def tracefonc(f, i, A, B, xmin, xmax, ymin, ymax):
"""**tracefonc\ (*f*\ , *i*\ , *A*\ , *B*\ , *xmin*\ , *xmax*\ , *ymin*\ , *ymax*\ )
*A* est sur l'axe des ordonnées, *f* est le nom de la fonction
Génère la 2e queston et sa réponse
>>> from pyromaths.classes.Fractions import Fraction
>>> affine.tracefonc('f', 1, (0,-2),(3,2),-4,4,-4,-4)
[u'Tracer la droite repr\xe9sentative ($d_1$) de la fonction $f:x\\longmapsto \\
dfrac{4}{3}\\,x-2$.', 'On sait que $f(0)=-2$ et $f(-3)=\\dfrac{4}{3}\\times \\le
ft( -3\\right) -2=\\dfrac{4\\times \\cancel{3}\\times -1}{\\cancel{3}\\times 1}-
2=-4-2=-6', '\\psdot [dotsize=4.5pt,dotstyle=x](0, -2)', '\\psdot [dotsize=4.5pt
,dotstyle=x](-3, -6.0)']
:rtype: list of string
"""
u = coefdir(A, B)
if isinstance(u, int) or u.d == 1:
x1 = decimaux(B[0])
else:
B = (u.d, u.n + float(A[1]))
if not dansrep(B, xmin, xmax, ymin, ymax):
B = (-u.d, -u.n + float(A[1]))
x1 = decimaux(str(B[0]))
l = Priorites3.texify([Polynome([[u, 1], [A[1], 0]], "x")(B[0])])
l.extend(Priorites3.texify(Priorites3.priorites(Polynome([[u, 1], [A[1], 0]], "x")(B[0]))))
l = [u'Tracer la droite représentative ($d_' + str(i) + '$) de la fonction $' + f + ':x\\longmapsto ' + str(Polynome([[u, 1], [A[1], 0]], "x")) + '$.',
'On sait que $' + f + '(0)=' + decimaux(str(A[1])) + '$ et $' + f + '(' + x1 + ')=' + "=".join(l) + "$.",
'\\psdot [dotsize=4.5pt,dotstyle=x]' + str(A),
'\\psdot [dotsize=4.5pt,dotstyle=x]' + str(B),
]
return l
def id_rem():
"""Génère un exercice de développement des 3 identités remarquables avec une situation piège.
Dans un premier temps, on n'utilise que des nombres entiers, puis des fractions, puis l'opposé
d'une expression littérale.
"""
l = [randrange(1, 11) for dummy in range(14)]
while pgcd(l[8], l[9]) != 1 or pgcd(l[10], l[11]) != 1 or (l[9] == 1 and l[11] == 1):
# On crée deux rationnels irréductibles non tous deux entiers.
l = [randrange(1, 11) for dummy in range(14)]
lpoly = [id_rem1(l[0], l[1]), id_rem2(l[2], l[3]), id_rem3(l[4], l[5]), id_rem4(l[6], l[7])]
shuffle(lpoly)
lid = [id_rem1, id_rem2, id_rem3, id_rem4]
lpoly2 = [lid.pop(randrange(4))(Fraction(l[8], l[9]), Fraction(l[10], l[11]))]
lpoly2.append('-' + lid.pop(randrange(3))(l[12], l[13]))
shuffle(lpoly2)
lpoly.extend(lpoly2)
expr = [Priorites3.texify([Priorites3.splitting(lpoly[i])]) for i in range(6)]
exo = ["\\exercice", u"Développer chacune des expressions littérales suivantes :"]
exo.append("\\begin{multicols}{2}")
exo.append('\\\\\n'.join(['$%s=%s$' % (chr(i + 65), expr[i][0]) for i in range(6)]))
exo.append("\\end{multicols}")
cor = ["\\exercice*", u"Développer chacune des expressions littérales suivantes :"]
cor.append("\\begin{multicols}{2}")
for i in range(6):
