220 lines
6.6 KiB
Python
220 lines
6.6 KiB
Python
#!/usr/bin/env python
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# encoding: utf-8
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from .polynom import Polynom
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from .expression import Expression
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from .operator import op
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from .random_expression import RdExpression
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from math import sqrt
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__all__ = ["Polynom_deg2"]
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class Polynom_deg2(Polynom):
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""" Degree 2 polynoms
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Child of Polynom with some extra tools
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"""
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@classmethod
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def random(self, coefs_form = ["{c}", "{b}", "{a}"], conditions = [], letter = "x"):
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""" Create a 2nd degree poly from coefs_form ans 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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"""
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if len(coefs_form) != 3:
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raise ValueError("Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(len(coefs_form)))
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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_deg2(coefs = coefs, letter = letter)
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def __init__(self, coefs = [0, 0, 1], letter = "x"):
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if len(coefs) < 3 or len(coefs) > 4:
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raise ValueError("Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(len(coefs)))
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if coefs[2] == 0:
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raise ValueError("Polynom_deg2 have to be degree 2 polynoms, coefficient of x^2 can't be 0")
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Polynom.__init__(self, coefs, letter)
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@property
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def a(self):
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return self._coef[2]
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@property
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def b(self):
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return self._coef[1]
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@property
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def c(self):
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return self._coef[0]
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@property
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def delta(self):
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"""Compute the discriminant expression
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:returns: discriminant expression
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>>> P = Polynom_deg2([1,2,3])
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>>> P.delta
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-8
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>>> for i in P.delta.explain():
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... print(i)
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2^{ 2 } - 4 \\times 3 \\times 1
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4 - 4 \\times 3
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4 - 12
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-8
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"""
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return Expression([self.b, 2, op.pw, 4, self.a, self.c, op.mul, op.mul, op.sub]).simplify()
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@property
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def alpha(self):
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""" Compute alpha the abcisse of the extremum
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>>> P = Polynom_deg2([1,2,3])
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>>> P.alpha
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< Fraction -1 / 3>
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>>> for i in P.alpha.explain():
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... print(i)
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\\frac{ - 2 }{ 2 \\times 3 }
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\\frac{ -2 }{ 6 }
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\\frac{ ( -1 ) \\times 2 }{ 3 \\times 2 }
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\\frac{ -1 }{ 3 }
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"""
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return Expression([self.b, op.sub1, 2, self.a, op.mul, op.div]).simplify()
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@property
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def beta(self):
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""" Compute beta the extremum of self
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>>> P = Polynom_deg2([1,2,3])
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>>> P.beta
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< Fraction 2 / 3>
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>>> for i in P.beta.explain(): # Ça serait bien que l'on puisse enlever des étapes maintenant...
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... print(i)
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3 \\times \\frac{ -1 }{ 3 }^{ 2 } + 2 \\times \\frac{ -1 }{ 3 } + 1
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3 \\times \\frac{ 1 }{ 9 } + \\frac{ -2 }{ 3 } + 1
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\\frac{ 1 }{ 3 } + \\frac{ -2 }{ 3 } + 1
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\\frac{ -1 }{ 3 } + 1
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\\frac{ 2 }{ 3 }
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"""
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return self(self.alpha).simplify()
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def roots(self):
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""" Compute roots of the polynom
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/!\ Can't manage exact solution because of pymath does not handle sqare root yet
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# TODO: Pymath has to know how to compute with sqare root |mar. févr. 24 18:40:04 CET 2015
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>>> P = Polynom_deg2([1, 1, 1])
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>>> P.roots()
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[]
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>>> P = Polynom_deg2([1, 2, 1])
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>>> P.roots()
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[-1.0]
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>>> P = Polynom_deg2([-1, 0, 1])
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>>> P.roots()
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[-1.0, 1.0]
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"""
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if self.delta > 0:
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self.roots = [(-self.b - sqrt(self.delta))/(2*self.a), (-self.b + sqrt(self.delta))/(2*self.a)]
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elif self.delta == 0:
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self.roots = [-self.b /(2*self.a)]
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else:
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self.roots = []
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return self.roots
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def tbl_sgn(self):
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""" Return the sign line for tkzTabLine
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>>> P = Polynom_deg2([2, 5, 2])
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>>> print(P.tbl_sgn())
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\\tkzTabLine{, +, z, -, z , +,}
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>>> P = Polynom_deg2([2, 1, -2])
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>>> print(P.tbl_sgn())
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\\tkzTabLine{, -, z, +, z , -,}
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>>> P = Polynom_deg2([1, 2, 1])
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>>> print(P.tbl_sgn())
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\\tkzTabLine{, +, z, +,}
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>>> P = Polynom_deg2([0, 0, -2])
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>>> print(P.tbl_sgn())
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\\tkzTabLine{, -, z, -,}
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>>> P = Polynom_deg2([1, 0, 1])
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>>> print(P.tbl_sgn())
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\\tkzTabLine{, +,}
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>>> P = Polynom_deg2([-1, 0, -1])
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>>> print(P.tbl_sgn())
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\\tkzTabLine{, -,}
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"""
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if self.delta > 0:
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if self.a > 0:
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return "\\tkzTabLine{, +, z, -, z , +,}"
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else:
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return "\\tkzTabLine{, -, z, +, z , -,}"
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elif self.delta == 0:
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if self.a > 0:
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return "\\tkzTabLine{, +, z, +,}"
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else:
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return "\\tkzTabLine{, -, z, -,}"
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else:
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if self.a > 0:
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return "\\tkzTabLine{, +,}"
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else:
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return "\\tkzTabLine{, -,}"
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def tbl_variation(self, limits = False):
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"""Return the variation line for tkzTabVar
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:param limit: Display or not limits in tabular
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>>> P = Polynom_deg2([1,2,3])
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>>> print(P.tbl_variation())
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\\tkzTabVar{+/{}, -/{$\\frac{ 2 }{ 3 }$}, +/{}}
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>>> print(P.tbl_variation(limits = True))
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\\tkzTabVar{+/{$+\\infty$}, -/{$\\frac{ 2 }{ 3 }$}, +/{$+\\infty$}}
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"""
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beta = self.beta
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if limits:
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if self.a > 0:
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return "\\tkzTabVar{+/{$+\\infty$}, -/{$" + str(beta) + "$}, +/{$+\\infty$}}"
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else:
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return "\\tkzTabVar{-/{$-\\infty$}, +/{$" + str(beta) + "$}, -/{$-\\infty$}}"
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else:
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if self.a > 0:
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return "\\tkzTabVar{+/{}, -/{$" + str(beta) + "$}, +/{}}"
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else:
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return "\\tkzTabVar{-/{}, +/{$" + str(beta) + "$}, -/{}}"
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if __name__ == '__main__':
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# from .render import txt
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# with Expression.tmp_render(txt):
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# P = Polynom_deg2([2, 3, 4])
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# print(P)
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# print("Delta")
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# for i in P.delta.simplify():
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# print(i)
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import doctest
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doctest.testmod()
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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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