def tex_systeme(v, p=None): # renvoie l'écriture au format tex d'un système d'équations. v[] est de la forme ((a0, b0, c0), (a1, b1, c1), (x,y))
if p == None:
tv = (tex_coef(v[0][0], 'x'), signe(v[0][1]),
tex_coef(abs(v[0][1]), 'y'), v[0][2],
tex_coef(v[1][0], 'x'), signe(v[1][1]),
tex_coef(abs(v[1][1]), 'y'), v[1][2])
return '''\\left\\lbrace
\\begin{array}{rcrcl}
%s & %s & %s & = & %s \\\\\n %s & %s & %s & = & %s
\\end{array}
\\right.''' % \
tv
else:
tv = (
tex_coef(v[0][0], 'x'),
signe(v[0][1]),
tex_coef(abs(v[0][1]), 'y'),
v[0][2],
'\\qquad\\hbox{\\footnotesize$\\mathit{(\\times %s)}$}' %
tex_coef(p[0], '', bpn=1),
tex_coef(v[1][0], 'x'),
signe(v[1][1]),
tex_coef(abs(v[1][1]), 'y'),
v[1][2],
'\\qquad\\hbox{\\footnotesize$\\mathit{(\\times %s)}$}' %
tex_coef(p[1], '', bpn=1),
)
return '''\\left\\lbrace
\\begin{array}{rcrcll}
%s & %s & %s & = & %s & %s \\\\\n %s & %s & %s & = & %s & %s
\\end{array}
\\right.''' % \
tv
def main():
exo = ["\\exercice", "Effectuer sans calculatrice :",
"\\begin{multicols}{3}\\noindent", " \\begin{enumerate}"]
cor = ["\\exercice*", "Effectuer sans calculatrice :",
"\\begin{multicols}{3}\\noindent", " \\begin{enumerate}"]
modules = (plus, moins, plus, div)
calculs = [i for i in range(20)]
for i in range(20):
j = random.randrange(0, len(calculs))
(a, b) = modules[calculs[j] // 5](10)
if calculs[j] // 5 == 0:
choix_trou(a, tex_coef(b, '', bpn=1), a + b, '+', exo,
cor)
if calculs[j] // 5 == 1:
choix_trou(a, tex_coef(b, '', bpn=1), a - b, '-', exo,
cor)
if calculs[j] // 5 == 2:
choix_trou(a, tex_coef(b, '', bpn=1), a * b,
'\\times', exo, cor)
if calculs[j] // 5 == 3:
choix_trou(a, tex_coef(b, '', bpn=1), a // b, '\\div',
exo, cor)
calculs.pop(j)
exo.extend([" \\end{enumerate}", "\\end{multicols}"])
cor.extend([" \\end{enumerate}", "\\end{multicols}"])
return (exo, cor)
def calcul_mental():
exo = [
"\\exercice", "Effectuer sans calculatrice :",
"\\begin{multicols}{3}\\noindent", " \\begin{enumerate}"
]
cor = [
"\\exercice*", "Effectuer sans calculatrice :",
"\\begin{multicols}{3}\\noindent", " \\begin{enumerate}"
]
modules = (plus, moins, plus, div)
calculs = [i for i in range(20)]
for i in range(20):
j = random.randrange(0, len(calculs))
(a, b) = modules[calculs[j] // 5](10)
if calculs[j] // 5 == 0:
choix_trou(a, tex_coef(b, '', bpn=1), a + b, '+', exo, cor)
if calculs[j] // 5 == 1:
choix_trou(a, tex_coef(b, '', bpn=1), a - b, '-', exo, cor)
if calculs[j] // 5 == 2:
choix_trou(a, tex_coef(b, '', bpn=1), a * b, '\\times', exo, cor)
if calculs[j] // 5 == 3:
choix_trou(a, tex_coef(b, '', bpn=1), a // b, '\\div', exo, cor)
calculs.pop(j)
exo.extend([" \\end{enumerate}", "\\end{multicols}"])
cor.extend([" \\end{enumerate}", "\\end{multicols}"])
return (exo, cor)
def tex_equation4(valeurs): # renvoie l'ecriture de l'equation avec l'inconnue d'un cote de l'egalite
texte = tex_coef(valeurs[4][0] + valeurs[4][2] * valeurs[3][1], 'x') + tex_coef(-valeurs[4][4],
