def test_executer():
f = Feuille()
o = f.objets
f.executer("A = (1, 2)")
f.executer("A.x += 1")
assert(o.A.x == 2)
f.executer("A' = 3, 4")
f.executer("s = [A A']")
f.executer("I = Milieu(s)")
assertAlmostEqual(o.I.xy, (2.5, 3))
f.executer("del")
assert("I" not in o.noms)
assert("A_prime" in o.noms)
f.executer("del")
f.executer("del")
assert("A_prime" not in o.noms)
f.executer("= (1, 2)")
assert(o.M1.coordonnees == (1, 2))
f.executer("txt0 = `Bonjour !`")
f.executer(r"txt1 = `$P\`ere et m\`ere ont un accent grave.$`")
f.executer("chaine_vide = ``")
assert(o.txt0.texte == "Bonjour !")
assert(o.txt1.texte == r"$P\`ere et m\`ere ont un accent grave.$")
assert(o.chaine_vide.texte == "")
f.executer("M = (5, 7)")
f.executer("C = _")
assert(o.C.x == 5)
f.executer("=((i,sqrt(i)) for i in (3,4,5,6))")
assert(o.M2.xy == (3, sqrt(3)))
assert(o.M3.xy == (4, sqrt(4)))
assert(o.M4.xy == (5, sqrt(5)))
assert(o.M5.xy == (6, sqrt(6)))
def test_Droite_equation():
a = randint(50) - randint(50) + 0.1 # afin que a ne soit pas nul
b = randint(50) - randint(50) + random()
c = randint(50) - randint(50) + random()
d, e, f = Droite_equation(a, b, c).equation
assertAlmostEqual((e / d, f / d), (b / a, c / a))
assertEqual(Droite_equation(a, 0, 0).equation[1:], (0, 0))
assertEqual((Droite_equation(0, a, 0).equation[0], Droite_equation(
0, a, 0).equation[2]), (0, 0))
assert (not Droite_equation(0, 0, 0).existe)
d = Droite_equation("y=-5/2x-3/2")
assert (Point(0, -1.5) in d)
assert (Point(-1, 1) in d)
d = Droite_equation("x=2*10**2")
assert (Point(200, -1000) in d)
assert (Point(100, -1000) not in d)
d = Droite_equation("2*x+2*y=1")
assert (Point(0.5, 0) in d)
assert (Point(1, -0.5) in d)
d = Droite_equation("x+y=1")
assert (Point(0, 1) in d)
assert (Point(1, 0) in d)
d = Droite_equation("x+2y=-2")
assert (Point(0, -1) in d)
assert (Point(-2, 0) in d)
def test_Reflexion():
d = Droite_equation(1, 6, -2)
r = Reflexion(d)
M = Point(random()+randint(50)-randint(50), random()+randint(50)-randint(50))
m = Mediatrice(M, r(M))
assertAlmostEqual(d.equation_reduite, m.equation_reduite)
assert(r(d) is d)
def test_Parallele():
d0 = Droite_equation(2, 1, 7)
A = Point(-2, 3)
d = Parallele(d0, A)
assert(d.parallele(d0))
assert(d.droite is d0 and d.point is A)
assertAlmostEqual(d0.equation[:1], d.equation[:1])
def test_session():
i = Interprete(verbose = VERBOSE)
i.evaluer("1+7")
i.evaluer("x-3")
i.evaluer("ans()+ans(1)")
assertDernier(i, "x + 5")
i.evaluer("f(x, y, z)=2x+3y-z")
i.evaluer("f(-1, 5, a)")
assertDernier(i, "-a + 13")
i.evaluer("f(x)=x^2-7x+3")
i.evaluer("f'(x)")
assertDernier(i, "2*x - 7")
# Noms réservés
assertRaises(NameError, i.evaluer, "e=3")
assertRaises(NameError, i.evaluer, "pi=3")
assertRaises(NameError, i.evaluer, "i=3")
assertRaises(NameError, i.evaluer, "oo=3")
assertRaises(NameError, i.evaluer, "factorise=3")
# Etc.
# Test des générateurs
i.evaluer('f(x)=x+3')
i.evaluer('[f(j) for j in range(1, 11)]')
assertDernier(i, '[4, 5, 6, 7, 8, 9, 10, 11, 12, 13]')
i.evaluer('tuple(i for i in range(7))')
assertDernier(i, '(0, 1, 2, 3, 4, 5, 6)')
i.evaluer('[j for j in range(7)]')
assertDernier(i, '[0, 1, 2, 3, 4, 5, 6]')
# _11 is an alias for ans(11)
i.evaluer('_11 == _')
assertDernier(i, 'True')
i.evaluer('_7')
assertDernier(i, "2*x - 7")
# _ is an alias for ans(-1), __ is an alias for ans(-2), and so on.
i.evaluer('_ == -7 + 2*x')
assertDernier(i, 'True')
i.evaluer('__')
assertDernier(i, "2*x - 7")
i.evaluer('______') # ans(-6)
assertDernier(i, '(0, 1, 2, 3, 4, 5, 6)')
# Affichage des chaînes en mode text (et non math)
i.evaluer('"Bonjour !"')
