Mapytex/mapytex/calculus/core/MO/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.
from mapytex.calculus.core.tree import Tree
from . import MO, MOstr
from .mo import Molecule
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from .exceptions import MOError
from .monomial import MOMonomial, MOstrPower
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__all__ = ["MOpolynomial"]
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class MOpolynomial(Molecule):
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""" MO polynomial"""
MAINOP = "+"
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def __init__(self, variable, coefs):
""" Initiate a MOpolynomial
:param variable: variable of the monomial (a MOstr or later a MOSqrt)
:param coefs: dictionnary {deg: coef} or a list [coef0, coef1...]
:example:
>>> MOpolynomial('x', [1, 2, 3])
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<MOpolynomial 3x^2 + 2x + 1>
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>>> MOpolynomial('x', [1, 0, 3])
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<MOpolynomial 3x^2 + 1>
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>>> MOpolynomial('x', {0: 1, 1: 2, 2: 3})
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<MOpolynomial 3x^2 + 2x + 1>
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>>> MOpolynomial('x', {0: 1, 3: 4})
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<MOpolynomial 4x^3 + 1>
>>> MOpolynomial('x', {0: 1, 3: 1})
<MOpolynomial x^3 + 1>
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"""
_variable = MO.factory(variable)
if not isinstance(_variable, MOstr):
raise MOError("The variable of a monomial should be convertible into MOstr")
self._variable = _variable
if isinstance(coefs, dict):
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_coefs = {
MO.factory(d): MO.factory(c) for (d, c) in coefs.items() if c != 0
}
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elif isinstance(coefs, list):
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_coefs = {
MO.factory(d): MO.factory(c) for (d, c) in enumerate(coefs) if c != 0
}
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else:
raise TypeError("Coefs needs to be a dictionnary or a list")
self._coefs = _coefs
monomials = {}
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for deg, coef in self._coefs.items():
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if deg == 0:
monomials[deg] = coef
elif deg == 1 and coef == 1:
monomials[deg] = MOstr(self._variable)
elif coef == 1:
monomials[deg] = MOstrPower(self._variable, deg)
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else:
monomials[deg] = MOMonomial(coef, self._variable, deg)
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self._monomials = monomials
tree = Tree.from_list("+", list(self._monomials.values())[::-1])
Molecule.__init__(self, tree)
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@property
def variable(self):
return self._variable
@property
def degree(self):
"""
Maximum degree of its coefficient
:example:
>>> p = MOpolynomial('x', [1, 2, 3])
>>> p.degree
2
>>> p = MOpolynomial('x', {0: 1, 3: 4})
>>> p.degree
3
"""
return self.power.value
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@property
def power(self):
"""
Maximum degree of its coefficient
:example:
>>> p = MOpolynomial('x', [1, 2, 3])
>>> p.power
<MOnumber 2>
>>> p = MOpolynomial('x', {0: 1, 3: 4})
>>> p.power
<MOnumber 3>
"""
return max(self._coefs.keys())
@property
def coefficients(self):
return self._coefs
@property
def monomials(self):
""" Return dictionnary with degree in keys and monomial in value
:example:
>>> p = MOpolynomial('x', [1, 2, 3])
>>> p.monomials
{<MOnumber 0>: <MOnumber 1>, <MOnumber 1>: <MOMonomial 2x>, <MOnumber 2>: <MOMonomial 3x^2>}
>>> p.monomials.values()
dict_values([<MOnumber 1>, <MOMonomial 2x>, <MOMonomial 3x^2>])
"""
return self._monomials
def differentiate(self):
""" Differentiate a MOMonomial and get a tree
:example:
>>> p = MOpolynomial('x', [1, 2, 3])
>>> print(p)
3x^2 + 2x + 1
>>> print(p.differentiate())
+
> 0
> +
| > 2
| > *
| | > 3
| | > *
| | | > 2
| | | > x
"""
monomials_d = [m.differentiate() for m in self.monomials.values()]
return Tree.from_list("+", monomials_d)
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