'x', bplus=1)
texte = texte + '=' + tex_coef(valeurs[4][5], '') + \
tex_coef(-valeurs[4][1] - valeurs[4][3] * valeurs[3][1],
'', bplus=1)
return texte
def tex_systeme(
v,
p=None
): # renvoie l'écriture au format tex d'un système d'équations. v[] est de la forme ((a0, b0, c0), (a1, b1, c1), (x,y))
if p == None:
tv = (tex_coef(v[0][0], 'x'), signe(v[0][1]),
tex_coef(abs(v[0][1]), 'y'), v[0][2], tex_coef(v[1][0], 'x'),
signe(v[1][1]), tex_coef(abs(v[1][1]), 'y'), v[1][2])
return '''\\left\\lbrace
\\begin{array}{rcrcl}
%s & %s & %s & = & %s \\\\\n %s & %s & %s & = & %s
\\end{array}
\\right.''' % \
tv
else:
tv = (
tex_coef(v[0][0], 'x'),
signe(v[0][1]),
tex_coef(abs(v[0][1]), 'y'),
v[0][2],
'\\qquad\\hbox{\\footnotesize$\\mathit{(\\times %s)}$}' %
tex_coef(p[0], '', bpn=1),
tex_coef(v[1][0], 'x'),
signe(v[1][1]),
tex_coef(abs(v[1][1]), 'y'),
v[1][2],
'\\qquad\\hbox{\\footnotesize$\\mathit{(\\times %s)}$}' %
tex_coef(p[1], '', bpn=1),
)
return '''\\left\\lbrace
\\begin{array}{rcrcll}
%s & %s & %s & = & %s & %s \\\\\n %s & %s & %s & = & %s & %s
\\end{array}
\\right.''' % \
tv
def relatifs():
exo = ["\\exercice", _("Effectuer sans calculatrice :"),
"\\begin{multicols}{3}\\noindent", " \\begin{enumerate}"]
cor = ["\\exercice*", _("Effectuer sans calculatrice :"),
"\\begin{multicols}{3}\\noindent", " \\begin{enumerate}"]
modules = (plus, moins,)
modules_dec = (plus_dec, moins_dec,)
calculs = [i for i in range(20)]
random.shuffle(calculs)
for j in range(4):
(a, b) = modules[calculs[j] // 10](10)
choix_trou(a, tex_coef(b, '', bpn=1), a + b, '+', exo,
cor)
for j in range(4, 14):
(a, b) = modules[calculs[j] // 10](10)
if calculs[j] // 10 == 0:
choix_trou(a, tex_coef(b, '', bpn=1), a + b, '+', exo,
cor)
if calculs[j] // 10 == 1:
choix_trou(a, tex_coef(b, '', bpn=1), a - b, '-', exo,
cor)
for j in range(14, 20):
(a, b) = modules_dec[calculs[j] // 10](10)
if calculs[j] // 10 == 0:
choix_trou(TeX(a), tex_coef(b, '', bpn=1), TeX(a + b), '+', exo,
cor)
if calculs[j] // 10 == 1:
choix_trou(TeX(a), tex_coef(b, '', bpn=1), TeX(a - b), '-', exo,
cor)
exo.extend([" \\end{enumerate}", "\\end{multicols}"])
cor.extend([" \\end{enumerate}", "\\end{multicols}"])
return (exo, cor)
def tex_comb3(v):
if v[0]:
tv = (tex_coef(v[0], 'x'), tex_coef(v[2],
''))
else:
tv = (tex_coef(v[1], 'y'), tex_coef(v[2],
''))
return '%s=%s' % tv
def tex_comb4(v):
if v[0]:
tv = (tex_coef(1, 'x'), v[2], v[0],
tex_coef(v[2] // v[0], ''))
else:
tv = (tex_coef(1, 'y'), v[2], v[1],
tex_coef(v[2] // v[1], ''))
return '%s=\\frac{%s}{%s}=%s' % tv
def tex_equation5(
valeurs
): # renvoie l'ecriture reduite de l'equation avec l'inconnue d'un cote de l'egalite
texte = tex_coef(
(valeurs[4][0] + valeurs[4][2] * valeurs[3][1]) - valeurs[4][4], 'x')
texte = texte + '=' + tex_coef(
(valeurs[4][5] - valeurs[4][1]) - valeurs[4][3] * valeurs[3][1], '')
return texte
def tex_equation4(
valeurs
): # renvoie l'ecriture de l'equation avec l'inconnue d'un cote de l'egalite
