249 lines
7.8 KiB
Python
249 lines
7.8 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 .fraction import Fraction
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from .operator import op
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from .random_expression import RdExpression
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from sympy import sqrt, latex
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# from sympy.fractions import Fraction as sp.Fraction
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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(
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self,
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coefs_form=[
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"{c}",
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"{b}",
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"{a}"],
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conditions=[],
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letter="x",
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name="P"):
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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(
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"Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(
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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 isinstance(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, name=name)
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def __init__(self, coefs=[0, 0, 1], letter="x", name="P", poly=0):
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if poly:
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coefs = poly._coef
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letter = poly._letter
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name = poly.name
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if len(coefs) < 3 or len(coefs) > 4:
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raise ValueError(
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"Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(
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len(coefs)))
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if coefs[2] == 0:
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raise ValueError(
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"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, name=name)
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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,
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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,
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op.mul, op.div]).simplify()
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@property
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def beta(self):
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r""" 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 }{ 3 } )^{ 2 } + \frac{ -1 }{ 3 } \times 2 + 1
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3 \times \frac{ ( -1 )^{ 2 } }{ 3^{ 2 } } + \frac{ -1 \times 2 }{ 3 } + 1
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3 \times \frac{ 1 }{ 9 } + \frac{ -2 }{ 3 } + 1
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\frac{ 1 }{ 9 } \times 3 + \frac{ -2 }{ 3 } + 1
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\frac{ 1 \times 3 }{ 3 \times 3 } + \frac{ -2 }{ 3 } + 1
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\frac{ 1 }{ 3 } + \frac{ -2 }{ 3 } + 1
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\frac{ 1 - 2 }{ 3 } + 1
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\frac{ -1 }{ 3 } + 1
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\frac{ -1 \times 1 }{ 3 \times 1 } + \frac{ 1 \times 3 }{ 1 \times 3 }
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\frac{ -1 }{ 3 } + \frac{ 3 }{ 3 }
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\frac{ -1 + 3 }{ 3 }
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\frac{ 2 }{ 3 }
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"""
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return self(self.alpha)
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def roots(self, after_coma=2):
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""" Compute roots of the polynom
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/!\ Can't manage nice rendering because of sqrt.
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It use sympy to compute roots
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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]
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>>> P = Polynom_deg2([-1, 0, 1])
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>>> P.roots()
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['-1', '1']
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>>> P = Polynom_deg2([1, 4, 1])
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>>> P.roots()
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['-2 - \\\\sqrt{3}', '-2 + \\\\sqrt{3}']
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"""
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if self.delta > 0:
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self._roots = [latex((-self.b - sqrt(self.delta)) / (2 * self.a)),
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latex((-self.b + sqrt(self.delta)) / (2 * self.a))]
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elif self.delta == 0:
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self._roots = [Fraction(-self.b, 2 * self.a).simplify()]
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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_header(self):
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""" Return header of the sign line for tkzTabLine"""
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if self.delta > 0:
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return "{$-\\infty$, $" + str(min(self.roots())) + \
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"$ , $" + str(max(self.roots())) + "$ , $+\\infty$}"
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elif self.delta == 0:
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return "{$-\\infty$, $" + str(self.roots()[0]) + "$ , $+\\infty$}"
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else:
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return "{$-\\infty$, $+\\infty$}"
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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{+/{$+\\infty$}, -/{$" + \
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str(beta) + "$}, +/{$+\\infty$}}"
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else:
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return "\\tkzTabVar{-/{$-\\infty$}, +/{$" + \
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str(beta) + "$}, -/{$-\\infty$}}"
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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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# -----------------------------
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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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