assert i.latex_dernier_resultat == u'\u201CBonjour !\u201D'
# Virgule comme séparateur décimal
resultat, latex = i.evaluer('1,2')
assert resultat == '1,2'
assertAlmostEqual(i.derniers_resultats[-1], 1.2)
# Avec un espace, c'est une liste (tuple) par contre
resultat, latex = i.evaluer('1, 2')
assertEqual(resultat, '(1 ; 2)')
resultat, latex = i.evaluer('"1.2"')
assert resultat == '"1.2"'
i.evaluer('?aide')
i.evaluer('aide?')
i.evaluer('aide(aide)')
msg_aide = u"\n== Aide sur aide ==\nRetourne (si possible) de l'aide sur la fonction saisie."
resultats = i.derniers_resultats
assert resultats[-3:] == [msg_aide, msg_aide, msg_aide]
# LaTeX
latex = i.evaluer("gamma(x)")[1]
assertEqual(latex, r'$\mathrm{\Gamma}\left(x\right)$')
def test_Carre_centre():
O = rand_pt()
M = rand_pt()
p = Carre_centre(O, M)
assert(p.centre.existe and p.centre is O)
assert(len(p.cotes) == 4)
assertAlmostEqual(p.aire, p.cotes[0].longueur**2)
def test_Quadrilatere():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
p = Quadrilatere(A, B, C, D)
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D).coordonnees)
def test_Triangle():
A = rand_pt()
B = rand_pt()
C = rand_pt()
t = Triangle(A, B, C)
O = t.centre_cercle_circonscrit
assertAlmostEqual(Segment(O, A).longueur, Segment(O, C).longueur)
def test_reecriture():
f = Feuille()
H = f.objets.H = Fonction("2x^2+3x(1+x)", 'R')
def h(x):
return 2*x**2+3*x*(1+x)
assertAlmostEqual(H(17), h(17))
assertAlmostEqual(H(_VAL0), h(_VAL0))
def test_Secteur_angulaire():
u = Vecteur_libre(5.458, -2.546)
v = Vecteur_libre(-5.75, 12.6)
P = Point(2.54, -5.68)
a = Secteur_angulaire(P, u, v)
assert(isinstance(a.etiquette, Label_angle))
assertAlmostEqual(a.val, 2.43538435941)
assertAlmostEqual(a.degre, 139.537245287)
def test_Pentagone():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
p = Pentagone(A, B, C, D, E)
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D, E).coordonnees)
def test_variables():
f = Feuille()
o = f.objets
a = o.a = 3
b = o.b = 5
g = o.g = Fonction("a*x+b")
assertAlmostEqual(g(4), a*4+b)
assertAlmostEqual(g(_VAL0), a*_VAL0+b)
def test_Point_equidistant():
A = rand_pt()
B = rand_pt()
C = rand_pt()
P = Point_equidistant(A, B, C)
assertAlmostEqual(Segment(A, P).longueur, Segment(B, P).longueur)
assertAlmostEqual(Segment(A, P).longueur, Segment(C, P).longueur)
assert(P in Mediatrice(A, B))
def test_Droite_vectorielle():
v = Vecteur_libre(1, 7)
A = Point(-2, 3)
d = Droite_vectorielle(A, v)
assert(d.vecteur is v and d.point is A)
assertAlmostEqual(v.y/v.x, -d.equation[0]/d.equation[1])
B = rand_pt()
d1 = Droite_vectorielle(B, v)
assert(d.parallele(d1))
def test_Bissectrice():
A = Point(1, -5)
B = Point(1.5, -5.3)
C = Point(3, -4)
d = Bissectrice(A, B, C)
a, b, c = d.equation
d, e = (0.0870545184921, -1.03861105199)
assertAlmostEqual(b/a, d)
assertAlmostEqual(c/a, e)
def test_Hexagone():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
F = rand_pt()
p = Hexagone(A, B, C, D, E, F)
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D, E, F).coordonnees)
def test_Perpendiculaire():
d = Droite_equation(-1, 2, 0)
M = Point()
d0 = Perpendiculaire(d, M)
a, b, c = d.equation
a0, b0, c0 = d0.equation
assert(d.perpendiculaire(d0))
assertAlmostEqual(a*a0 + b*b0, 0)
assert(M in d0)
def test_Extremite():
v=Vecteur_libre(-4.2, -6.7)
w = Representant(v)
A = w.origine
B = w.extremite
assertAlmostEqual((B.x - A.x, B.y - A.y), (v.x, v.y))
C = Extremite(w, couleur = 'purple')
assert C is B
assert C.style('couleur') == 'purple'
def test_Arc_points():
A = Point(-1.2561, 45.236)
B = Point(251.2561, 41.256)
C = Point(-42.25, 2.351)
a = Arc_points(A, B, C)