dev = Priorites3.texify(Priorites3.priorites(lpoly[i]))
dev.insert(0, expr[i][0])
cor.append('\\\\\n'.join(['$%s=%s$' % (chr(i + 65), dev[j]) for j in range(len(dev) - 1)]))
cor.append('\\\\')
cor.append('\\fbox{$%s=%s$}\\\\\n' % (chr(i + 65), dev[-1]))
cor.append("\\end{multicols}")
return exo, cor
def corrige(nom, fct, ant):
from pyromaths.outils import Priorites3
sol = []
calc = fct(ant)
res = Priorites3.priorites(calc)
res = Priorites3.texify(res)
sol.append(r"\par $%s\,(%s)=%s$\par" % (nom, ant, Priorites3.texify([Priorites3.splitting(calc)])[0]))
sol.append('\\par\n'.join(['$%s\\,(%s)=%s$' % (nom, ant, res[j]) for j in range(len(res) - 1)]))
sol.append(r'\par')
sol.append('\\fbox{$%s\\,(%s)=%s$}\\\\\n' % (nom, ant, res[-1]))
return sol
def corrige(nom, fct, ant):
from pyromaths.outils import Priorites3
sol = []
calc = fct(ant)
res = Priorites3.priorites(calc)
res = Priorites3.texify(res)
sol.append(r"\par $%s\,(%s)=%s$\par" %
(nom, ant, Priorites3.texify([Priorites3.splitting(calc)])[0]))
sol.append('\\par\n'.join(
['$%s\\,(%s)=%s$' % (nom, ant, res[j]) for j in range(len(res) - 1)]))
sol.append(r'\par')
sol.append('\\fbox{$%s\\,(%s)=%s$}\\\\\n' % (nom, ant, res[-1]))
return sol
def factorisation():
"""Génère un exercice de factorisation utilisant les identités remarquables ou
la distributivité
"""
l = [randrange(1, 11) for dummy in range(21)]
diff = [True, False, False]
shuffle(diff)
exo = [id_rem1, id_rem2]
lexo = [exo[randrange(2)](l[0], l[1])]
lexo.append(id_rem3(l[2], l[3]))
lexo.append(id_rem3bis(l[4], l[5], l[6]))
lexo.append(facteur_commun1(l[7:13], diff=diff.pop()))
shuffle(lexo)
exo = [facteur_commun2, facteur_commun3]
shuffle(exo)
lexo.append(exo[0](l[13:17], diff=diff.pop()))
lexo.append(exo[1](l[17:21], diff=diff.pop()))
exo = [
"\\exercice",
u"Factoriser chacune des expressions littérales suivantes :"
]
exo.append("\\begin{multicols}{2}")
cor = [
"\\exercice*",
u"Factoriser chacune des expressions littérales suivantes :"
]
cor.append("\\begin{multicols}{2}")
for i in range(len(lexo)):
p = [lexo[i]]
while True:
fact = factoriser(p[-1])
if fact:
p.append(fact)
else:
break
p = Priorites3.texify(
[Priorites3.splitting(p[j]) for j in range(len(p))])
cor.append('\\\\\n'.join(
['$%s=%s$' % (chr(i + 65), p[j]) for j in range(len(p) - 1)]))
cor.append('\\\\')
cor.append('\\fbox{$%s=%s$}\\\\\n' % (chr(i + 65), p[-1]))
exo.append('\\\\\n'.join([
'$%s=%s$' %
(chr(i + 65), Priorites3.texify([Priorites3.splitting(lexo[i])])[0])
for i in range(len(lexo))
]))
exo.append("\\end{multicols}")
cor.append("\\end{multicols}")
return exo, cor
def tex_answer(self):
exo = [r'\exercice*']
exo.append(_(u'Donner la forme canonique des polynômes $P$ , $Q$ , $R$ et $S$ .'))
