import math
import cmath

# ====================================================
# OUTILS D'AFFICHAGE OPTIMISES (LARGEUR 52 CAR)
# ====================================================
def sep():
    print("-" * 52)

def double_sep():
    print("=" * 52)

def titre(texte):
    double_sep()
    # Centrage manuel pour eviter les erreurs de calcul
    l = len(texte)
    espace = int((52 - l) / 2)
    print(" " * espace + texte.upper())
    double_sep()

def pause():
    sep()
    input("  >>> Appuie sur EXE pour continuer...")

# ====================================================
# 1. PHYSIQUE : OSCILLATEUR
# ====================================================
def menu_osc():
    titre("OSCILLATEUR HARMONIQUE")
    print("Equation : m.x'' + c.x' + k.x = 0")
    sep()
    
    try:
        m = float(input("Masse (m) : "))
        c = float(input("Amortissement (c) : "))
        k = float(input("Raideur (k) : "))
    except:
        print("ERREUR : Nombres requis !")
        return

    if m <= 0:
        print("ERREUR : m doit etre > 0")
        return

    w0 = math.sqrt(k / m)
    zeta = c / (2 * math.sqrt(k * m))

    titre("RESULTATS")
    # Utilisation de virgules pour eviter les erreurs de syntaxe
    print("Pulsation w0 :", round(w0, 5), "rad/s")
    print("Frequence f0 :", round(w0/(2*math.pi), 5), "Hz")
    print("Amortissement:", round(zeta, 5))
    sep()

    print("REGIME :")
    if zeta == 0:
        print(">> NON AMORTI")
        print("   Oscillation perpetuelle.")
    elif 0 < zeta < 1:
        print(">> SOUS-AMORTI")
        print("   Oscillations qui diminuent.")
        wd = w0 * math.sqrt(1 - zeta**2)
        print("   Pseudo-puls wd :", round(wd, 5))
    elif zeta == 1:
        print(">> CRITIQUE")
        print("   Retour equilibre ultra-rapide.")
    else:
        print(">> SUR-AMORTI")
        print("   Retour lent, pas d'oscillation.")
    
    pause()

# ====================================================
# 2. MATHS : EQUATION 2ND DEGRE
# ====================================================
def menu_eq():
    titre("EQUATION AX^2 + BX + C = 0")
    try:
        a = float(input("a : "))
        b = float(input("b : "))
        c = float(input("c : "))
    except:
        return

    delta = b**2 - 4*a*c
    print("Delta =", delta)
    sep()

    s1 = (-b - cmath.sqrt(delta)) / (2*a)
    s2 = (-b + cmath.sqrt(delta)) / (2*a)

    print("SOLUTIONS :")
    
    if delta > 0:
        print("REELLES :")
        print(" x1 =", round(s1.real, 5))
        print(" x2 =", round(s2.real, 5))
    elif delta == 0:
        print("DOUBLE :")
        print(" x0 =", round(s1.real, 5))
    else:
        print("COMPLEXES :")
        # Affichage manuel sans f-string
        print(" z1 =", round(s1.real,4), "+", round(s1.imag,4), "i")
        print(" z2 =", round(s2.real,4), "+", round(s2.imag,4), "i")
        
        sep()
        print("POLAIRE :")
        r, phi = cmath.polar(s1)
        print(" Mod (r) :", round(r, 5))
        print(" Arg (deg):", round(math.degrees(phi), 2))
    
    pause()

# ====================================================
# 3. GEOMETRIE : AIRES ET VOLUMES
# ====================================================
def menu_geo():
    titre("GEOMETRIE")
    print(" 1. Sphere")
    print(" 2. Cylindre")
    print(" 3. Cone")
    print(" 4. Tore")
    print(" 5. Ellipse (2D)")
    sep()
    
    try:
        ch = input("Choix : ")
    except:
        return
    
    res_v = 0
    res_s = 0
    nom = ""

    if ch == '1':
        nom = "SPHERE"
        r = float(input("Rayon r : "))
        res_v = (4/3) * math.pi * r**3
        res_s = 4 * math.pi * r**2
        