assert(A in a)
assert(B in a)
assert(C in a)
assertAlmostEqual(a.longueur, 1208.25931027)
assertAlmostEqual(a.centre.coordonnees, (122.51970100911581, -114.11725498641933))
def test_Point_translation():
u = Vecteur_libre(1.56, 2.78)
v = Vecteur(Point(1.1457, 2.7895), Point(2.458, -8.25))
A = Point(5.256, -7.231)
tu = Translation(u)
tv = Translation(v)
Au = Point_translation(A, tu)
Av = Point_translation(A, tv)
assertAlmostEqual(Au.coordonnees, (6.816, -4.451))
assertAlmostEqual(Av.coordonnees, (6.5683, -18.2705))
def test_modification_variable():
f = Feuille()
o = f.objets
o.a = Variable(1)
o.fa = "5*sin(4/(a+.5))-1.5"
o.A = Point(o.a, o.fa)
o.fa = "-5*sin(4/(a+.5))+5.5"
o.A = Point(o.a, o.fa)
assertAlmostEqual(o.A.x, o.a)
assertAlmostEqual(o.A.y, o.fa)
def test_Representant():
A=Point(1,2)
B=Point(2,4)
v=Vecteur(A, B)
w = Representant(v, B)
assert(w.x == v.x and w.y == v.y and w.z == v.z)
assert(w.origine == v.point2)
assertEqual(type(w.coordonnees), tuple)
assertAlmostEqual(w.extremite.coordonnees, (3, 6))
assert(w._hierarchie < w.extremite._hierarchie < w._hierarchie + 1)
def test_Point_final():
A = Point(random(),random())
C = Point(random(),random())
u = Vecteur_libre(random(),random())
v = Vecteur(Point(random(), random()), Point(random(), random()))
w = Representant(Vecteur(Point(random(), random()), Point(random(), random())), A)
F = Point_final(C, (u, v, w), (-2, 1.5, 4))
assertEqual(type(F.coordonnees), tuple)
assertAlmostEqual(F.x, C.x -2*u.x+1.5*v.x+4*w.x)
assertAlmostEqual(F.y, C.y -2*u.y+1.5*v.y+4*w.y)
def test_Rectangle():
A = rand_pt()
B = rand_pt()
r = Rectangle(A, B)
M, N, O, P = r.sommets
diagonale1 = Segment(M, O)
diagonale2 = Segment(N, P)
assertAlmostEqual(diagonale1.longueur, diagonale2.longueur)
cote = Droite(M, N)
cote_oppose = Droite(O, P)
assert (cote.parallele(cote_oppose))
def test_Arc_points():
A = Point(-1.2561, 45.236)
B = Point(251.2561, 41.256)
C = Point(-42.25, 2.351)
a = Arc_points(A, B, C)
assert (A in a)
assert (B in a)
assert (C in a)
assertAlmostEqual(a.longueur, 1208.25931027)
assertAlmostEqual(a.centre.coordonnees,
(122.51970100911581, -114.11725498641933))
def test_Heptagone():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
F = rand_pt()
G = rand_pt()
p = Heptagone(A, B, C, D, E, F, G)
assertAlmostEqual(p.centre.coordonnees,
Barycentre(A, B, C, D, E, F, G).coordonnees)
def test_Octogone():
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
F = rand_pt()
G = rand_pt()
H = rand_pt()
p = Octogone(A, B, C, D, E, F, G, H)
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D, E, F, G, H).coordonnees)
def test_Rectangle():
A = rand_pt()
B = rand_pt()
r = Rectangle(A, B)
M, N, O, P = r.sommets
diagonale1 = Segment(M, O)
diagonale2 = Segment(N, P)
assertAlmostEqual(diagonale1.longueur, diagonale2.longueur)
cote = Droite(M, N)
cote_oppose = Droite(O, P)
assert(cote.parallele(cote_oppose))
def test_Point_rotation():
A = Point(1, -4)
r = Rotation(Point(-2, 7.56), 4.25)
B = Point_rotation(A, r)
assertAlmostEqual(r(A).coordonnees, B.coordonnees)
assertAlmostEqual(B.coordonnees, (-13.684339450863803, 10.031803308717693))
A = Point('1', '0')
r = Rotation(('0', '0'), 'pi/4')
B = Point_rotation(A, r)
C = Point('sqrt(2)/2', 'sqrt(2)/2')
assert(C.x == B.x and C.y == B.y)
def test_Polygone():
# cas général : polygone à 11 côtés :
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
F = rand_pt()
G = rand_pt()
H = rand_pt()
I = rand_pt()
J = rand_pt()
K = rand_pt()
p = p0 = Polygone(A, B, C, D, E, F, G, H, I, J, K)
assert (isinstance(p.etiquette, Label_polygone))
assert (p.sommets[0] == A and p.sommets[10] == K)