texte = tex_coef(valeurs[4][0] + valeurs[4][2] * valeurs[3][1],
'x') + tex_coef(-valeurs[4][4], 'x', bplus=1)
texte = texte + '=' + tex_coef(valeurs[4][5], '') + \
tex_coef(-valeurs[4][1] - valeurs[4][3] * valeurs[3][1],
'', bplus=1)
return texte
def tex_proprietes_neg():
exo = ["\\exercice",
u"Écrire sous la forme d'une puissance de 10 puis donner l'écriture",
u" décimale de ces nombres :", "\\begin{multicols}{2}",
" \\noindent%", " \\begin{enumerate}"]
cor = ["\\exercice*",
u"Écrire sous la forme d'une puissance de 10 puis donner l'écriture",
u" décimale de ces nombres :", "\\begin{multicols}{2}",
" \\noindent%", " \\begin{enumerate}"]
lexos = [0, 1, 2, 3, 0, 1, 2, 3]
# 0: a^n*a^p ; 1: (a^n)^p ; 2:a^n/a^p
for dummy in range(len(lexos)):
lexp = [randrange(-6, 6) for dummy in range(2)]
j = lexos.pop(randrange(len(lexos)))
# FIXME : À finir
if j == 0:
while abs(lexp[0] + lexp[1]) > 10:
lexp = [randrange(-6, 6) for dummy in range(2)]
exo.append("\\item $10^{%s} \\times 10^{%s} = \\dotfill$" %
tuple(lexp))
cor.append("\\item $10^{%s}\\times 10^{%s}=" % tuple(lexp))
cor.append("10^{%s+%s}=" % (lexp[0], tex_coef(lexp[1],
'', bpn=1)))
cor.append("10^{%s}=%s$" % (lexp[0] + lexp[1],
decimaux(10 ** (lexp[0] + lexp[1]), 1)))
elif j == 1:
while abs(lexp[0] * lexp[1]) > 10:
lexp = [randrange(-6, 6) for dummy in range(2)]
exo.append("\\item $(10^{%s})^{%s}=\\dotfill$" % (lexp[0],
lexp[1]))
cor.append("\\item $(10^{%s})^{%s}=" % tuple(lexp))
cor.append("10^{%s \\times %s}=" % (lexp[0], tex_coef(lexp[1],
'', bpn=1)))
cor.append("10^{%s}=%s$" % (lexp[0] * lexp[1],
decimaux(10 ** (lexp[0] * lexp[1]), 1)))
elif j == 2:
while abs(lexp[0] - lexp[1]) > 10:
lexp = [randrange(-6, 6) for dummy in range(2)]
exo.append("\\item $\\dfrac{10^{%s}}{10^{%s}}=\\dotfill$" %
tuple(lexp))
cor.append("\\item $\\dfrac{10^{%s}}{10^{%s}}=" % tuple(lexp))
cor.append("10^{%s-%s}=" % (lexp[0], tex_coef(lexp[1],
'', bpn=1)))
cor.append("10^{%s}=%s$" % (lexp[0] - lexp[1],
decimaux(10 ** (lexp[0] - lexp[1]), 1)))
exo.append("\\end{enumerate}")
exo.append("\\end{multicols}\n")
cor.append("\\end{enumerate}")
cor.append("\\end{multicols}\n")
return (exo, cor)
def exo_entier1(exo, cor, v):
a = (tex_coef(v[0], '\\sqrt{%s}' % (v[1] ** 2 * v[4])), tex_coef(v[2],
'\\sqrt{%s}' % (v[3] ** 2 * v[4])))
exo.append(u'\\[ \\thenocalcul = ' + '\\frac{%s}{%s}' % a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '\\frac{%s}{%s}' % a + '\\] ')
a = (v[0], v[1] ** 2, v[4], v[2], v[3] ** 2, v[4])
cor.append(u'\\[ \\thenocalcul = ' +
'\\frac{%s\\times\\sqrt{%s}\\times\\cancel{\\sqrt{%s}}}{%s\\times\\sqrt{%s}\\times\\cancel{\\sqrt{%s}}}' %
a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '\\frac{%s\\times %s}{%s\\times %s}' % v[0:4] + '\\] ')
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s' % (((v[0] * v[1]) // v[2]) // v[3]) + '} \\] ')
def exo_entier0(exo, cor, v):
a = (v[0], tex_coef(v[1], '\\sqrt{%s}' % v[2], bplus=1), v[0],