noms = [r'P\,(x) &= ', r'Q\,(x) &= ', r'R\,(x) &= ', r'S\,(x) &= ']
exercice = list(self.exercice)
for i in range(len(exercice)):
exercice[i] = Priorites3.texify(exercice[i])
exercice[i][0] = noms[i] + exercice[i][0] # [0]
for j in range(1, len(exercice[i]) - 1):
exercice[i][j] = r' &= ' + exercice[i][j]
exercice[i][-1] = r'\Aboxed{' + noms[i] + exercice[i][-1] + r'}'
tri = []
for i in range(len(exercice)):
tri.append((i, len(exercice[i])))
tri = sorted(tri, key=lambda nblgn: nblgn[1])
if tri[0][0] < tri[1][0]:
exercice[tri[0][0]].extend(exercice.pop(tri[1][0]))
else:
exercice[tri[1][0]].extend(exercice.pop(tri[0][0]))
exo.append(r'\begin{align*}')
for j in range(max(len(exercice[0]), len(exercice[1]), len(exercice[2]))):
sol = ''
for i in range(3):
if j < len(exercice[i]):
sol += exercice[i][j]
else:
sol += r'& '
if i == 2:
sol += r'\\'
else:
sol += r' & '
exo.append(sol)
exo.append(r'\end{align*}')
return exo
def tex_answer(self):
exo = [r'\exercice*']
exo.append(_(u'Donner la forme canonique des polynômes $P$ , $Q$ , $R$ et $S$ .'))
noms = [r'P\,(x) &= ', r'Q\,(x) &= ', r'R\,(x) &= ', r'S\,(x) &= ']
exercice = list(self.exercice)
for i in range(len(exercice)):
exercice[i] = Priorites3.texify(exercice[i])
exercice[i][0] = noms[i] + exercice[i][0] # [0]
for j in range(1, len(exercice[i]) - 1):
exercice[i][j] = r' &= ' + exercice[i][j]
exercice[i][-1] = r'\Aboxed{' + noms[i] + exercice[i][-1] + r'}'
tri = []
for i in range(len(exercice)):
tri.append((i, len(exercice[i])))
tri = sorted(tri, key=lambda nblgn: nblgn[1])
if tri[0][0] < tri[1][0]:
exercice[tri[0][0]].extend(exercice.pop(tri[1][0]))
else:
exercice[tri[1][0]].extend(exercice.pop(tri[0][0]))
exo.append(r'\begin{align*}')
for j in range(max(len(exercice[0]), len(exercice[1]), len(exercice[2]))):
sol = ''
for i in range(3):
if j < len(exercice[i]):
sol += exercice[i][j]
else:
sol += r'& '
if i == 2:
sol += r'\\'
else:
sol += r' & '
exo.append(sol)
exo.append(r'\end{align*}')
return exo
def tex_statement(self):
exo = [r'\exercice']
exo.append(_(u'Résoudre les équations :'))
exo.append('\\begin{align*}')
for e in self.exercice:
if len(e) == 2:
exo.append(Priorites3.texify([[repr(Polynome(e[0])), '*', repr(Polynome(e[1]))]])[0] + ' &= 0 & ')
else:
exo.append(r'\cfrac{%s}{%s} &= %s & ' % (Polynome(e[0]), Polynome(e[1]), Polynome(e[2])))
exo[-1] = exo[-1][:-3] # Suppression du dernier " &"
exo.append('\\end{align*}')
return exo
def tex_statement(self):
exo = [r'\exercice']
exo.append(_(u'Résoudre les équations :'))
exo.append('\\begin{align*}')
for e in self.exercice:
if len(e) == 2:
exo.append(Priorites3.texify([[repr(Polynome(e[0])), '*', repr(Polynome(e[1]))]])[0] + ' &= 0 & ')
else:
exo.append(r'\cfrac{%s}{%s} &= %s & ' % (Polynome(e[0]), Polynome(e[1]), Polynome(e[2])))
exo[-1] = exo[-1][:-3] # Suppression du dernier " &"
exo.append('\\end{align*}')
return exo
def tracefonc(f, i, A, B, xmin, xmax, ymin, ymax):
"""**tracefonc\ (*f*\ , *i*\ , *A*\ , *B*\ , *xmin*\ , *xmax*\ , *ymin*\ , *ymax*\ )
*A* est sur l'axe des ordonnées, *f* est le nom de la fonction
Génère la 2e queston et sa réponse
>>> from pyromaths.classes.Fractions import Fraction