assert (Milieu(B, C) in p.cotes[1])
assertAlmostEqual(p.centre.coordonnees,
Barycentre(A, B, C, D, E, F, G, H, I, J, K).coordonnees)
# cas particuliers :
t = Polygone(A, B, C)
O = t.centre_cercle_circonscrit
assertAlmostEqual(Segment(O, A).longueur, Segment(O, C).longueur)
assert (Droite(t.orthocentre, C).perpendiculaire(Droite(A, B)))
assert (t.__class__ is Triangle)
p = Polygone(A, B, C, D)
assert (p.__class__ is Quadrilatere)
p = Polygone(A, B, C, D, E)
assert (p.__class__ is Pentagone)
p = Polygone(A, B, C, D, E, F)
assert (p.__class__ is Hexagone)
p = Polygone(A, B, C, D, E, F, G)
assert (p.__class__ is Heptagone)
p = Polygone(A, B, C, D, E, F, G, H)
assert (p.__class__ is Octogone)
assert (p._hierarchie < p.sommets[0]._hierarchie < p.sommets[1]._hierarchie
< p.sommets[7]._hierarchie < p._hierarchie + 1)
# Test keyword 'points'
p = Polygone(points=(A, B, C, D, E, F, G, H, I, J, K))
assert (p.centre.coordonnees == p0.centre.coordonnees)
assert ("points" not in p.style())
# Syntaxe spéciale : Polygone créé sans arguments, ou avec un entier comme argument.
p = Polygone()
p = Polygone(2)
assert (isinstance(p, Segment))
p = Polygone(3)
assert (isinstance(p, Triangle))
p = Polygone(n=5)
assert (isinstance(p, Pentagone))
p = Polygone(n=12)
assert (len(p.points) == 12)
p = Polygone(23)
assert (len(p.points) == 23)
assert (len(str(p.points)) < 30000)
def test_Cercle_equation():
c = Cercle_equation()
assertAlmostEqual(c.centre.coordonnees, (0, 0))
assert(c.rayon == 1)
c.a = -2
c.b = 4
c.c = -4
assertAlmostEqual(c.centre.coordonnees, (1, -2))
assert(c.rayon == 3)
assert(c.existe)
c.c = 6
assert(not c.existe)
def test_abreviations():
f = Feuille(titre = u"Feuille de travail n°1")
o = f.objets
assert(o.has_key("Point"))
assert(o.has_key("Variable"))
assert(o.has_key("Texte"))
assert(o.has_key("point"))
assert(o.has_key("variable"))
assert(o.has_key("texte"))
o.txt = ["salut"]
assert(isinstance(o.txt, Texte))
assert(o.txt.texte == "salut")
o.s = [u"Hé, ça marche !"]
assert(isinstance(o.s, Texte))
assert(o.s.texte == u"Hé, ça marche !")
o.A = (1, 2)
o.k = 7
assert(isinstance(o.A, Point))
assert(isinstance(o.k, Variable))
o.h = 'A.x'
o.A.x = 15
assert(o.h == 15)
o.h = "A.x-10"
assert(o.h == 5)
assert(o.h - 3 == 2)
o.h = pi/3
assertAlmostEqual(cos(o.h), 1/2)
o.B = (-1, 3)
o.u = o.A>o.B
assert(isinstance(o.u, Vecteur))
assert(o.u.coordonnees == (o.B.x - o.A.x, o.B.y - o.A.y))
o.C = 2-3j
assert(isinstance(o.C, Point))
assert(o.C.z == 2-3j)
o.C.x = "A.x"
#print 'o.C.x.val:', o.C.x.val, type(o.C.x.val)
assert(isinstance(o.C.x.val, (float, int, long)))
assert(o.C.x == o.A.x)
o.A.coordonnees = -11, 3
assert(o.C.coordonnees[0] == -11)
o.B.x = "A.x + 1"
assert(isinstance(o.B.x.val, (float, int, long)))
assert(o.B.x == o.A.x + 1)
o.A.coordonnees = 30, -5
assert(o.B.coordonnees[0] == 31)
o.A(-3.6, 0.4)
assert(o.C.coordonnees[0] ==-3.6)
# 'o.EFG = Triangle' doit être accepté comme alias de 'o.EFG = Triangle()'
o.EFG = Triangle
assert(isinstance(o.EFG, Triangle))
def test_Cercle_equation():
c = Cercle_equation()
assertAlmostEqual(c.centre.coordonnees, (0, 0))
assert (c.rayon == 1)
c.a = -2
c.b = 4
c.c = -4
assertAlmostEqual(c.centre.coordonnees, (1, -2))
assert (c.rayon == 3)
assert (c.existe)
c.c = 6
assert (not c.existe)
def test_abreviations():
f = Feuille(titre = u"Feuille de travail n°1")
o = f.objets
assert(o.has_key("Point"))
assert(o.has_key("Variable"))
assert(o.has_key("Texte"))
assert(o.has_key("point"))
assert(o.has_key("variable"))
assert(o.has_key("texte"))
o.txt = ["salut"]
assert(isinstance(o.txt, Texte))
assert(o.txt.texte == "salut")
o.s = [u"Hé, ça marche !"]