tex_coef(-v[1], '\\sqrt{%s}' % v[2], bplus=1))
exo.append(u'\\[ \\thenocalcul = ' + '\\left( %s%s \\right)\\left( %s%s \\right)' %
a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '\\left( %s%s \\right)\\left( %s%s \\right)' %
a + '\\] ')
a = (tex_coef(v[0], '', bpc=1), tex_coef(abs(v[1]), '\\sqrt{%s}' % v[2],
bpc=1))
cor.append(u'\\[ \\thenocalcul = ' + '%s^2-%s^2' % a + '\\] ')
a = (v[0] ** 2, v[1] ** 2, v[2])
cor.append(u'\\[ \\thenocalcul = ' + '%s-%s\\times %s' % a + '\\] ')
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s' % (v[0] ** 2 - v[1] ** 2 * v[2]) + '} \\] ')
def exo_aPbRc(exo, cor, v):
a = (tex_coef(v[0], '\\sqrt{%s}' % v[1]),
tex_coef(v[2], '\\sqrt{%s}' % v[3], bplus=1))
exo.append(u'\\[ \\thenocalcul = ' + '\\left( %s%s \\right)^2' % a +
'\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '\\left( %s%s \\right)^2' % a +
'\\] ')
if v[2] > 0:
sgn = '+'
else:
sgn = '-'
a = (tex_coef(v[0], '\\sqrt{%s}' % v[1],
bpc=1), sgn, tex_coef(v[0], '\\sqrt{%s}' % v[1]),
tex_coef(abs(v[2]), '\\sqrt{%s}' % v[3]),
tex_coef(abs(v[2]), '\\sqrt{%s}' % v[3], bpc=1))
cor.append(u'\\[ \\thenocalcul = ' + '%s^2%s2\\times%s\\times%s+%s^2' % a +
'\\] ')
a = (v[0]**2, v[1],
tex_coef((2 * v[0]) * v[2], '\\sqrt{%s}' % (v[1] * v[3]),
bplus=1), v[2]**2, v[3])
cor.append(u'\\[ \\thenocalcul = ' + '%s\\times %s %s+%s\\times %s' % a +
'\\] ')
a = (v[0]**2 * v[1] + v[2]**2 * v[3],
tex_coef((2 * v[0]) * v[2], '\\sqrt{%s}' % (v[1] * v[3]), bplus=1))
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s%s' % a + '} \\] ')
def exo_entier1(exo, cor, v):
a = (tex_coef(v[0], '\\sqrt{%s}' % (v[1]**2 * v[4])),
tex_coef(v[2], '\\sqrt{%s}' % (v[3]**2 * v[4])))
exo.append(u'\\[ \\thenocalcul = ' + '\\frac{%s}{%s}' % a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '\\frac{%s}{%s}' % a + '\\] ')
a = (v[0], v[1]**2, v[4], v[2], v[3]**2, v[4])
cor.append(
u'\\[ \\thenocalcul = ' +
'\\frac{%s\\times\\sqrt{%s}\\times\\cancel{\\sqrt{%s}}}{%s\\times\\sqrt{%s}\\times\\cancel{\\sqrt{%s}}}'
% a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' +
'\\frac{%s\\times %s}{%s\\times %s}' % v[0:4] + '\\] ')
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s' %
(((v[0] * v[1]) // v[2]) // v[3]) + '} \\] ')
def exo_entier0(exo, cor, v):
a = (v[0], tex_coef(v[1], '\\sqrt{%s}' % v[2], bplus=1), v[0],
tex_coef(-v[1], '\\sqrt{%s}' % v[2], bplus=1))
exo.append(u'\\[ \\thenocalcul = ' +
'\\left( %s%s \\right)\\left( %s%s \\right)' % a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' +
'\\left( %s%s \\right)\\left( %s%s \\right)' % a + '\\] ')
a = (tex_coef(v[0], '',
bpc=1), tex_coef(abs(v[1]), '\\sqrt{%s}' % v[2], bpc=1))
cor.append(u'\\[ \\thenocalcul = ' + '%s^2-%s^2' % a + '\\] ')
a = (v[0]**2, v[1]**2, v[2])
cor.append(u'\\[ \\thenocalcul = ' + '%s-%s\\times %s' % a + '\\] ')
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s' %
(v[0]**2 - v[1]**2 * v[2]) + '} \\] ')
def exoaRb1(exo, cor, v):
