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Add alpha and beta method to polynomDeg2

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Lafrite 2015-02-25 10:23:24 +01:00
parent 720eb37a4f
commit de338e914f
1 changed files with 80 additions and 17 deletions
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97
pymath/polynomDeg2.py
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@ -14,7 +14,6 @@ class Polynom_deg2(Polynom):
"""
def __init__(self, coefs = [0, 0, 1], letter = "x"):
"""@todo: to be defined1. """
if len(coefs) < 3 or len(coefs) > 4:
raise ValueError("Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(len(coefs)))
if coefs[2] == 0:
@ -42,9 +41,9 @@ class Polynom_deg2(Polynom):
>>> P.delta
< Expression [2, 2, '^', 4, 3, 1, '*', '*', '-']>
>>> for i in P.delta.simplify():
print(i)
2^{ 2 } - 4 \times 3 \times 1
4 - 4 \times 3
... print(i)
2^{ 2 } - 4 \\times 3 \\times 1
4 - 4 \\times 3
4 - 12
-8
>>> P.delta.simplified()
@ -53,6 +52,58 @@ class Polynom_deg2(Polynom):
return Expression([self.b, 2, op.pw, 4, self.a, self.c, op.mul, op.mul, op.sub])
@property
def alpha(self):
""" Compute alpha the abcisse of the extremum
>>> P = Polynom_deg2([1,2,3])
>>> P.alpha
< Expression [2, '-', 2, 3, '*', '/']>
>>> for i in P.alpha.simplify():
... print(i)
\\frac{ - 2 }{ 2 \\times 3 }
\\frac{ -2 }{ 6 }
\\frac{ ( -1 ) \\times 2 }{ 3 \\times 2 }
\\frac{ -1 }{ 3 }
\\frac{ -2 }{ 6 }
>>> P.alpha.simplified() # Bug avec les fractions ici, on devrait avoir -1/3 pas -2/6...
< Fraction -2 / 6 >
"""
return Expression([self.b, op.sub1, 2, self.a, op.mul, op.div])
@property
def beta(self):
""" Compute beta the extremum of self
>>> P = Polynom_deg2([1,2,3])
>>> P.beta
< Expression [3, < Fraction -2 / 6>, 2, '^', '*', 2, < Fraction -2 / 6>, '*', '+', 1, '+']>
>>> for i in P.beta.simplify(): # Ça serait bien que l'on puisse enlever des étapes maintenant...
... print(i)
3 \times \frac{ -2 }{ 6 }^{ 2 } + 2 \times \frac{ -2 }{ 6 } + 1
3 \times \frac{ ( -2 )^{ 2 } }{ 6^{ 2 } } + \frac{ ( -2 ) \times 1 \times 2 }{ 3 \times 2 } + 1
3 \times \frac{ 4 }{ 36 } + \frac{ ( -2 ) \times 2 }{ 6 } + 1
3 \times \frac{ 1 \times 4 }{ 9 \times 4 } + \frac{ -4 }{ 6 } + 1
3 \times \frac{ 1 }{ 9 } + \frac{ ( -2 ) \times 2 }{ 3 \times 2 } + 1
3 \times \frac{ 1 }{ 9 } + \frac{ -2 }{ 3 } + 1
\frac{ 1 \times 1 \times 3 }{ 3 \times 3 } + \frac{ -2 }{ 3 } + 1
\frac{ 1 \times 3 }{ 9 } + \frac{ -2 }{ 3 } + 1
\frac{ 3 }{ 9 } + \frac{ -2 }{ 3 } + 1
\frac{ 1 \times 3 }{ 3 \times 3 } + \frac{ -2 }{ 3 } + 1
\frac{ 1 }{ 3 } + \frac{ -2 }{ 3 } + 1
\frac{ 1 + ( -2 ) }{ 3 } + 1
\frac{ -1 }{ 3 } + 1
\frac{ ( -1 ) \times 1 }{ 3 \times 1 } + \frac{ 1 \times 3 }{ 1 \times 3 }
\frac{ -1 }{ 3 } + \frac{ 3 }{ 3 }
\frac{ ( -1 ) + 3 }{ 3 }
\frac{ 2 }{ 3 }
>>> P.beta.simplified()
< Fraction 2 / 3>
"""
return self(self.alpha.simplified())
def roots(self):
""" Compute roots of the polynom
@ -82,23 +133,23 @@ class Polynom_deg2(Polynom):
""" Return the sign line for tkzTabLine
>>> P = Polynom_deg2([2, 5, 2])
>>> P.tbl_sgn()
'\\tkzTabLine{, +, z, -, z , +,}'
>>> print(P.tbl_sgn())
\\tkzTabLine{, +, z, -, z , +,}
>>> P = Polynom_deg2([2, 1, -2])
>>> P.tbl_sgn()
'\\tkzTabLine{, -, z, +, z , -,}'
>>> print(P.tbl_sgn())
\\tkzTabLine{, -, z, +, z , -,}
>>> P = Polynom_deg2([1, 2, 1])
>>> P.tbl_sgn()
'\\tkzTabLine{, +, z, +,}'
>>> print(P.tbl_sgn())
\\tkzTabLine{, +, z, +,}
>>> P = Polynom_deg2([0, 0, -2])
>>> P.tbl_sgn()
'\\tkzTabLine{, -, z, -,}'
>>> print(P.tbl_sgn())
\\tkzTabLine{, -, z, -,}
>>> P = Polynom_deg2([1, 0, 1])
>>> P.tbl_sgn()
'\\tkzTabLine{, +,}'
>>> print(P.tbl_sgn())
\\tkzTabLine{, +,}
>>> P = Polynom_deg2([-1, 0, -1])
>>> P.tbl_sgn()
'\\tkzTabLine{, -,}'
>>> print(P.tbl_sgn())
\\tkzTabLine{, -,}
"""
if self.delta.simplified() > 0:
if self.a > 0:
@ -116,8 +167,20 @@ class Polynom_deg2(Polynom):
else:
return "\\tkzTabLine{, -,}"
def tbl_variation(self, limit = False):
"""Return the variation line for tkzTabVar
:param limit: Display or not limits in tabular
>>> P = Polynom_deg2([1,1,1])
"""
alpha = -self.b / (2*self.a)
beta = self(alpha).simplied()
#\tkzTabVar{-/{}, +/{$f(-10)$}, -/{}}