assert(isinstance(o.s, Texte))
assert(o.s.texte == u"Hé, ça marche !")
o.A = (1, 2)
o.k = 7
assert(isinstance(o.A, Point))
assert(isinstance(o.k, Variable))
o.h = 'A.x'
o.A.x = 15
assert(o.h == 15)
o.h = "A.x-10"
assert(o.h == 5)
assert(o.h - 3 == 2)
o.h = pi/3
assertAlmostEqual(cos(o.h), 1/2)
o.B = (-1, 3)
o.u = o.A>o.B
assert(isinstance(o.u, Vecteur))
assert(o.u.coordonnees == (o.B.x - o.A.x, o.B.y - o.A.y))
o.C = 2-3j
assert(isinstance(o.C, Point))
assert(o.C.z == 2-3j)
o.C.x = "A.x"
#print 'o.C.x.val:', o.C.x.val, type(o.C.x.val)
assert(isinstance(o.C.x.val, (float, int, long)))
assert(o.C.x == o.A.x)
o.A.coordonnees = -11, 3
assert(o.C.coordonnees[0] == -11)
o.B.x = "A.x + 1"
assert(isinstance(o.B.x.val, (float, int, long)))
assert(o.B.x == o.A.x + 1)
o.A.coordonnees = 30, -5
assert(o.B.coordonnees[0] == 31)
o.A(-3.6, 0.4)
assert(o.C.coordonnees[0] ==-3.6)
# 'o.EFG = Triangle' doit être accepté comme alias de 'o.EFG = Triangle()'
o.EFG = Triangle
assert(isinstance(o.EFG, Triangle))
def test_sympy():
x = Symbol('x', real=True)
assert -oo < oo
assert not (-1.5 < -oo)
assert (1 - exp(x)).is_negative is None
assert Matrix([[1, 2], [3, 4]])**Integer(2) == Matrix([[7, 10], [15, 22]])
assertAlmostEqual(E._evalf(50), math.e)
assert solve(1 / x, x) == [] # issue 1694
assert solve(-(1 + x) / (2 + x)**2 + 1 / (2 + x), x) == [] # issue 1694
assert limit(1 + 1 / x, x, 0, dir='-') == -oo
assert limit(1 / x**2, x, 0, dir='-') == oo
assert sympify(u'45') == 45 # issue 2508
def test_sympy():
x = Symbol('x', real = True)
assert -oo < oo
assert not(-1.5 < -oo)
assert (1 - exp(x)).is_negative is None
assert Matrix([[1, 2], [3, 4]])**Integer(2) == Matrix([[7, 10], [15, 22]])
assertAlmostEqual(E._evalf(50), math.e)
assert solve(1/x, x) == [] # issue 1694
assert solve(-(1 + x)/(2 + x)**2 + 1/(2 + x), x) == [] # issue 1694
assert limit(1 + 1/x, x, 0, dir='-') == -oo
assert limit(1/x**2, x, 0, dir='-') == oo
assert sympify(u'45') == 45 # issue 2508
def test_Polygone():
# cas général : polygone à 11 côtés :
A = rand_pt()
B = rand_pt()
C = rand_pt()
D = rand_pt()
E = rand_pt()
F = rand_pt()
G = rand_pt()
H = rand_pt()
I = rand_pt()
J = rand_pt()
K = rand_pt()
p = p0 = Polygone(A, B, C, D, E, F, G, H, I, J, K)
assert(isinstance(p.etiquette, Label_polygone))
assert(p.sommets[0] == A and p.sommets[10] == K)
assert(Milieu(B, C) in p.cotes[1])
assertAlmostEqual(p.centre.coordonnees, Barycentre(A, B, C, D, E, F, G, H, I, J, K).coordonnees)
# cas particuliers :
t = Polygone(A, B, C)
O = t.centre_cercle_circonscrit
assertAlmostEqual(Segment(O, A).longueur, Segment(O, C).longueur)
assert(Droite(t.orthocentre, C).perpendiculaire(Droite(A, B)))
assert(t.__class__ is Triangle)
p = Polygone(A, B, C, D)
assert(p.__class__ is Quadrilatere)
p = Polygone(A, B, C, D, E)
assert(p.__class__ is Pentagone)
p = Polygone(A, B, C, D, E, F)
assert(p.__class__ is Hexagone)
p = Polygone(A, B, C, D, E, F, G)
assert(p.__class__ is Heptagone)
p = Polygone(A, B, C, D, E, F, G, H)
assert(p.__class__ is Octogone)
assert(p._hierarchie < p.sommets[0]._hierarchie < p.sommets[1]._hierarchie < p.sommets[7]._hierarchie < p._hierarchie + 1)
# Test keyword 'points'
p = Polygone(points = (A, B, C, D, E, F, G, H, I, J, K))
assert(p.centre.coordonnees == p0.centre.coordonnees)
assert("points" not in p.style())
