230 lines
6.7 KiB
Python
230 lines
6.7 KiB
Python
#!/usr/bin/env python
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# encoding: utf-8
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from .expression import Expression
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from .operator import op
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from .generic import isNumerand
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from .random_expression import RdExpression
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from .abstract_polynom import AbstractPolynom
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from functools import wraps
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import inspect
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__all__ = ["Polynom"]
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def polynom_factory(func):
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""" Decorator which specify the type of polynom that the function returns """
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@wraps(func)
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def wrapper(*args, **kwrds):
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P = func(*args, **kwrds)
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if isinstance(P,Polynom) and P.degree == 2:
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from .polynomDeg2 import Polynom_deg2
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new_P = Polynom_deg2(poly=P)
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new_P.steps = P.steps
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return new_P
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else:
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return P
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return wrapper
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class Polynom(AbstractPolynom):
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"""Polynom view as a function.
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It can be initiate like a AbstractPolynom
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# Put example
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Randomly
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# Put example
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It can be evaluate
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# Put example
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And derivate
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# Put example
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"""
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@classmethod
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def random(self, coefs_form=[], conditions=[], letter = "x", degree = 0, name = "P"):
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""" Create a random polynom from coefs_form and conditions
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:param coefs_form: list of forms (one by coef) (ascending degree sorted)
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:param conditions: condition on variables
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:param letter: the letter for the polynom
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:param degree: degree of the polynom (can't be used with coefs_form, it will be overwrite) - can't be higher than 26 (number of letters in alphabet)
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/!\ variables need to be in brackets {}
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>>> Polynom.random(["{b}", "{a}"]) # doctest:+ELLIPSIS
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< Polynom ...
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>>> Polynom.random(degree = 2) # doctest:+ELLIPSIS
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< Polynom ...
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>>> Polynom.random(degree = 2, conditions=["{b**2-4*a*c}>0"]) # Polynom deg 2 with positive Delta (ax^2 + bx + c)
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< Polynom ...
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>>> Polynom.random(["{c}", "{b}", "{a}"], conditions=["{b**2-4*a*c}>0"]) # Same as above
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< Polynom ...
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"""
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if (degree > 0 and degree < 26):
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# Générer assez de lettre pour les coefs
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coefs_name = map(chr, range(97, 98+degree))
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coefs_form = ["{" + i + "}" for i in coefs_name][::-1]
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form = str(coefs_form)
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# On créé les valeurs toutes concaténées dans un string
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coefs = RdExpression(form, conditions)()
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# On "parse" ce string pour créer les coefs
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coefs = [eval(i) if type(i)==str else i for i in eval(coefs)]
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# Création du polynom
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return Polynom(coefs = coefs, letter = letter, name = name)
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def __init__(self, coefs = [1], letter = "x", name = "P"):
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"""Initiate the polynom
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:param coef: coefficients of the polynom (ascending degree sorted)
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3 possibles type of coefficent:
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- a : simple "number". [1,2] designate 1 + 2x
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- [a,b,c]: list of coeficient for same degree. [1,[2,3],4] designate 1 + 2x + 3x + 4x^2
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- a: a Expression. [1, Expression("2+3"), 4] designate 1 + (2+3)x + 4x^2
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:param letter: the string describing the unknown
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:param name: Name of the polynom
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>>> P = Polynom([1, 2, 3])
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>>> P.mainOp
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'+'
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>>> P.name
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'P'
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>>> P._letter
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'x'
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>>> Polynom([1]).mainOp
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'*'
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>>> Polynom([0, 0, 3]).mainOp
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'*'
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>>> Polynom([1, 2, 3])._letter
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'x'
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>>> Polynom([1, 2, 3], "y")._letter
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'y'
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>>> Polynom([1, 2, 3], name = "Q").name
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'Q'
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"""
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super(Polynom, self).__init__(coefs, letter, name)
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def __call__(self, value):
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""" Evaluate the polynom in value
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:returns: Expression ready to be simplify
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>>> P = Polynom([1, 2, 3])
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>>> P(2)
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17
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>>> for i in P(2).explain():
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... print(i)
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3 \\times 2^{ 2 } + 2 \\times 2 + 1
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3 \\times 4 + 4 + 1
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12 + 4 + 1
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16 + 1
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17
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>>> Q = P("1+h")
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>>> print(Q)
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3 h^{ 2 } + 8 h + 6
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>>> R = P(Q)
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"""
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if isNumerand(value) or Expression.isExpression(value):
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postfix_exp = [value if i==self._letter else i for i in self.postfix_tokens]
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else:
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postfix_exp = [Expression(value) if i==self._letter else i for i in self.postfix_tokens]
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return Expression(postfix_exp).simplify()
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def derivate(self):
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""" Return the derivated polynom
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>>> P = Polynom([1, 2, 3])
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>>> Q = P.derivate()
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>>> Q
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< Polynom [2, 6]>
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>>> print(Q.name)
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P'
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>>> for i in Q.explain():
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... print(i)
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2 \\times 3 x + 1 \\times 2
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6 x + 2
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"""
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derv_coefs = []
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for (i,c) in enumerate(self._coef):
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derv_coefs += [Expression([i, c, op.mul])]
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ans = Polynom(derv_coefs[1:]).simplify()
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ans.name = self.name + "'"
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return ans
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# Decorate methods which may return Polynoms
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methods_list = ["__add__", "__call__", "__mul__", "__neg__", "__pow__",
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"__radd__", "__rmul__", "__rsub__", "__sub__", "derivate",
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"reduce", "simplify", "random"]
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for name, func in inspect.getmembers(Polynom):
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if name in methods_list:
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setattr(Polynom, name, polynom_factory(func))
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def test(p,q):
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print("---------------------")
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print("---------------------")
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print("p : ",p)
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print("q : ",q)
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print("\n Plus ------")
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print(p, "+", q)
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for i in (p + q):
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#print(repr(i))
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#print("\t", str(i.postfix_tokens))
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print(i)
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print("\n Moins ------")
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for i in (p - q):
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#print(repr(i))
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#print("\t", str(i.postfix_tokens))
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print(i)
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print("\n Multiplier ------")
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for i in (p * q):
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#print(repr(i))
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#print("\t", str(i.postfix_tokens))
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print(i)
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print("\n Evaluer p ------")
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for i in p(3).simplify():
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print(i)
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print("\n Evaluer q ------")
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for i in q(3).simplify():
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print(i)
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if __name__ == '__main__':
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#from .fraction import Fraction
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#with Expression.tmp_render(txt):
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# p = Polynom([1, 2, 3])
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# q = Polynom([4, 5, 6])
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# for i in (p*q).explain():
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# print(i)
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# r = Polynom([0,1])
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# for i in (r*3).explain():
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# print(i)
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# print("q = ", q)
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# r = q.reduce()
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# print("r = ", r)
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# for i in r.explain():
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# print("q = ", i)
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# print(p-q)
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# for i in p-q:
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# print(i)
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#Polynom.random(degree = 2, conditions=["{b**2-4*a*c}>0"]) # Polynom deg 2 with positive Delta (ax^2 + bx + c)
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import doctest
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doctest.testmod(optionflags=doctest.ELLIPSIS)
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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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