def axiome_init():
"""
"""
v = myVars()
print('\n\nAXIOME_INIT')
print('Pour un complexe cartesien :')
z = Complexe(v.f1, v.s1, 1)
_ = ""
_ += "%r " % (z.reel == v.f1)
_ += "%r " % (z.imag == v.s1)
_ += "%r " % (z.isCartesien == 1)
print(_ + "\n")
_ = ""
print('Pour un complexe polaire : ')
z = Complexe(v.f4, v.s4, 0)
_ += "%r " % (z.module == v.f4)
_ += "%r " % (round(abs(z.argument - v.s4 % (2 * pi)), 9) == 0)
_ += "%r " % (z.isCartesien == 0)
print(_ + "\n")
_ = ""
print('Pour un complexe cartesien : par defaut')
z = Complexe(v.f1, v.s1)
_ += "%r " % (z.isCartesien == 1)
print(_ + "\n")
def axiome_mul():
"""
"""
print('\n\nAXIOME_MUL')
v = myVars()
print('Avec un complexe cartesien en premier : ')
print('Transmission isCartesien : ', (v.zCart * v.zCart2).isCartesien == 1)
print(
'Element neutre : ',
v.zCart * Complexe(1, 0, 1) == v.zCart * Complexe(1, 0, 0) == v.zCart)
print('Commutativite : ', v.zCart * v.zCart2 == v.zCart2 * v.zCart)
print('Associativite : ',
v.zCart * (v.zCart2 * v.zCart3) == (v.zCart * v.zCart2) * v.zCart3)
print(
"Distributive par rapport à l'addition : ",
v.zCart * (v.zCart2 + v.zCart3) == (v.zCart * v.zCart2) +
(v.zCart * v.zCart3))
print('Avec un complexe polaire en premier : ')
print('Transmission isPolaire : ', (v.zPol * v.zCart2).isCartesien == 0)
print('Element neutre : ',
v.zPol * Complexe(1, 0, 1) == v.zPol * Complexe(1, 0, 0) == v.zPol)
print('Commutativite : ', v.zPol * v.zPol2 == v.zPol2 * v.zPol)
print('Associativite : ',
v.zPol * (v.zPol2 * v.zPol3) == (v.zPol * v.zPol2) * v.zPol3)
print("Distributive par rapport à l'addition : ",
v.zPol * (v.zPol2 + v.zPol3) == (v.zPol * v.zPol2) +
(v.zPol * v.zPol3)) #PROBLEME
def axiome_conjugue():
"""
"""
print('\n\nAXIOME_CONJUGUE')
v = myVars()
z = v.zCart
y = v.zPol
_ = ""
_ += "%r " % (z * z.conjugue == Complexe(z.module**2, 0, 1))
_ += "%r " % (z.conjugue.conjugue == z)
_ += "%r " % (v.zR.conjugue == v.zR)
_ += "%r " % (v.zIm.conjugue == v.zIm.oppose)
_ += "%r " % ((z + z.conjugue) == Complexe(2 * z.reel, 0, 1))
_ += "%r " % ((z - z.conjugue) == Complexe(0, 2 * z.imag, 1))
_ += "%r " % ((z + y).conjugue == z.conjugue + y.conjugue)
_ += "%r " % ((z * y).conjugue == z.conjugue * y.conjugue)
_ += "%r " % (v.zPos.inverse.conjugue == v.zPos.conjugue.inverse)
_ += "%r " % ((z**v.n).conjugue == z.conjugue**v.n)
_ += "%r " % ((z / v.zPos).conjugue == z.conjugue / v.zPos.conjugue)
print(_ + "\n")
_ = ""
print('Pour un complexe cartesien :')
_ += "%r " % (v.zCart.conjugue.reel == v.zCart.reel)
_ += "%r " % (v.zCart.conjugue.imag == (-v.zCart.imag))
_ += "%r " % (v.zCart.conjugue.isCartesien == 1)
print(_ + "\n")
_ = ""
print('Pour un complexe polaire : ')
_ += "%r " % (v.zPol.conjugue.module == v.zPol.module)
_ += "%r " % (round(
abs(v.zPol.conjugue.argument - (-v.zPol.argument) %
(2 * pi)), 10) == 0)