# Syntaxe spéciale : Polygone créé sans arguments, ou avec un entier comme argument.
p = Polygone()
p = Polygone(2)
assert(isinstance(p, Segment))
p = Polygone(3)
assert(isinstance(p, Triangle))
p = Polygone(n = 5)
assert(isinstance(p, Pentagone))
p = Polygone(n = 12)
assert(len(p.points) == 12)
p = Polygone(23)
assert(len(p.points) == 23)
assert(len(str(p.points)) < 30000)
def test_Cercle():
A = Point(2.78841, -5.25)
O = Point(27.8841, -0.525)
c = Cercle(O, A)
assert (c.centre is O)
assert (c.point is A)
assertAlmostEqual(c.rayon, 25.5366262763)
# Test du typage dynamique
c = Cercle(Point(1, 1), 1)
assert (Point(1, 2) in c)
c = Cercle(Point(1, 1), Point(0, 2), Point(-1, 1))
assert (Point(0, 0) in c)
assertAlmostEqual(c.centre.coordonnees, (0, 1))
def test_Disque():
A = Point(2.78841, -5.25)
B = Point(27.8841, -0.525)
C = Point(-42.25, 2.351)
c = Cercle_points(A, B, C)
d = Disque(c)
assertAlmostEqual(d.centre.coordonnees, c.centre.coordonnees)
assertAlmostEqual(d.rayon, c.rayon)
assert (A in d)
assert (B in d)
assert (C in d)
assert (d.centre in d)
assert (Point(-500, -500) not in d)
def test_Mediatrice():
A = Point(4.5, 7.3)
B = Point(-4.147, 2.1)
s = Segment(A, B)
d0 = Mediatrice(s)
d1 = Mediatrice(A, B)
I = Milieu(A, B)
assert (I in d0)
assert (I in d1)
a, b, c = s.equation
a0, b0, c0 = d0.equation
assertAlmostEqual(a * a0 + b * b0, 0)
assertAlmostEqual(d0.equation, d1.equation)
def test_Projete_arc_cercle():
O = Point(23.15, -12.75)
A = Point(-12.5, 7.14)
B = Point(7.15, 8.64)
a = Arc_cercle(O, A, B)
M = rand_pt()
P = Projete_arc_cercle(M, a)
assert (P in a)
M.coordonnees = a.centre.coordonnees
assert (not P.existe)
M.coordonnees = -17.826266675199999, 11.760911186
assert (type(P.coordonnees) is tuple)
assertAlmostEqual(A.coordonnees, P.coordonnees)
assertEqual(A, P)
def test_Glisseur_segment():
A = rand_pt()
B = rand_pt()
s = Segment(A, B)
M = Glisseur_segment(s)
assert (M in s)
M.k = 0
assertEqual(M.k, 0)
assertAlmostEqual(M.coordonnees, A.coordonnees)
P = Point(*M.coordonnees)
M.k = 1
assertEqual(M.k, 1)
assertAlmostEqual(M.coordonnees, B.coordonnees)
M.k = 2
assertEqual(M.k, 1) # 0<=k<=1 pour un segment
assert (M in s)
M.k = -1
assertEqual(M.k, 0) # 0<=k<=1 pour un segment
assert (M in s)
M.k = 1
Q = Point(*M.coordonnees)
assertAlmostEqual(Droite(P, Q).equation_reduite, s.equation_reduite)
M.k = 1.7
M(*M.coordonnees)
assertAlmostEqual(M.k, 1)
def test_operations():
for i in xrange(10):
a = randint(50) - randint(50)
b = randint(50) - randint(50)
if i >= 5:
a += random()
b += random()
u = Variable(a)
v = Variable(b)
# Test opérations :
if i < 5:
assertEqual(u + v, a + b)
assertEqual(u - v, a - b)
assertEqual(u * v, a * b)
if a != 0:
assertEqual(u**v, a**b)
if b != 0:
assertEqual(u / v, a / b)
assertEqual(u // v, a // b)
assertEqual(u % v, a % b)
else:
assertAlmostEqual(u + v, a + b)
assertAlmostEqual(u - v, a - b)
assertAlmostEqual(u * v, a * b)
if a != 0:
assertAlmostEqual(abs(u)**v, abs(a)**b)
# Test assignations :
u += v
a += b
assertEqual(u, a)
u *= v
a *= b
assertEqual(u, a)
def test_Segment():
A = Point(4.5, 7.3)
B = Point(4, 2.1)
s = Segment(A, B)