>>> affine.tracefonc('f', 1, (0,-2),(3,2),-4,4,-4,-4)
[u'Tracer la droite repr\xe9sentative ($d_1$) de la fonction $f:x\\longmapsto \\
dfrac{4}{3}\\,x-2$.', 'On sait que $f(0)=-2$ et $f(-3)=\\dfrac{4}{3}\\times \\le
ft( -3\\right) -2=\\dfrac{4\\times \\cancel{3}\\times -1}{\\cancel{3}\\times 1}-
2=-4-2=-6', '\\psdot [dotsize=4.5pt,dotstyle=x](0, -2)', '\\psdot [dotsize=4.5pt
,dotstyle=x](-3, -6.0)']
:rtype: list of string
"""
u = coefdir(A, B)
if isinstance(u, int) or u.d == 1:
x1 = decimaux(B[0])
else:
B = (u.d, u.n + float(A[1]))
if not dansrep(B, xmin, xmax, ymin, ymax):
B = (-u.d, -u.n + float(A[1]))
x1 = decimaux(str(B[0]))
l = Priorites3.texify([Polynome([[u, 1], [A[1], 0]], "x")(B[0])])
l.extend(
Priorites3.texify(
Priorites3.priorites(Polynome([[u, 1], [A[1], 0]], "x")(B[0]))))
l = [
u'Tracer la droite représentative ($d_' + str(i) +
'$) de la fonction $' + f + ':x\\longmapsto ' +
str(Polynome([[u, 1], [A[1], 0]], "x")) + '$.',
'On sait que $' + f + '(0)=' + decimaux(str(A[1])) + '$ et $' + f +
'(' + x1 + ')=' + "=".join(l) + "$.",
'\\psdot [dotsize=4.5pt,dotstyle=x]' + str(A),
'\\psdot [dotsize=4.5pt,dotstyle=x]' + str(B),
]
return l
def print_coef(coef):
"""Gère le format du coef
"""
if isinstance(coef, (float, int)):
if coef > 0: return "+" + decimaux(coef)
else: return decimaux(coef)
if isinstance(coef, Fraction):
if isinstance(coef.n, int) and isinstance(coef.d, int) and coef.n < 0 and coef.d > 0:
return "-" + str(Fraction(-coef.n, coef.d, coef.code))
return "+" + str(coef)
if isinstance(coef, str):
texte = "(" + "".join(Priorites3.texify([Priorites3.splitting(coef)])) + ")"
if texte[0] != "-": return "+" + texte
else: return texte
def factorisation():
"""Génère un exercice de factorisation utilisant les identités remarquables ou
la distributivité
"""
l = [randrange(1, 11) for dummy in range(21)]
diff = [True, False, False]
shuffle(diff)
exo = [id_rem1, id_rem2]
lexo = [exo[randrange(2)](l[0], l[1])]
lexo.append(id_rem3(l[2], l[3]))
lexo.append(id_rem3bis(l[4], l[5], l[6]))
lexo.append(facteur_commun1(l[7:13], diff=diff.pop()))
shuffle(lexo)
exo = [facteur_commun2, facteur_commun3]
shuffle(exo)
lexo.append(exo[0](l[13:17], diff=diff.pop()))
lexo.append(exo[1](l[17:21], diff=diff.pop()))
exo = ["\\exercice", u"Factoriser chacune des expressions littérales suivantes :"]
exo.append("\\begin{multicols}{2}")
cor = ["\\exercice*", u"Factoriser chacune des expressions littérales suivantes :"]
cor.append("\\begin{multicols}{2}")
for i in range(len(lexo)):
p = [lexo[i]]
while True:
fact = factoriser(p[-1])
if fact:
p.append(fact)
else: break
p = Priorites3.texify([Priorites3.splitting(p[j]) for j in range(len(p))])
cor.append('\\\\\n'.join(['$%s=%s$' % (chr(i + 65), p[j]) for j in range(len(p) - 1)]))
cor.append('\\\\')
cor.append('\\fbox{$%s=%s$}\\\\\n' % (chr(i + 65), p[-1]))
exo.append('\\\\\n'.join(['$%s=%s$' % (chr(i + 65), Priorites3.texify([Priorites3.splitting(lexo[i])])[0]) for i in range(len(lexo))]))
exo.append("\\end{multicols}")
cor.append("\\end{multicols}")
return exo, cor
def tex_statement(self):
exo = [r'\exercice']
exo.append(_(u'Donner la forme canonique des polynômes $P$ , $Q$ , $R$ et $S$ .'))