_ += "%r " % (v.zPol.conjugue.isCartesien == 0)
print(_ + "\n")
def axiome_find():
"""
"""
print('\n\nAXIOME_FIND')
_=""
v=myVars()
l=[v.zCart,v.zPol,v.zCart2,v.zPol2,v.zCart3,v.zPol3,v.zPos,v.zPosPol,
v.zUn,v.zIm,v.zR,v.zI,v.zZero]
random.shuffle(l)
i=random.randint(0,len(l)-1)
a=l[i]
_+="%r "%(a.find(l)==i)
g=[v.zUn,v.zIm,v.zR,v.zI,v.zZero]
a=Complexe(4,1,1)
_+="%r "%(a.find(g)==None)
print(_+"\n")
def axiome_find():
"""
"""
print('\n\nAXIOME_FIND')
_ = ""
v = myVars()
l = [
v.zCart, v.zPol, v.zCart2, v.zPol2, v.zCart3, v.zPol3, v.zPos,
v.zPosPol, v.zUn, v.zIm, v.zR, v.zI, v.zZero
]
random.shuffle(l)
i = random.randint(0, len(l) - 1)
a = l[i]
_ += "%r " % (a.find(l) == i)
g = [v.zUn, v.zIm, v.zR, v.zI, v.zZero]
a = Complexe(4, 1, 1)
_ += "%r " % (a.find(g) == None)
print(_ + "\n")
def axiome_lt():
"""
"""
print('\n\nAXIOME_LT')
v = myVars()
print('Pour un complexe cartesien :')
z = v.zPos
_ = ""
_ += "%r " % ((z < z) == 0)
u = Complexe(z.reel / 5, z.imag / 5, 1)
_ += "%r " % ((u < z) == 1)
t = Complexe(z.reel, z.imag / 5, 1)
_ += "%r " % ((t < z) == 1)
print(_ + "\n")
_ = ""
print('Pour un complexe polaire : ')
z = v.zPosPol
_ += "%r " % ((z < z) == 0)
u = Complexe(z.module / 5, z.argument, 0)
_ += "%r " % ((u < z) == 1)
t = Complexe(z.module, -z.argument, 0)
_ += "%r " % ((t < z) == 1)
print(_ + "\n")
def axiome_truediv():
"""
"""
print("\n\nAXIOME_TRUEDIV")
v = myVars()
_ = ""
_ += "%r " % (v.zCart / Complexe(1, 0, 1) == v.zCart / Complexe(1, 0, 0) ==
v.zCart)
_ += "%r " % (Complexe(0, 0, 1) / v.zCart == Complexe(0, 0, 0))
_ += "%r " % (v.zCart.conjugue.isCartesien == 1)
_ += "%r " % (v.zCart / v.zCart2 == v.zCart * v.zCart2.inverse)
print(_ + "\n")
_ = ""
_ += "%r " % (v.zPol / Complexe(1, 0, 1) == v.zPol / Complexe(1, 0, 0) ==
v.zPol)
_ += "%r " % (Complexe(0, 0, 1) / v.zPol == Complexe(0, 0, 0))
_ += "%r " % (v.zPol / v.zPol2 == v.zPol * v.zPol2.inverse)
_ += "%r " % (v.zCart.conjugue.isCartesien == 1)
print(_ + "\n")
def main_basique():
print('INIT et GETTER SETTER')
print('A DEVIENT EST CARTESIEN')
a = Complexe(0, 0, 1)
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print("a.isCartesien : ", a.isCartesien)
print("a.isPolaire : ", a.isPolaire)
print('A DEVIENT I+1')
a.reel = 1
a.imag = 1
print("a.reel=1; a.reel : ", a.reel)
print("a.imag=1; a.imag : ", a.imag)
print('pi/4 : ', pi / 4)
print('sqrt(2) : ', sqrt(2))
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print('MODULE DEVIENT 1')
a.module = 1
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print('argument DEVIENT pi/2')
a.argument = pi / 2
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print()
#TESTS
print('TESTS')
print('Cartesien : ')
a = Complexe(1, 2, True)
b = Complexe(1, 2, True)
c = Complexe(1, 1, True)
print('a : ', a)
print('b : ', b)
print('c : ', c)