assert (isinstance(s.etiquette, Label_segment))
assertAlmostEqual(s.longueur, sqrt((B.x - A.x)**2 + (B.y - A.y)**2))
I = Milieu(s.point1, s.point2)
assertEqual(I.coordonnees, ((A.x + B.x) / 2, (A.y + B.y) / 2))
M = Barycentre((A, 1), (B, -2))
N = Barycentre((A, -2), (B, 1))
assert (I in s)
assert (M not in s)
assert (N not in s)
assert (s.style("legende") == RIEN)
def test_Polygone_regulier():
O = rand_pt()
M = rand_pt()
p = Polygone_regulier(O, M, 15)
assert(len(p.cotes) == 15)
assert(p.centre in Mediatrice(O, M))
for i in xrange(15):
assertAlmostEqual(Segment(p.sommets[i%15], p.sommets[(i+1)%15]).longueur, Segment(p.sommets[(i+2)%15], p.sommets[(i+3)%15]).longueur)
p = Polygone_regulier(O, M, 3)
assert(isinstance(p, Triangle))
p = Polygone_regulier(O, M, 4)
assert(isinstance(p, Quadrilatere))
# Test de régression :
# la taille de str(p.points) croissait exponentiellement.
assert(len(str(p.points)) < 30000)
def test_Cercle_rayon():
A = Point(-2.586, 7.541)
c_1 = Cercle_rayon(A, -1)
c0 = Cercle_rayon(A, 0)
c2 = Cercle_rayon(A, 2)
assert (isinstance(c_1.etiquette, Label_cercle))
assert (not c_1.existe)
assert (c0.existe)
assert (c2.existe)
assertAlmostEqual(A.coordonnees, c0.centre.coordonnees)
assert (A not in c_1)
assert (A in c0)
assert (A not in c2)
assertEqual(c_1.rayon, -1)
assertEqual(c0.rayon, 0)
assertEqual(c2.rayon, 2)
k = random()
B = Point(A.x + 2 * sin(k), A.y + 2 * cos(k))
assert (B in c2)
def test_Triangle_isocele():
A = rand_pt()
B = rand_pt()
tri = Triangle_isocele(A, B, 2*pi/13)
C = tri.point3
a = Angle(B, A, C)
assertAlmostEqual(a.radian, 2*pi/13)
assertAlmostEqual(Segment(A, B).longueur, Segment(A, C).longueur)
t1 = Triangle_isocele((0, 0), (1, 1), u'90°')
assertAlmostEqual(t1.point3.xy, (-1, 1))
t2 = Triangle_isocele((0, 0), (2, 0), pi/3)
assertAlmostEqual(t2.point3.xy, (2*cos(pi/3), 2*sin(pi/3)))
def test_contexte_degre():
with contexte(unite_angle='d'):
a = Angle_libre('pi rad')
assertAlmostEqual(a.deg, 180)
a = Angle_libre('100 grad')
assertAlmostEqual(a.deg, 90)
b = Angle_libre(30)
assertAlmostEqual(b.rad, math.pi / 6)
# En interne, tout doit être stocké en radians
assert float(b.val) == float(b.rad)
# On doit avoir eval(repr(b)) == b
assertAlmostEqual(eval(repr(b)).deg, 30)
def test_Polygone_regulier_centre():
O = rand_pt()
M = rand_pt()
p = Polygone_regulier_centre(O, M, 15)
assert(len(p.cotes) == 15)
assert(p.centre is O)
for Mi in p.sommets:
assertAlmostEqual(Segment(O, Mi).longueur, Segment(O, M).longueur)
for i in xrange(10):
coeffs = tuple(random() for i in xrange(15))
G = Barycentre(*zip(p.sommets, coeffs))
assert(G in p)
G.points_ponderes[randint(11)].coefficient = -5
assert(G not in p)
# cas particuliers :
p = Polygone_regulier_centre(O, M, 3)
assert(isinstance(p, Triangle))
p = Polygone_regulier_centre(O, M, 4)
assert(isinstance(p, Quadrilatere))
assert(len(str(p.points)) < 30000)
def test_Demicercle():
A = Point(-1.2561, 45.236)
B = Point(251.2561, 41.256)
c = Demicercle(A, B)
assertAlmostEqual(Milieu(A, B).coordonnees, c.centre.coordonnees)
assertAlmostEqual(c.diametre, Segment(A, B).longueur)
assertAlmostEqual(c.rayon, Segment(A, B).longueur / 2)
def test_Cercle_diametre():