exo.append(r'\begin{align*}')
noms = [r'P\,(x) &= ', r'Q\,(x) &= ', r'R\,(x) &= ', r'S\,(x) &= ']
exercice = list(self.exercice)
sol = ''
for i in range(len(exercice)):
exercice[i][0] = Priorites3.texify(exercice[i][0])
sol += noms[i] + exercice[i][0][0]
if i < len(exercice) - 1: sol += r' & '
else: sol += r' \\ '
exo.append(sol)
exo.append(r'\end{align*}')
return exo
def tex_statement(self):
exo = [r'\exercice']
exo.append(_(u'Donner la forme canonique des polynômes $P$ , $Q$ , $R$ et $S$ .'))
exo.append(r'\begin{align*}')
noms = [r'P\,(x) &= ', r'Q\,(x) &= ', r'R\,(x) &= ', r'S\,(x) &= ']
exercice = list(self.exercice)
sol = ''
for i in range(len(exercice)):
exercice[i][0] = Priorites3.texify(exercice[i][0])
sol += noms[i] + exercice[i][0][0]
if i < len(exercice) - 1: sol += r' & '
else: sol += r' \\ '
exo.append(sol)
exo.append(r'\end{align*}')
return exo
def print_coef(coef):
"""Gère le format du coef
"""
if isinstance(coef, (float, int)):
if coef > 0: return "+" + decimaux(coef)
else: return decimaux(coef)
if isinstance(coef, Fraction):
if isinstance(coef.n, int) and isinstance(
coef.d, int) and coef.n < 0 and coef.d > 0:
return "-" + str(Fraction(-coef.n, coef.d, coef.code))
return "+" + str(coef)
if isinstance(coef, str):
texte = "(" + "".join(
Priorites3.texify([Priorites3.splitting(coef)])) + ")"
if texte[0] != "-": return "+" + texte
else: return texte
def tex_answer(self):
exo = [r'\exercice*']
exo.append(_(u'Déterminer les racines des polynômes :\\par'))
noms = [r'P\,(x) &= ', r'Q\,(x) &= ', r'R\,(x) &= ']
r = ''
question = [[], [], []]
for i in range(3):
p = []
m = Polynome(list(self.exercice[i])).ordonne()
if factoriser('%r' % Polynome(m)):
p = [factoriser('%r' % Polynome(m))]
while factoriser(p[-1]):
p.append(factoriser(p[-1]))
if p and eval(Priorites3.splitting(p[-1])[0]).degre() > 0:
tmp = Priorites3.texify([Priorites3.splitting(p[j]) for j in range(len(p))])
question[i].append('{$\\! \\begin{aligned}')
question[i].append(noms[i] + str(Polynome(m, 'x')) + r'\\')
question[i].append('\\\\\n'.join(['&=%s' % (tmp[j]) for j in range(len(tmp))]))
question[i].append(r'\end{aligned}$}\par')
lp = Priorites3.splitting(p[-1])
racines = []
for e in lp:
if e[:9] == 'Polynome(':
e = eval(e)
if len(e) == 2:
racines.append(str(Fraction(-e[1][0], e[0][0]).simplifie()))
else:
racines.append('0')
if len(racines) > 1:
question[i].append(_(u'\\underline{Les racines de $%s$ sont }\\fbox{$%s$}') % (noms[i].rstrip(r' &= '), '$}\\underline{ et }\\fbox{$'.join(racines)))
elif len(racines) == 1:
question[i].append(_(u'\\underline{L\'unique racine de $%s$ est }\\fbox{$%s$}') % (noms[i].rstrip(r' &= '), racines[0]))
elif len(m) == 2 and m[0][1] == 2 and m[1][1] == 0 and m[0][0] * m[1][0] > 0:
question[i].append('$' + noms[i] + str(Polynome(m, 'x')) + r'$\par')
question[i][-1] = question[i][-1].replace('&', '')
if m[1][0] > 0: question[i].append('$' + noms[i][:7] + ' \\ge %r$' % m[1][0])
else: question[i].append('$' + noms[i][:7] + ' \\le %r$' % m[1][0])
question[i].append(_(u'car un carré est toujours positif.\\par\n\\underline{$%s$ n\'a donc pas de racine.}') % (noms[i].rstrip(r' &= ')))