print('a==b : ', a == b)
print('a==c : ', a == c)
print('a<b : ', a < b)
print('c<a : ', c < a)
print('Polaire : ')
a = Complexe(1.0, pi / 4, 0)
b = Complexe(2, pi / 4, 0)
c = Complexe(2, pi / 2, 0)
print('a==b : ', a == b)
print('a==c : ', a == c)
print('a<b : ', a < b)
print('c<a : ', c < a)
print()
#ADDITION:
print('ADDITION')
print('Cartesien ')
a = Complexe(1, 2, True)
b = Complexe(1, 2, True)
print('a : ', a)
print('b : ', b)
print('a+b :', a + b)
print('Polaire ')
a = Complexe(2, pi / 2, False)
b = Complexe(2, pi / 4, 0)
print('a : ', a)
print('b : ', b)
print('a+b : ', a + b)
print()
#MULTIPLICATION
print('MULTIPLICATION')
print('Cartesien ')
a = Complexe(1, 1, True)
b = Complexe(1, 1, True)
print('a : ', a)
print('b : ', b)
print('a*b : ', a * b)
a = Complexe(1, 2, True)
b = Complexe(1, 2, True)
print('a : ', a)
print('b : ', b)
print('a*b : ', a * b)
print('Polaire ')
a = Complexe(1, pi / 2, 0)
b = Complexe(2, pi / 4, 0)
print('a : ', a)
print('b : ', b)
print('3pi/4 : ', 3 * pi / 4)
print('a*b : ', a * b)
print()
#OPPOSE
print('OPPOSE')
print('Cartesien : ')
a = Complexe(-3, 0, True)
print('a : ', a)
print('a.oppose : ', a.oppose)
print('a.cartesien : ', a.cartesien)
print('a.polaire : ', a.polaire)
print('a.oppose.cartesien : ', a.oppose.cartesien)
print('a.oppose.polaire : ', a.oppose.polaire)
print('Polaire : ')
a = Complexe(2, pi, 0)
print('a : ', a)
print('a.oppose : ', a.oppose)
print('a.cartesien : ', a.cartesien)
print('a.polaire : ', a.polaire)
print('a.oppose.cartesien : ', a.oppose.cartesien)
print('a.oppose.polaire : ', a.oppose.polaire)
print()
#INVERSE
print('INVERSE')
print('Cartesien ')
a = Complexe(1, 1, 1)
print('a : ', a)
print(a.inverse)
print('Polaire ')
a = Complexe(2, 2 * pi / 3, 0)
print('a : ', a)
print(a.inverse)
print()
#CONJUGUE
print('CONJUGUE')
print('Cartesien')
a = Complexe(1, 2, 1)
print('a : ', a)
print(a.conjugue)
print('Polaire')
a = Complexe(1, 5 * pi / 6, 0)
print('a : ', a)
print(a.conjugue)
print()
#VALEUR ABSOLUE
print('VALEUR ABSOLUE')
print('Cartesien')
a = Complexe(1, 1, 1)
print('a : ', a)
print(abs(a))
print(sqrt(0.5))
print(abs(a.inverse))
print('Polaire')
a = Complexe(87, pi / 3, 0)
print('a : ', a)
print(abs(a))
print()
#SOUSTRACTION
print('SOUSTRACTION')
print('Cartesien')
a = Complexe(1, 1, 1)
b = Complexe(1, -3, 1)
print('a : ', a)
print('b : ', b)
print('a-b : ', a - b)
print('Polaire')
a = Complexe(sqrt(2), pi / 4, 0)
b = Complexe(1, pi / 2, 0)
print('a : ', a)
print('b : ', b)
print('a-b : ', a - b)
print()
#DIVISION
print('DIVISION')
print('Cartesien: ')
a = Complexe(1, 1, 1)
print('a : ', a)
print('a/a : ', a / a)
print('Polaire : ')
a = Complexe(42, pi / 2, 0)
b = Complexe(2, pi / 4, 0)
print('a : ', a)
print('b : ', b)
print('pi/4 ', (pi / 4))
print('a/b : ', a / b)
print()
#PUISSANCE ENTIERE