A = Point(2.78841, -5.25)
B = Point(27.8841, -0.525)
c = Cercle_diametre(A, B)
c1 = Cercle(A, B)
assertAlmostEqual(c.diametre, c1.rayon)
assertAlmostEqual(c.diametre, Segment(A, B).longueur)
assertAlmostEqual(c.centre.coordonnees, Milieu(A, B).coordonnees)
def test_Projete_demidroite():
d = Demidroite(rand_pt(), rand_pt())
M = rand_pt()
assert (Projete_demidroite(M, d) in d)
A = Point(0, 1)
B = Point(2, 1)
s = Demidroite(A, B)
M = Point(1, 7.15)
P = Projete_demidroite(M, s)
assertAlmostEqual(Milieu(A, B).coordonnees, P.coordonnees)
M.x = .5
assertAlmostEqual(Barycentre((A, 3), (B, 1)).coordonnees, P.coordonnees)
M.x = -1
assertAlmostEqual(A.coordonnees, P.coordonnees)
M.x = 3
assertAlmostEqual(Barycentre((A, -1), (B, 3)).coordonnees, P.coordonnees)
def test_Projete_segment():
s = Segment(rand_pt(), rand_pt())
M = rand_pt()
assert (Projete_segment(M, s) in s)
A = Point(0, 1)
B = Point(2, 1)
s = Segment(A, B)
M = Point(1, 7.15)
P = Projete_segment(M, s)
assertAlmostEqual(Milieu(A, B).coordonnees, P.coordonnees)
M.x = .5
assertAlmostEqual(Barycentre((A, 3), (B, 1)).coordonnees, P.coordonnees)
M.x = -1
assertAlmostEqual(A.coordonnees, P.coordonnees)
M.x = 3
assertAlmostEqual(B.coordonnees, P.coordonnees)
def test_Rotation():
A = Point(1.523, 45.35211)
r = Rotation(A, pi/4)
M = Point(1.4452, -1.2545)
assertAlmostEqual(r(M).coordonnees, (34.423837071540447, 12.341247113306926))
assertAlmostEqual(r(A).coordonnees, A.coordonnees)
d = Droite(A, M)
d1 = Droite(A, r(M))
assertAlmostEqual(r(d).equation_reduite, d1.equation_reduite)
assert(r(A) is A)
def test_Centre_gravite():
A = rand_pt()
B = rand_pt()
C = rand_pt()
I = Milieu(B, C)
J = Milieu(A, C)
K = Milieu(A, B)
G = Centre_gravite(Triangle(A, B, C))
assertAlmostEqual(Segment(A, G).longueur, 2 * Segment(I, G).longueur)
assertAlmostEqual(Segment(B, G).longueur, 2 * Segment(J, G).longueur)
assertAlmostEqual(Segment(C, G).longueur, 2 * Segment(K, G).longueur)
def test_Glisseur_droite():
A = rand_pt()
B = rand_pt()
d = Droite(A, B)
M = Glisseur_droite(d)
assert (M in d)
M.k = 0
assertEqual(M.k, 0)
assertAlmostEqual(M.coordonnees, A.coordonnees)
P = Point(*M.coordonnees)
M.k = 1
assertEqual(M.k, 1)
assertAlmostEqual(M.coordonnees, B.coordonnees)
M.k = 2
assertEqual(M.k, 2)
M.k = -1
assertEqual(M.k, -1)
Q = Point(*M.coordonnees)
assertAlmostEqual(Droite(P, Q).equation_reduite, d.equation_reduite)
M.k = 1.7
M(*M.coordonnees)
assertAlmostEqual(M.k, 1.7)
def test_Carre():
O = rand_pt()
M = rand_pt()
p = Carre(O, M)
A, B, C, D = p.sommets
assert(p.centre == Milieu(A, C) == Milieu(B, D))
assert(A == O and B == M)
assert(len(p.cotes) == 4)
assertAlmostEqual(p.aire, p.cotes[0].longueur**2)
# Test redéfinition d'un sommet
c = Carre((3, 2), (7, 2))
M = Point(0, 2)
c.point1 = M
assert(c.point1 is M)
assert(c.regulier)
assertAlmostEqual(c.aire, 49)
assertAlmostEqual(c.point4.coordonnees, (0, 9))
def test_Point_sympy():
A = Point('1/2', '2/3')
assertEqual(A.x, symp('1/2'))
assertAlmostEqual(A.coordonnees, (1 / 2, 2 / 3))
def test_Centre():
c = rand_cercle()
O = Centre(c)
M = Glisseur_cercle(c)
assertAlmostEqual(Segment(O, M).longueur, c.rayon)
