def valeurs_somme_positive():
"""Travail sur les sommes de fractions en quatrième"""
l = []
op = "+-"[random.randrange(2)]
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
if op == "-" and 1 - n2 / d2 > 0:
l.append('1 %s Fraction(%s, %s)' % (op, n2, d2))
else:
l.append('Fraction(%s, %s) %s 1' % (n2, d2, op))
op = "+-"[random.randrange(2)]
n1 = random.randrange(2, 11)
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
if op == "-" and n1 - n2 / d2 > 0:
l.append('%s %s Fraction(%s, %s)' % (n1, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s %s' % (n2, d2, op, n1))
op = "+-"[random.randrange(2)]
n1 = random.randrange(1, 9) + random.randrange(1, 9) / 10.
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
if op == "-" and n1 - n2 / d2 > 0:
l.append('%s %s Fraction(%s, %s)' % (n1, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s %s' % (n2, d2, op, n1))
op = "+-"[random.randrange(2)]
n1 = random.randrange(1, 11)
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
if op == "-" and n1 - n2 > 0:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n1, d2, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n2, d2, op, n1, d2))
op = "+-"[random.randrange(2)]
n1, d1 = random.randrange(1, 11), random.randrange(2, 11)
n2, d2 = random.randrange(1, 11), random.randrange(2, 11) * d1
if op == "-" and n1 / d1 - n2 / d2 > 0:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n1, d1, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n2, d2, op, n1, d1))
for dummy in range(3):
op = "+-"[random.randrange(2)]
d1, d2 = 2, 2
lepgcd = Arithmetique.pgcd(d1, d2)
while lepgcd == d1 or lepgcd == d2:
n1, d1 = random.randrange(1, 11), random.randrange(2, 11)
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
lepgcd = Arithmetique.pgcd(d1, d2)
if op == "-" and n1 / d1 - n2 / d2 > 0:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' %
(n1, d1, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' %
(n2, d2, op, n1, d1))
random.shuffle(l)
return l
def valeurs_somme_positive():
"""Travail sur les sommes de fractions en quatrième"""
l = []
op = "+-"[random.randrange(2)]
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
if op == "-" and 1 - n2 / d2 > 0:
l.append('1 %s Fraction(%s, %s)' % (op, n2, d2))
else:
l.append('Fraction(%s, %s) %s 1' % (n2, d2, op))
op = "+-"[random.randrange(2)]
n1 = random.randrange(2, 11)
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
if op == "-" and n1 - n2 / d2 > 0:
l.append('%s %s Fraction(%s, %s)' % (n1, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s %s' % (n2, d2, op, n1))
op = "+-"[random.randrange(2)]
n1 = random.randrange(1, 9) + random.randrange(1, 9) / 10.
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
if op == "-" and n1 - n2 / d2 > 0:
l.append('%s %s Fraction(%s, %s)' % (n1, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s %s' % (n2, d2, op, n1))
op = "+-"[random.randrange(2)]
n1 = random.randrange(1, 11)
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
if op == "-" and n1 - n2 > 0:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n1, d2, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n2, d2, op, n1, d2))
op = "+-"[random.randrange(2)]
n1, d1 = random.randrange(1, 11), random.randrange(2, 11)
n2, d2 = random.randrange(1, 11), random.randrange(2, 11) * d1
if op == "-" and n1 / d1 - n2 / d2 > 0:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n1, d1, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n2, d2, op, n1, d1))
for dummy in range(3):
op = "+-"[random.randrange(2)]
d1, d2 = 2, 2
lepgcd = Arithmetique.pgcd(d1, d2)
while lepgcd == d1 or lepgcd == d2:
n1, d1 = random.randrange(1, 11), random.randrange(2, 11)
n2, d2 = random.randrange(1, 11), random.randrange(2, 11)
lepgcd = Arithmetique.pgcd(d1, d2)
if op == "-" and n1 / d1 - n2 / d2 > 0:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n1, d1, op, n2, d2))
else:
l.append('Fraction(%s, %s) %s Fraction(%s, %s)' % (n2, d2, op, n1, d1))
random.shuffle(l)
return l
def valeurs_produit():
l = []
for dummy in range(4):
n1 = d1 = n2 = d2 = a = b = 2
while Arithmetique.pgcd(a, b) > 1:
a = random.randrange(1, 11)
b = random.randrange(2, 11)
while Arithmetique.pgcd(n1 * a, d1 * b) > 1:
n1 = random.randrange(1, 11)
d1 = random.randrange(2, 11)
while Arithmetique.pgcd(n2 * b, d2 * a) > 1:
n2 = random.randrange(1, 11)
d2 = random.randrange(2, 11)
l.append(_('Fraction(%s, %s)*Fraction(%s,%s)') % (n1 * a, d1 * b, n2 * b, d2 * a))
return l
def valeurs_produit():
l = []
for dummy in range(4):
n1 = d1 = n2 = d2 = a = b = 2
while Arithmetique.pgcd(a, b) > 1:
a = random.randrange(1, 11)
b = random.randrange(2, 11)
while Arithmetique.pgcd(n1 * a, d1 * b) > 1:
n1 = random.randrange(1, 11)
d1 = random.randrange(2, 11)
while Arithmetique.pgcd(n2 * b, d2 * a) > 1:
n2 = random.randrange(1, 11)
d2 = random.randrange(2, 11)
l.append(
_('Fraction(%s, %s)*Fraction(%s,%s)') %
(n1 * a, d1 * b, n2 * b, d2 * a))
return l
def valeurs_entier1(pyromax): # renvoie (coef0, coef1, coef2, carre0, carre1, carre2, b)
a = carres[random.randrange(len(carres))]
while True:
v0 = random.randrange(2, pyromax)
v1 = random.randrange(2, pyromax)
b0 = random.randrange(2, pyromax)
b1 = random.randrange(2, pyromax)
a0 = (b1 * v0) * v1
a1 = v1 * b0
if b0 < b1 and Arithmetique.pgcd(a0, a1) != a1:
break
return (a0, b0, a1, b1, a)
def valeurs_aPbRc(pyromax): # renvoie (coef0, coef1, coef2, carre0, carre1, carre2, b)
while True:
a = carres[random.randrange(len(carres))]
b = carres[random.randrange(len(carres))]
if a != b and Arithmetique.pgcd(a, b) != min(a, b):
break
while True:
c = random.randrange(2, pyromax)
d = Arithmetique.valeur_alea(-pyromax, pyromax)
if c != d:
break
return (c, a, d, b)
def valeurs_entier1(
pyromax): # renvoie (coef0, coef1, coef2, carre0, carre1, carre2, b)
a = carres[random.randrange(len(carres))]
while True:
v0 = random.randrange(2, pyromax)
v1 = random.randrange(2, pyromax)
b0 = random.randrange(2, pyromax)
b1 = random.randrange(2, pyromax)
a0 = (b1 * v0) * v1
a1 = v1 * b0
if b0 < b1 and Arithmetique.pgcd(a0, a1) != a1:
break
return (a0, b0, a1, b1, a)
def valeurs_aPbRc(
pyromax): # renvoie (coef0, coef1, coef2, carre0, carre1, carre2, b)
while True:
a = carres[random.randrange(len(carres))]
b = carres[random.randrange(len(carres))]
if a != b and Arithmetique.pgcd(a, b) != min(a, b):
break
while True:
c = random.randrange(2, pyromax)
d = Arithmetique.valeur_alea(-pyromax, pyromax)
if c != d:
break
return (c, a, d, b)