print('PUISSANCE ENTIERE')
print('Cartesien')
a = Complexe(1, 1, 1)
print('a : ', a)
print('a**2 : ', a**2)
print('a**3 : ', a**3)
print('a**4 : ', a**4)
print('Polaire')
a = Complexe(1, pi, 0)
print('a : ', a)
print('a**2 : ', a**2)
print('a**3 : ', a**3)
print('a**4 : ', a**4)
print()
#CHERCHE DANS LISTE DE COMPLEXES
print('CHERCHE')
l = [Complexe(i, j, 1) for i in range(2) for j in range(5)]
print(l)
print()
g = [Complexe(i, j, 0) for i in range(2) for j in range(5)]
print(g)
a = Complexe(1, 4, 1)
print('a : ', a)
print('a.find(l) : ', a.find(l))
print('a.find(g) : ', a.find(g))
a = Complexe(1, 4, 0)
print('a : ', a)
print('a.find(g) : ', a.find(g))
print()
#TRI LISTE DE COMPLEXES
print('TRI LISTE')
print('Cartesien')
print('Liste:')
y = [Complexe(1, 1, 1), Complexe(2, 1, 1), Complexe(1, 3, 1)]
print(y)
r = tri(y)
print('tri de la liste')
print(r)
print()
print('Nouvelle liste:')
u = [Complexe(1, 1, 1), Complexe(2, 1, 1), Complexe(1, 3, 1)] * 3
print(u)
o = tri(u)
print('tri de la liste')
print(o)
print()
print('Polaire')
print('Nouvelle liste:')
g = [Complexe(1, pi / 4, 0), Complexe(2, pi / 4, 0), Complexe(1, pi, 0)]
print(g)
h = tri(g)
print('tri de la liste')
print(h)
print()
print('Nouvelle liste:')
q = [Complexe(1, pi / 4, 0),
Complexe(2, pi / 4, 0),
Complexe(1, pi, 0)] * 3
print(q)
j = tri(q)
print('tri de la liste')
print(j)
print()
a = Complexe(1, 4 * pi, 0)
b = Complexe(1, -10 * pi, 0)
print('a : ', a)
print('b : ', b)
print('a==b :', a == b)
a = Complexe(1, 1, 1)
b = Complexe(sqrt(2), pi / 4 + 1000 * pi, 0)
print('a : ', a)
print('b : ', b)
print('a==b :', a == b)
def __init__(self):
self.f1 = round(random.uniform(-10, 10), 10) #cartesiens
self.s1 = round(random.uniform(-10, 10), 10)
self.f2 = round(random.uniform(-10, 10), 10)
self.s2 = round(random.uniform(-10, 10), 10)
self.f3 = round(random.uniform(-10, 10), 10)
self.s3 = round(random.uniform(-10, 10), 10)
self.f4 = round(random.uniform(0, 10), 10) #polaires
self.s4 = round(random.uniform(-10, 10), 10)
self.f5 = round(random.uniform(0, 10), 10)
self.s5 = round(random.uniform(-10, 10), 10)
self.f6 = round(random.uniform(0, 10), 10)
self.s6 = round(random.uniform(-10, 10), 10)
self.f7 = round(random.uniform(1, 10), 10)
self.s7 = round(random.uniform(1, 10), 10)
self.f8 = round(random.uniform(1, 10), 10)
self.s8 = round(random.uniform(0, pi / 2), 10)
self.n = random.randint(0, 10)
self.zCart = Complexe(self.f1, self.s1, 1) #un complexe cartesien
self.zCart2 = Complexe(self.f2, self.s2,
1) #un autre complexe cartesien
self.zCart3 = Complexe(self.f3, self.s3,
1) #un autre complexe cartesien
self.zPol = Complexe(self.f4, self.s4, 0) #un complexe polaire
self.zPol2 = Complexe(self.f5, self.s5, 0) #un autre complexe polaire
self.zPol3 = Complexe(self.f6, self.s6, 0) #un autre complexe polaire
