Example #1
0
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)))
Example #2
0
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)
Example #3
0
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)
Example #4
0
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])
Example #5
0
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'$\mathrm{\Gamma}\left(x\right)$')
Example #6
0
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)
Example #7
0
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)
Example #8
0
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)
Example #9
0
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))
Example #10
0
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)
Example #11
0
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)
Example #12
0
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)
Example #13
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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))
Example #14
0
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))
Example #15
0
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)
Example #16
0
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)
Example #17
0
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)
Example #18
0
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'
Example #19
0
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))
Example #20
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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))
Example #21
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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)
Example #22
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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)
Example #23
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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)
Example #24
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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))
Example #25
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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))
Example #26
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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)
Example #27
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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)
Example #28
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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))
Example #29
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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)
Example #30
0
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)
Example #31
0
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)
Example #32
0
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))
Example #33
0
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)
Example #34
0
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))
Example #35
0
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
Example #36
0
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
Example #37
0
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)
Example #38
0
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))
Example #39
0
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)
Example #40
0
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)
Example #41
0
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)
Example #42
0
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)
Example #43
0
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)
Example #44
0
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)
Example #45
0
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)
Example #46
0
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)
Example #47
0
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)))
Example #48
0
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)
Example #49
0
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)
Example #50
0
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)
Example #51
0
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)
Example #52
0
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)
Example #53
0
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)
Example #54
0
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)
Example #55
0
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)
Example #56
0
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)
Example #57
0
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))
Example #58
0
def test_Point_sympy():
    A = Point('1/2', '2/3')
    assertEqual(A.x, symp('1/2'))
    assertAlmostEqual(A.coordonnees, (1 / 2, 2 / 3))
Example #59
0
def test_Centre():
    c = rand_cercle()
    O = Centre(c)
    M = Glisseur_cercle(c)
    assertAlmostEqual(Segment(O, M).longueur, c.rayon)