else:
question[i].append('$' + noms[i] + str(Polynome(m, 'x')) + r'\quad$')
question[i][-1] = question[i][-1].replace('&', '')
question[i].append(_(u'On calcule le discriminant de $%s$ avec $a=%s$, $b=%s$ et $c=%s$ :\\par\\medskip') % (noms[i].rstrip(r' &= '), m[0][0], m[1][0], m[2][0]))
question[i].append(r'\begin{tabularx}{\linewidth}[t]{XXX}')
question[i].append(r'{$\! \begin{aligned}')
sol = [[str(m[1][0]), '**', '2', '-', '4', '*', str(m[0][0]), '*', str(m[2][0])]]
sol.extend(Priorites3.priorites('%s**2-4*%s*%s' % (m[1][0], m[0][0], m[2][0])))
solTeX = Priorites3.texify(sol)
for s in solTeX:
question[i].append(u'\\Delta &= %s\\\\' % s)
question[i].append(r'\end{aligned}$}')
question[i].append(r'&')
question[i].append(r'{$\! \begin{aligned}')
delta = sol[-1][0]
sol = [['Fraction(SquareRoot([[%s, None], [-1, %s]]),\'2*%s\')' % (-m[1][0], delta, m[0][0])]]
sol.extend(Priorites3.priorites(sol[0][0]))
sol = Priorites3.texify(sol)
for s in sol:
question[i].append(u'x_1 &= %s\\\\' % s)
racines = [sol[-1]]
question[i].append(r'\end{aligned}$}')
question[i].append(r'&')
question[i].append(r'{$\! \begin{aligned}')
sol = [['Fraction(SquareRoot([[%s, None], [1, %s]]),\'2*%s\')' % (-m[1][0], delta, m[0][0])]]
sol.extend(Priorites3.priorites(sol[0][0]))
sol = Priorites3.texify(sol)
for s in sol:
question[i].append(u'x_2 &= %s\\\\' % s)
racines.append(sol[-1])
question[i].append(r'\end{aligned}$}')
question[i].append(r'\end{tabularx}\par')
question[i].append(_(u'\\underline{Les racines de $%s$ sont }\\fbox{$%s$}') % (noms[i].rstrip(r' &= '), _('$}\\underline{ et }\\fbox{$').join(racines)))
if i == 1: question.append(question[1])
if len(question) == 4:
question.pop(1)
if question[0][0][-6:] == r'\quad$':
question[1].insert(0, r'\par\medskip\begin{tabularx}{\linewidth}[t]{XX}')
question[2].insert(0, r'&')
question[2].append(r'\end{tabularx}\par\medskip')
else:
question[0].insert(0, r'\begin{tabularx}{\linewidth}[t]{XX}')
question[1].insert(0, r'&')
question[1].append(r'\end{tabularx}\par\medskip')
for i in range(3): exo.extend(question[i])
return exo
def tex_answer(self):
exo = [r'\exercice*']
exo.append(_(u'Déterminer les racines des polynômes :\\par'))
noms = [r'P\,(x) &= ', r'Q\,(x) &= ', r'R\,(x) &= ']
r = ''
question = [[], [], []]
for i in range(3):
p = []
m = Polynome(list(self.exercice[i])).ordonne()
if factoriser('%r' % Polynome(m)):
p = [factoriser('%r' % Polynome(m))]
while factoriser(p[-1]):
p.append(factoriser(p[-1]))
if p and eval(Priorites3.splitting(p[-1])[0]).degre() > 0:
tmp = Priorites3.texify([Priorites3.splitting(p[j]) for j in range(len(p))])
question[i].append('{$\\! \\begin{aligned}')
question[i].append(noms[i] + str(Polynome(m, 'x')) + r'\\')
question[i].append('\\\\\n'.join(['&=%s' % (tmp[j]) for j in range(len(tmp))]))
question[i].append(r'\end{aligned}$}\par')
lp = Priorites3.splitting(p[-1])
racines = []
for e in lp:
if e[:9] == 'Polynome(':
e = eval(e)
if len(e) == 2:
racines.append(str(Fraction(-e[1][0], e[0][0]).simplifie()))
else:
racines.append('0')
