from ...core.MO.polynomial import MOpolynomial, MOMonomial
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>>> P = Linear(MOpolynomial('x', [1, 2]))
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>>> P.roots
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[<Integer - 2>]
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>>> P = Linear(MOpolynomial('x', [2, 1]))
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>>> P.roots
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[<Fraction - 1 / 2>]
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>>> for i in P.roots[0].explain():
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... print(i)
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- 1 / 2
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>>> P = Linear(MOpolynomial('x', [10, 6]))
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>>> P.roots
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[<Fraction - 3 / 5>]
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>>> for i in P.roots[0].explain():
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... print(i)
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- 6 / 10
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- 3 / 5
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"""
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try:
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return [Expression.from_str(f"-{self.a}/{self.b}").simplify()]
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except AttributeError:
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return [Expression.from_str(f"-{self.a}/{self.b}")]
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class Quadratic(Polynomial):
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""" Token representing a quadratic ax^2 + bx + c
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:examples:
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>>> from ...core.MO.polynomial import MOpolynomial
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>>> P = Quadratic(MOpolynomial('x', [1, 2, 3]))
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>>> P
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<Quadratic 3x^2 + 2x + 1>
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>>> P.a
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<Integer 3>
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>>> P.b
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<Integer 2>
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>>> P.c
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<Integer 1>
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>>> P.delta
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<Integer - 8>
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>>> for s in P.delta.explain():
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... print(s)
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2^2 - 4 * 3 * 1
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4 - 12 * 1
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4 - 12
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- 8
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>>> P.differentiate()
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<Linear 6x + 2>
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>>> P.roots
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[]
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"""
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def __init__(self, mo, name="", ancestor=None):
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""" Initiate Quadratic from MO
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>>> from ...core.MO.polynomial import MOpolynomial
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>>> P = Quadratic(MOpolynomial('x', [1, 2, 3]))
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>>> P
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<Quadratic 3x^2 + 2x + 1>
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"""
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Polynomial.__init__(self, mo, name, ancestor)
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self._mathtype = "polynome du 2nd degré"
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@property
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@to_be_token
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def a(self):
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try:
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return self[2]
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except KeyError:
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return 0
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@property
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@to_be_token
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def b(self):
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try:
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return self[1]
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except KeyError:
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return 0
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@property
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@to_be_token
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def c(self):
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try:
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return self[0]
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except KeyError:
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return 0
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@property
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@to_be_token
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def delta(self):
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return Expression.from_str(f"{self.b}^2-4*{self.a}*{self.c}").simplify()
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@property
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@to_be_token
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def roots(self):
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""" Roots of the polynom
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:example:
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>>> from ...core.MO.polynomial import MOpolynomial
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>>> P = Quadratic(MOpolynomial('x', [1, 0, 1]))
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>>> P.roots
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[]
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>>> P = Quadratic(MOpolynomial('x', [4, -4, 1]))
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>>> P.roots
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[<Integer 2>]
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>>> P = Quadratic(MOpolynomial('x', [1, 0, -1]))
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>>> P.roots
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[<Integer - 1>, <Integer 1>]
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"""
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if self.delta._mo < 0:
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return []
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elif self.delta._mo == 0:
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# return [Expression.from_str(f"-{self.b}/(2*{self.a})").simplify()]
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return [round(eval(f"-{self.b}/(2*{self.a})"), 2)]
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else:
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from math import sqrt
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roots = [
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str(eval(f"(-{self.b}-sqrt({self.delta}))/(2*{self.a})")),
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str(eval(f"(-{self.b}+sqrt({self.delta}))/(2*{self.a})")),
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]
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roots.sort()
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return roots
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# -----------------------------
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# Reglages pour 'vim'
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# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del
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