def discriminant(polynome):
u"Calcule le discriminant d'un polynôme du second degré."
a = Wild('a')
b = Wild('b')
c = Wild('c')
x = Wild('x')
dico = polynome.match(a*x**2 + b*x + c)
if dico is None:
raise NotImplementedError
a, b, c, x = dico[a], dico[b], dico[c], dico[x]
if not x.is_Symbol or a.has(x) or b.has(x) or c.has(x):
raise NotImplementedError
return b**2 - 4*a*c
def canonique(polynome):
u"Met un polynôme du second degré sous forme canonique."
a = Wild('a')
b = Wild('b')
c = Wild('c')
x = Wild('x')
dico = polynome.match(a*x**2 + b*x + c)
if dico is None:
return polynome
a, b, c, x = dico[a], dico[b], dico[c], dico[x]
if not x.is_Symbol or a.has(x) or b.has(x) or c.has(x):
return polynome
alpha = -b/(2*a)
beta = (4*a*c - b**2)/(4*a)
return a*(x - alpha)**2 + beta