a = (v[3] * v[0]**2, v[3] * v[1]**2, v[3] * v[2]**2)
exo.append(u'\\[ \\thenocalcul = ' +
'\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}' % a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' +
'\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}' % a + '\\] ')
a = (v[0]**2, v[3], v[1]**2, v[3], v[2]**2, v[3])
cor.append(
u'\\[ \\thenocalcul = ' +
'\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}'
% a + '\\] ')
a = (v[0], v[3], v[1], v[3], v[2], v[3])
cor.append(
u'\\[ \\thenocalcul = ' +
'%s\\times\\sqrt{%s}\\times%s\\times\\sqrt{%s}\\times%s\\times\\sqrt{%s}'
% a + '\\] ')
a = ((v[0] * v[1]) * v[2], v[3], v[3])
cor.append(u'\\[ \\thenocalcul = ' +
'%s\\times\\left(\\sqrt{%s}\\right)^2\\times\\sqrt{%s}' % a +
'\\] ')
a = ((v[0] * v[1]) * v[2], v[3], v[3])
cor.append(u'\\[ \\thenocalcul = ' + '%s\\times%s\\times\\sqrt{%s}' % a +
'\\] ')
del a
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s' % tex_coef((
(v[0] * v[1]) * v[2]) * v[3], '\\sqrt{%s}' % v[3]) + '} \\] ')
def tex_eq3(v, c):
if c[0]:
tv = (tex_coef(1, 'y'), tex_coef(v[0][2] - v[0][0] * v[2][0], ''),
tex_coef(v[0][1], ''), tex_coef(v[2][1], ''))
t = '%s=\\frac{%s}{%s}=%s' % tv
else:
tv = (tex_coef(1, 'x'), tex_coef(v[0][2] - v[0][1] * v[2][1], ''),
tex_coef(v[0][0], ''), tex_coef(v[2][0], ''))
t = '%s=\\frac{%s}{%s}=%s' % tv
return t
def tex_eq3(v, c):
if c[0]:
tv = (tex_coef(1, 'y'), tex_coef(v[0][2] -
v[0][0] * v[2][0], ''), tex_coef(v[0][1],
''), tex_coef(v[2][1], ''))
t = '%s=\\frac{%s}{%s}=%s' % tv
else:
tv = (tex_coef(1, 'x'), tex_coef(v[0][2] -
v[0][1] * v[2][1], ''), tex_coef(v[0][0],
''), tex_coef(v[2][0], ''))
t = '%s=\\frac{%s}{%s}=%s' % tv
return t
def tex_equation(v, c):
tv = (tex_coef(v[0][0], 'x'), tex_coef(v[0][1],
'y', bplus=1), v[0][2])
t = '$%s%s=%s\\quad\\text{et}\\quad ' % tv
if c[0]:
t = t + 'x=%s\\quad\\text{donc :}$\n' % v[2][0]
tv = (tex_coef(v[0][0], ''), tex_coef(v[2][0],
'', bpn=1), tex_coef(v[0][1], 'y', bplus=1),
v[0][2])
t = t + '\\[%s\\times %s %s=%s\\]\n' % tv
else:
t = t + 'y=%s\\quad\\text{donc :}$\n' % v[2][1]
tv = (tex_coef(v[0][0], 'x'), tex_coef(v[0][1],
'', bplus=1), tex_coef(v[2][1], '', bpn=1),
v[0][2])
t = t + '\\[%s %s\\times %s=%s\\]\n' % tv
return t
def tex_eq2(v, c):
if c[0]:
tv = (tex_coef(v[0][1], 'y'), tex_coef(v[0][2], ''),
tex_coef(-v[0][0] * v[2][0], '', bplus=1))
t = '%s=%s%s' % tv
else:
tv = (tex_coef(v[0][0], 'x'), tex_coef(v[0][2], ''),
tex_coef(-v[0][1] * v[2][1], '', bplus=1))
t = '%s=%s%s' % tv
return t
def exo_aPbRc(exo, cor, v):
a = (tex_coef(v[0], '\\sqrt{%s}' % v[1]), tex_coef(v[2],
'\\sqrt{%s}' % v[3], bplus=1))
exo.append(u'\\[ \\thenocalcul = ' + '\\left( %s%s \\right)^2' % a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '\\left( %s%s \\right)^2' % a + '\\] ')
if v[2] > 0:
sgn = '+'
else:
sgn = '-'
a = (tex_coef(v[0], '\\sqrt{%s}' % v[1], bpc=1), sgn, tex_coef(v[0],
'\\sqrt{%s}' % v[1]), tex_coef(abs(v[2]), '\\sqrt{%s}' % v[3]),