self.zR = Complexe(self.f1, 0, 1) #un complexe reel
self.zIm = Complexe(0, self.s1, 1) #un complexe imaginaire pur
self.zPos = Complexe(self.f7, self.s7,
1) #un complexe cartesien strictement positif
self.zPosPol = Complexe(self.f8, self.s8,
0) #un complexe polaire strictement positif
self.zUn = Complexe(1, 0, 0) # 1
self.zI = Complexe(0, 1, 1) # i
self.zZero = Complexe(0, 0, 1) # 0
def main_basique():
print("INIT et GETTER SETTER")
print("A DEVIENT EST CARTESIEN")
a = Complexe(0, 0, 1)
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print("a.isCartesien : ", a.isCartesien)
print("a.isPolaire : ", a.isPolaire)
print("A DEVIENT I+1")
a.reel = 1
a.imag = 1
print("a.reel=1; a.reel : ", a.reel)
print("a.imag=1; a.imag : ", a.imag)
print("pi/4 : ", pi / 4)
print("sqrt(2) : ", sqrt(2))
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print("MODULE DEVIENT 1")
a.module = 1
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print("argument DEVIENT pi/2")
a.argument = pi / 2
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print()
# TESTS
print("TESTS")
print("Cartesien : ")
a = Complexe(1, 2, True)
b = Complexe(1, 2, True)
c = Complexe(1, 1, True)
print("a : ", a)
print("b : ", b)
print("c : ", c)
print("a==b : ", a == b)
print("a==c : ", a == c)
print("a<b : ", a < b)
print("c<a : ", c < a)
print("Polaire : ")
a = Complexe(1.0, pi / 4, 0)
b = Complexe(2, pi / 4, 0)
c = Complexe(2, pi / 2, 0)
print("a==b : ", a == b)
print("a==c : ", a == c)
print("a<b : ", a < b)
print("c<a : ", c < a)
print()
# ADDITION:
print("ADDITION")
print("Cartesien ")
a = Complexe(1, 2, True)
b = Complexe(1, 2, True)
print("a : ", a)
print("b : ", b)
print("a+b :", a + b)
print("Polaire ")
a = Complexe(2, pi / 2, False)
b = Complexe(2, pi / 4, 0)
print("a : ", a)
print("b : ", b)
print("a+b : ", a + b)
print()
# MULTIPLICATION
print("MULTIPLICATION")
print("Cartesien ")
a = Complexe(1, 1, True)
b = Complexe(1, 1, True)
print("a : ", a)
print("b : ", b)
print("a*b : ", a * b)
a = Complexe(1, 2, True)
b = Complexe(1, 2, True)
print("a : ", a)
print("b : ", b)
print("a*b : ", a * b)
print("Polaire ")
a = Complexe(1, pi / 2, 0)
b = Complexe(2, pi / 4, 0)
print("a : ", a)
print("b : ", b)
print("3pi/4 : ", 3 * pi / 4)
print("a*b : ", a * b)
print()
# OPPOSE
print("OPPOSE")
print("Cartesien : ")
a = Complexe(-3, 0, True)
print("a : ", a)
print("a.oppose : ", a.oppose)
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print("a.oppose.cartesien : ", a.oppose.cartesien)
print("a.oppose.polaire : ", a.oppose.polaire)
print("Polaire : ")
a = Complexe(2, pi, 0)
print("a : ", a)
print("a.oppose : ", a.oppose)
print("a.cartesien : ", a.cartesien)
print("a.polaire : ", a.polaire)
print("a.oppose.cartesien : ", a.oppose.cartesien)
print("a.oppose.polaire : ", a.oppose.polaire)
print()
# INVERSE
print("INVERSE")