    elif ch == '2':
        nom = "CYLINDRE"
        r = float(input("Rayon r : "))
        h = float(input("Hauteur h : "))
        res_v = math.pi * r**2 * h
        res_s = 2*math.pi*r*h + 2*math.pi*r**2
        
    elif ch == '3':
        nom = "CONE"
        r = float(input("Rayon r : "))
        h = float(input("Hauteur h : "))
        res_v = (1/3) * math.pi * r**2 * h
        s = math.sqrt(r**2 + h**2)
        res_s = math.pi * r * (r + s)
        
    elif ch == '4':
        nom = "TORE"
        R = float(input("Grand Rayon R : "))
        r = float(input("Petit Rayon r : "))
        res_v = (math.pi * r**2) * (2 * math.pi * R)
        res_s = (2 * math.pi * r) * (2 * math.pi * R)
        
    elif ch == '5':
        nom = "ELLIPSE"
        a = float(input("Demi-axe a : "))
        b = float(input("Demi-axe b : "))
        res_v = 0
        res_s = math.pi * a * b

    print(" ")
    # CORRECTION LIGNE 199 : Suppression de la f-string
    print("--- RESULTATS :", nom, "---")
    
    if ch == '5':
        print(" Aire   =", round(res_s, 5))
    else:
        print(" Volume =", round(res_v, 5))
        print(" Surface=", round(res_s, 5))
        
    pause()

# ====================================================
# 4. BIBLE
# ====================================================
def bible():
    while True:
        titre("BIBLE PRIMITIVES u(x)")
        print("RAPPEL: (f(u))' = u' * f'(u)")
        print("        INT(u' * f(u)) = F(u)")
        double_sep()
        print(" 1. Puissances")
        print(" 2. Log & Expo")
        print(" 3. Trigo")
        print(" 4. Trigo Inverse")
        print(" 5. Jacobien")
        print(" 0. RETOUR")
        sep()
        
        c = input("Choix : ")
        if c == '0': break
        
        sep()
        if c == '1':
            print(">> PUISSANCE")
            print(" f: u' * u^n")
            print(" F: u^(n+1)/(n+1)")
            print("\n>> INVERSE")
            print(" f: u'/u^2  -> F: -1/u")
            print("\n>> RACINE")
            print(" f: u'/sqrt(u) -> F: 2sqrt(u)")

        elif c == '2':
            print(">> LOGARITHME (Important)")
            print(" f: u'/u")
            print(" F: ln(|u|)")
            print("\n>> EXPO")
            print(" f: u'*e^u -> F: e^u")
            print(" f: u'*a^u -> F: a^u/ln(a)")

        elif c == '3':
            print(">> TRIGO")
            print(" u'*cos(u) -> sin(u)")
            print(" u'*sin(u) -> -cos(u)")
            print(" u'/cos^2(u) -> tan(u)")
            print("\n>> INT(TAN)")
            print(" -ln(|cos(u)|)")

        elif c == '4':
            print(">> ARCTAN (Phase)")
            print(" f: u'/(1+u^2)")
            print(" F: arctan(u)")
            print("\n>> ARCSIN")
            print(" f: u'/sqrt(1-u^2)")
            print(" F: arcsin(u)")

        elif c == '5':
            print(">> JACOBIEN (dV)")
            print(" POLAIRE: r dr dth")
            print(" CYL:     r dr dth dz")
            print(" SPHERE:  rho^2 sin(phi) ...")
            
        pause()

# ====================================================
# MAIN
# ====================================================
def main():
    while True:
        print("\n" * 3)
        double_sep()
        print("   INGENIEUR KIT - NUMWORKS")
        double_sep()
        print(" 1. Oscillateur")
        print(" 2. Equation Delta")
        print(" 3. Geometrie")
        print(" 4. Bible Formules")
        print(" 5. Quitter")
        sep()
        
        try:
            choix = input("Choix : ")
            if choix == '1': menu_osc()
            elif choix == '2': menu_eq()
            elif choix == '3': menu_geo()
            elif choix == '4': bible()
            elif choix == '5': break
        except:
            pass

main()