tex_coef(abs(v[2]), '\\sqrt{%s}' % v[3], bpc=1))
cor.append(u'\\[ \\thenocalcul = ' + '%s^2%s2\\times%s\\times%s+%s^2' % a + '\\] ')
a = (v[0] ** 2, v[1], tex_coef((2 * v[0]) * v[2], '\\sqrt{%s}' % (v[1] *
v[3]), bplus=1), v[2] ** 2, v[3])
cor.append(u'\\[ \\thenocalcul = ' + '%s\\times %s %s+%s\\times %s' % a + '\\] ')
a = (v[0] ** 2 * v[1] + v[2] ** 2 * v[3], tex_coef((2 * v[0]) * v[2],
'\\sqrt{%s}' % (v[1] * v[3]), bplus=1))
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s%s' % a + '} \\] ')
def tex_eq2(v, c):
if c[0]:
tv = (tex_coef(v[0][1], 'y'), tex_coef(v[0][2],
''), tex_coef(-v[0][0] * v[2][0], '', bplus=
1))
t = '%s=%s%s' % tv
else:
tv = (tex_coef(v[0][0], 'x'), tex_coef(v[0][2],
''), tex_coef(-v[0][1] * v[2][1], '', bplus=
1))
t = '%s=%s%s' % tv
return t
def tex_equation(v, c):
tv = (tex_coef(v[0][0], 'x'), tex_coef(v[0][1], 'y', bplus=1), v[0][2])
t = '$%s%s=%s\\quad\\text{et}\\quad ' % tv
if c[0]:
t = t + 'x=%s\\quad\\text{donc :}$\n' % v[2][0]
tv = (tex_coef(v[0][0],
''), tex_coef(v[2][0],
'', bpn=1), tex_coef(v[0][1],
'y',
bplus=1), v[0][2])
t = t + '\\[%s\\times %s %s=%s\\]\n' % tv
else:
t = t + 'y=%s\\quad\\text{donc :}$\n' % v[2][1]
tv = (tex_coef(v[0][0],
'x'), tex_coef(v[0][1],
'', bplus=1), tex_coef(v[2][1],
'',
bpn=1), v[0][2])
t = t + '\\[%s %s\\times %s=%s\\]\n' % tv
return t
def exoaRb1(exo, cor, v):
a = (v[3] * v[0] ** 2, v[3] * v[1] ** 2, v[3] * v[2] ** 2)
exo.append(u'\\[ \\thenocalcul = ' + '\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}' %
a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}' %
a + '\\] ')
a = (v[0] ** 2, v[3], v[1] ** 2, v[3], v[2] ** 2, v[3])
cor.append(u'\\[ \\thenocalcul = ' +
'\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}\\times\\sqrt{%s}' %
a + '\\] ')
a = (v[0], v[3], v[1], v[3], v[2], v[3])
cor.append(u'\\[ \\thenocalcul = ' +
'%s\\times\\sqrt{%s}\\times%s\\times\\sqrt{%s}\\times%s\\times\\sqrt{%s}' %
a + '\\] ')
a = ((v[0] * v[1]) * v[2], v[3], v[3])
cor.append(u'\\[ \\thenocalcul = ' +
'%s\\times\\left(\\sqrt{%s}\\right)^2\\times\\sqrt{%s}' %
a + '\\] ')
a = ((v[0] * v[1]) * v[2], v[3], v[3])
cor.append(u'\\[ \\thenocalcul = ' + '%s\\times%s\\times\\sqrt{%s}' % a + '\\] ')
del a
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s' % tex_coef(((v[0] * v[1]) * v[2]) * v[3],
'\\sqrt{%s}' % v[3]) + '} \\] ')
def tex_comb2(v, c):
if c[0]:
tv = (tex_coef(v[0][0], 'x'), '\\cancel{' +
tex_coef(v[0][1], 'y', bplus=1) + '}',
tex_coef(v[1][0], 'x', bplus=1),
'\\cancel{' + tex_coef(v[1][1], 'y', bplus=
1) + '}', tex_coef(v[0][2], ''),
tex_coef(v[1][2], '', bplus=1))
else:
tv = ('\\cancel{' + tex_coef(v[0][0], 'x') + '}',
tex_coef(v[0][1], 'y', bplus=1),
'\\cancel{' + tex_coef(v[1][0], 'x', bplus=
1) + '}', tex_coef(v[1][1], 'y', bplus=1),
tex_coef(v[0][2], ''), tex_coef(v[1][2],
'', bplus=1))
return '%s%s%s%s=%s%s' % tv
def tex_verification(
v): # renvoie la vérification de lasolution du système d'équations.