print("Cartesien ")
a = Complexe(1, 1, 1)
print("a : ", a)
print(a.inverse)
print("Polaire ")
a = Complexe(2, 2 * pi / 3, 0)
print("a : ", a)
print(a.inverse)
print()
# CONJUGUE
print("CONJUGUE")
print("Cartesien")
a = Complexe(1, 2, 1)
print("a : ", a)
print(a.conjugue)
print("Polaire")
a = Complexe(1, 5 * pi / 6, 0)
print("a : ", a)
print(a.conjugue)
print()
# VALEUR ABSOLUE
print("VALEUR ABSOLUE")
print("Cartesien")
a = Complexe(1, 1, 1)
print("a : ", a)
print(abs(a))
print(sqrt(0.5))
print(abs(a.inverse))
print("Polaire")
a = Complexe(87, pi / 3, 0)
print("a : ", a)
print(abs(a))
print()
# SOUSTRACTION
print("SOUSTRACTION")
print("Cartesien")
a = Complexe(1, 1, 1)
b = Complexe(1, -3, 1)
print("a : ", a)
print("b : ", b)
print("a-b : ", a - b)
print("Polaire")
a = Complexe(sqrt(2), pi / 4, 0)
b = Complexe(1, pi / 2, 0)
print("a : ", a)
print("b : ", b)
print("a-b : ", a - b)
print()
# DIVISION
print("DIVISION")
print("Cartesien: ")
a = Complexe(1, 1, 1)
print("a : ", a)
print("a/a : ", a / a)
print("Polaire : ")
a = Complexe(42, pi / 2, 0)
b = Complexe(2, pi / 4, 0)
print("a : ", a)
print("b : ", b)
print("pi/4 ", (pi / 4))
print("a/b : ", a / b)
print()
# PUISSANCE ENTIERE
print("PUISSANCE ENTIERE")
print("Cartesien")
a = Complexe(1, 1, 1)
print("a : ", a)
print("a**2 : ", a ** 2)
print("a**3 : ", a ** 3)
print("a**4 : ", a ** 4)
print("Polaire")
a = Complexe(1, pi, 0)
print("a : ", a)
print("a**2 : ", a ** 2)
print("a**3 : ", a ** 3)
print("a**4 : ", a ** 4)
print()
# CHERCHE DANS LISTE DE COMPLEXES
print("CHERCHE")
l = [Complexe(i, j, 1) for i in range(2) for j in range(5)]
print(l)
print()
g = [Complexe(i, j, 0) for i in range(2) for j in range(5)]
print(g)
a = Complexe(1, 4, 1)
print("a : ", a)
print("a.find(l) : ", a.find(l))
print("a.find(g) : ", a.find(g))
a = Complexe(1, 4, 0)
print("a : ", a)
print("a.find(g) : ", a.find(g))
print()
# TRI LISTE DE COMPLEXES
print("TRI LISTE")
print("Cartesien")
print("Liste:")
y = [Complexe(1, 1, 1), Complexe(2, 1, 1), Complexe(1, 3, 1)]
print(y)
r = tri(y)
print("tri de la liste")
print(r)
print()
print("Nouvelle liste:")
u = [Complexe(1, 1, 1), Complexe(2, 1, 1), Complexe(1, 3, 1)] * 3
print(u)
o = tri(u)
print("tri de la liste")
print(o)
print()
print("Polaire")
print("Nouvelle liste:")
g = [Complexe(1, pi / 4, 0), Complexe(2, pi / 4, 0), Complexe(1, pi, 0)]
print(g)
h = tri(g)
print("tri de la liste")
print(h)
print()
print("Nouvelle liste:")
q = [Complexe(1, pi / 4, 0), Complexe(2, pi / 4, 0), Complexe(1, pi, 0)] * 3
print(q)
j = tri(q)
print("tri de la liste")
print(j)
print()
a = Complexe(1, 4 * pi, 0)
b = Complexe(1, -10 * pi, 0)
print("a : ", a)
print("b : ", b)
print("a==b :", a == b)
a = Complexe(1, 1, 1)
b = Complexe(sqrt(2), pi / 4 + 1000 * pi, 0)
print("a : ", a)
print("b : ", b)
print("a==b :", a == b)