if len(racines) > 1:
question[i].append(_(u'\\underline{Les racines de $%s$ sont }\\fbox{$%s$}') % (noms[i].rstrip(r' &= '), '$}\\underline{ et }\\fbox{$'.join(racines)))
elif len(racines) == 1:
question[i].append(_(u'\\underline{L\'unique racine de $%s$ est }\\fbox{$%s$}') % (noms[i].rstrip(r' &= '), racines[0]))
elif len(m) == 2 and m[0][1] == 2 and m[1][1] == 0 and m[0][0] * m[1][0] > 0:
question[i].append('$' + noms[i] + str(Polynome(m, 'x')) + r'$\par')
question[i][-1] = question[i][-1].replace('&', '')
if m[1][0] > 0: question[i].append('$' + noms[i][:7] + ' \\geqslant %r$' % m[1][0])
else: question[i].append('$' + noms[i][:7] + ' \\leqslant %r$' % m[1][0])
question[i].append(_(u'car un carré est toujours positif.\\par\n\\underline{$%s$ n\'a donc pas de racine.}') % (noms[i].rstrip(r' &= ')))
else:
question[i].append('$' + noms[i] + str(Polynome(m, 'x')) + r'\quad$')
question[i][-1] = question[i][-1].replace('&', '')
question[i].append(_(u'On calcule le discriminant de $%s$ avec $a=%s$, $b=%s$ et $c=%s$ :\\par\\medskip') % (noms[i].rstrip(r' &= '), m[0][0], m[1][0], m[2][0]))
question[i].append(r'\begin{tabularx}{\linewidth}[t]{XXX}')
question[i].append(r'{$\! \begin{aligned}')
if m[1][0]>0:
sol = [[str(m[1][0]), '**', '2', '-', '4', '*', str(m[0][0]), '*', str(m[2][0])]]
sol.extend(Priorites3.priorites('%s**2-4*%s*%s' % (m[1][0], m[0][0], m[2][0])))
else:
sol = [['(', str(m[1][0]), ')', '**', '2', '-', '4', '*', str(m[0][0]), '*', str(m[2][0])]]
sol.extend(Priorites3.priorites('(%s)**2-4*%s*%s' % (m[1][0], m[0][0], m[2][0])))
solTeX = Priorites3.texify(sol)
for s in solTeX:
question[i].append(u'\\Delta &= %s\\\\' % s)
question[i].append(r'\end{aligned}$}')
question[i].append(r'&')
question[i].append(r'{$\! \begin{aligned}')
delta = sol[-1][0]
print(sol)
sol = [['Fraction(SquareRoot([[%s, None], [-1, %s]]),\'2*%s\')' % (-m[1][0], delta, m[0][0])]]
sol.extend(Priorites3.priorites(sol[0][0]))
sol = Priorites3.texify(sol)
for s in sol:
question[i].append(u'x_1 &= %s\\\\' % s)
racines = [sol[-1]]
question[i].append(r'\end{aligned}$}')
question[i].append(r'&')
question[i].append(r'{$\! \begin{aligned}')
sol = [['Fraction(SquareRoot([[%s, None], [1, %s]]),\'2*%s\')' % (-m[1][0], delta, m[0][0])]]
sol.extend(Priorites3.priorites(sol[0][0]))
sol = Priorites3.texify(sol)
for s in sol:
question[i].append(u'x_2 &= %s\\\\' % s)
racines.append(sol[-1])
question[i].append(r'\end{aligned}$}')
question[i].append(r'\end{tabularx}\par')
question[i].append(_(u'\\underline{Les racines de $%s$ sont }\\fbox{$%s$}') % (noms[i].rstrip(r' &= '), _('$}\\underline{ et }\\fbox{$').join(racines)))
if i == 1: question.append(question[1])
if len(question) == 4:
question.pop(1)
if question[0][0][-6:] == r'\quad$':
question[1].insert(0, r'\par\medskip\begin{tabularx}{\linewidth}[t]{XX}')
question[2].insert(0, r'&')
question[2].append(r'\end{tabularx}\par\medskip')
else:
question[0].insert(0, r'\begin{tabularx}{\linewidth}[t]{XX}')
question[1].insert(0, r'&')
question[1].append(r'\end{tabularx}\par\medskip')
for i in range(3): exo.extend(question[i])
return exo