tv = (
tex_coef(v[0][0], '\\times %s' % tex_coef(v[2][0], '', bpn=1)),
tex_coef(v[0][1], '\\times %s' % tex_coef(v[2][1], '', bpn=1),
bplus=1),
tex_coef(v[0][0] * v[2][0], ''),
tex_coef(v[0][1] * v[2][1], '', bplus=1),
v[0][2],
tex_coef(v[1][0], '\\times %s' % tex_coef(v[2][0], '', bpn=1)),
tex_coef(v[1][1], '\\times %s' % tex_coef(v[2][1], '', bpn=1),
bplus=1),
tex_coef(v[1][0] * v[2][0], ''),
tex_coef(v[1][1] * v[2][1], '', bplus=1),
v[1][2],
)
return '''\\left\\lbrace
\\begin{array}{l}
%s %s=%s %s=%s \\\\\n %s %s=%s %s=%s
\\end{array}
\\right.''' % \
tv
def exoaRb0(exo, cor, v):
a = (tex_coef(v[0], '\\sqrt{%s}' % (v[6] * v[3] ** 2)), tex_coef(v[1],
'\\sqrt{%s}' % (v[6] * v[4] ** 2), bplus=1), tex_coef(v[2],
'\\sqrt{%s}' % (v[6] * v[5] ** 2), bplus=1))
exo.append(u'\\[ \\thenocalcul = ' + '%s%s%s' % a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '%s%s%s' % a + '\\] ')
a = (tex_coef(v[0], '\\sqrt{%s}' % v[3] ** 2), v[6], tex_coef(v[1],
'\\sqrt{%s}' % v[4] ** 2, bplus=1), v[6], tex_coef(v[2],
'\\sqrt{%s}' % v[5] ** 2, bplus=1), v[6])
cor.append(u'\\[ \\thenocalcul = ' +
'%s\\times\\sqrt{%s}%s\\times\\sqrt{%s}%s\\times\\sqrt{%s}' %
a + '\\] ')
a = (
tex_coef(v[0], ''),
v[3],
v[6],
tex_coef(v[1], '', bplus=1),
v[4],
v[6],
tex_coef(v[2], '', bplus=1),
v[5],
v[6],
)
cor.append(u'\\[ \\thenocalcul = ' +
'%s\\times%s\\times\\sqrt{%s}%s\\times%s\\times\\sqrt{%s}%s\\times%s\\times\\sqrt{%s}' %
a + '\\] ')
a = (tex_coef(v[0] * v[3], '\\sqrt{%s}' % v[6]), tex_coef(v[1] * v[4],
'\\sqrt{%s}' % v[6], bplus=1), tex_coef(v[2] * v[5],
'\\sqrt{%s}' % v[6], bplus=1))
cor.append(u'\\[ \\thenocalcul = ' + '%s%s%s' % a + '\\] ')
del a
cor.append(u'\\[ \\boxed{\\thenocalcul = ' + '%s' % tex_coef(v[0] * v[3] + v[1] * v[4] + v[2] *
v[5], '\\sqrt{%s}' % v[6]) + '} \\] ')
def tex_comb4(v):
if v[0]:
tv = (tex_coef(1, 'x'), v[2], v[0], tex_coef(v[2] // v[0], ''))
else:
tv = (tex_coef(1, 'y'), v[2], v[1], tex_coef(v[2] // v[1], ''))
return '%s=\\frac{%s}{%s}=%s' % tv
def tex_comb3(v):
if v[0]:
tv = (tex_coef(v[0], 'x'), tex_coef(v[2], ''))
else:
tv = (tex_coef(v[1], 'y'), tex_coef(v[2], ''))
return '%s=%s' % tv
def tex_equation5(valeurs): # renvoie l'ecriture reduite de l'equation avec l'inconnue d'un cote de l'egalite
texte = tex_coef((valeurs[4][0] + valeurs[4][2] *
valeurs[3][1]) - valeurs[4][4], 'x')
texte = texte + '=' + tex_coef((valeurs[4][5] -
valeurs[4][1]) - valeurs[4][3] * valeurs[3][1], '')
return texte
def exoaRb0(exo, cor, v):
a = (tex_coef(v[0], '\\sqrt{%s}' % (v[6] * v[3]**2)),
tex_coef(v[1], '\\sqrt{%s}' % (v[6] * v[4]**2), bplus=1),
tex_coef(v[2], '\\sqrt{%s}' % (v[6] * v[5]**2), bplus=1))
exo.append(u'\\[ \\thenocalcul = ' + '%s%s%s' % a + '\\] ')
cor.append(u'\\[ \\thenocalcul = ' + '%s%s%s' % a + '\\] ')
a = (tex_coef(v[0], '\\sqrt{%s}' % v[3]**2), v[6],
tex_coef(v[1], '\\sqrt{%s}' % v[4]**2, bplus=1), v[6],
tex_coef(v[2], '\\sqrt{%s}' % v[5]**2, bplus=1), v[6])
cor.append(u'\\[ \\thenocalcul = ' +
'%s\\times\\sqrt{%s}%s\\times\\sqrt{%s}%s\\times\\sqrt{%s}' %
a + '\\] ')
a = (
tex_coef(v[0], ''),
v[3],
v[6],
tex_coef(v[1], '', bplus=1),
v[4],
v[6],
tex_coef(v[2], '', bplus=1),
v[5],
v[6],
)
cor.append(
u'\\[ \\thenocalcul = ' +
'%s\\times%s\\times\\sqrt{%s}%s\\times%s\\times\\sqrt{%s}%s\\times%s\\times\\sqrt{%s}'
% a + '\\] ')
a = (tex_coef(v[0] * v[3], '\\sqrt{%s}' % v[6]),
tex_coef(v[1] * v[4], '\\sqrt{%s}' % v[6],
bplus=1), tex_coef(v[2] * v[5], '\\sqrt{%s}' % v[6],
bplus=1))
cor.append(u'\\[ \\thenocalcul = ' + '%s%s%s' % a + '\\] ')
del a
cor.append(u'\\[ \\boxed{\\thenocalcul = ' +
'%s' % tex_coef(v[0] * v[3] + v[1] * v[4] +
v[2] * v[5], '\\sqrt{%s}' % v[6]) + '} \\] ')
def tex_verification(v): # renvoie la vérification de lasolution du système d'équations.
tv = (
tex_coef(v[0][0], '\\times %s' % tex_coef(v[2][0],
'', bpn=1)),
tex_coef(v[0][1], '\\times %s' % tex_coef(v[2][1],
'', bpn=1), bplus=1),
tex_coef(v[0][0] * v[2][0], ''),
tex_coef(v[0][1] * v[2][1], '', bplus=1),
v[0][2],
tex_coef(v[1][0], '\\times %s' % tex_coef(v[2][0],
'', bpn=1)),
tex_coef(v[1][1], '\\times %s' % tex_coef(v[2][1],
'', bpn=1), bplus=1),
tex_coef(v[1][0] * v[2][0], ''),
tex_coef(v[1][1] * v[2][1], '', bplus=1),
v[1][2],
)
return '''\\left\\lbrace
\\begin{array}{l}
%s %s=%s %s=%s \\\\\n %s %s=%s %s=%s
\\end{array}
\\right.''' % \
tv
def tex_comb2(v, c):
if c[0]:
tv = (tex_coef(v[0][0], 'x'),
'\\cancel{' + tex_coef(v[0][1], 'y', bplus=1) + '}',
tex_coef(v[1][0], 'x', bplus=1),
'\\cancel{' + tex_coef(v[1][1], 'y', bplus=1) + '}',
tex_coef(v[0][2], ''), tex_coef(v[1][2], '', bplus=1))
else:
tv = ('\\cancel{' + tex_coef(v[0][0], 'x') + '}',
tex_coef(v[0][1], 'y', bplus=1),
'\\cancel{' + tex_coef(v[1][0], 'x', bplus=1) + '}',
tex_coef(v[1][1], 'y',
bplus=1), tex_coef(v[0][2],
''), tex_coef(v[1][2], '', bplus=1))
return '%s%s%s%s=%s%s' % tv
