import math

# REVISIONS ULTIMATE TOMIC
# Lignes < 32 car. Sans accent.
# PAS D APOSTROPHE.

def ed1_methode():
  print("--- ED ORDRE 1 ---")
  print("Forme: y1 + a(x)y = b(x)")
  print("")
  print("SUR TA COPIE:")
  print("1. HOMOGENE (y1 + ay = 0)")
  print("   Prim A(x) de a(x)...")
  print("   yh(x) = K * exp(-A(x))")
  print("")
  print("2. PARTICULIERE (yp)")
  print("   Methode Var Constante:")
  print("   Poser yp = K(x) * exp(-A)")
  print("   Deriver et injecter ds E")
  print("   Trouver K1(x) puis K(x)")
  print("")
  print("3. SOL GENERALE")
  print("   y(x) = yh(x) + yp(x)")
  print("   y(x) = K*exp(...) + ...")
  print("")
  print("4. SOL UNIQUE (C.I.)")
  print("   Avec y(x0) = y0")
  print("   Remplacer x par x0")
  print("   Trouver K.")
  input("EXE pour Menu...")

def ed2_ultimate():
  print("--- ED ORDRE 2 COMPLET ---")
  print("ay2 + by1 + cy = f(x)")
  try:
    a = float(input("a? "))
    b = float(input("b? "))
    c = float(input("c? "))
  except: return

  # 1. HOMOGENE
  delta = b*b - 4*a*c
  print("\n--- ETAPE 1: HOMOGENE ---")
  print("Eq carac: "+str(a)+"r^2+"+str(b)+"r+"+str(c)+"=0")
  print("Delta = " + str(delta))
  
  # Stockage des params pour C.I.
  mode = 0 # 0:Reel, 1:Double, 2:Cplx
  p1, p2 = 0, 0
  
  if delta > 0:
    r1 = (-b-math.sqrt(delta))/(2*a)
    r2 = (-b+math.sqrt(delta))/(2*a)
    mode = 0; p1=r1; p2=r2
    print("2 Racines reelles:")
    print("r1="+str(round(r1,2))+" r2="+str(round(r2,2)))
    print("yh(x) = A*exp(r1*x) +")
    print("        B*exp(r2*x)")
  elif delta == 0:
    r0 = -b/(2*a)
    mode = 1; p1=r0
    print("1 Racine double:")
    print("r0="+str(round(r0,2)))
    print("yh(x) = (Ax + B)*exp(r0*x)")
  else:
    alpha = -b/(2*a)
    beta = math.sqrt(-delta)/(2*a)
    mode = 2; p1=alpha; p2=beta
    print("Racines complexes:")
    print("r = "+str(round(alpha,2))+" +/- i"+str(round(beta,2)))
    print("yh(x) = exp(alph*x) * ...")
    print("(A*cos(bet*x) + B*sin(bet*x))")
  
  input("EXE: Sol Particuliere...")

  # 2. PARTICULIERE
  print("\n--- ETAPE 2: PARTICULIERE ---")
  print("Type de f(x)?")
  print("0:Rien 1:Cst 2:Poly 3:Sin")
  ch = input("Choix? ")
  
  if ch == "1":
    print("f(x) = Constante K")
    print("On cherche yp(x) = C (Cst)")
    print("Calcul: yp = K / c")
  elif ch == "2":
    print("f(x) = Polynome degre n")
    print("On cherche yp meme degre n")
    print("Ex: ax2+bx+c -> Ax2+Bx+C")
    print("Identifier coeff...")
  elif ch == "3":
    print("f(x) = K*cos(w*x)")
    print("On cherche yp forme:")
    print("C1*cos(wx) + C2*sin(wx)")
  else:
    print("Pas de 2nd membre (yp=0)")
  
  print("\n--- ETAPE 3: GENERALE ---")
  print("SOLUTION GENERALE S.G.:")
  print("y(x) = yh(x) + yp(x)")
  input("EXE: Cond. Initiales...")

  # 3. CONDITIONS INITIALES
  print("\n--- ETAPE 4: SOL UNIQUE ---")
  print("Systeme avec C.I.:")
  try:
    y0 = float(input("y(0) = ? "))
    v0 = float(input("y1(0) (derivee) = ? "))
  except: return

  print("Resolution systeme A,B...")
  A_val, B_val = 0, 0
  
  # RESOLUTION SYSTEME
  if mode == 0: # Reelles r1, r2
    # A + B = y0
    # A*r1 + B*r2 = v0
    # B = (v0 - r1*y0)/(r2-r1)
    if (p2-p1) != 0:
      B_val = (v0 - p1*y0)/(p2 - p1)
      A_val = y0 - B_val
      print("A = "+str(round(A_val,2)))
      print("B = "+str(round(B_val,2)))
      print("SOL FINALE:")
      print(str(round(A_val,2))+"e^("+str(round(p1,2))+"x)")
      print("+ "+str(round(B_val,2))+"e^("+str(round(p2,2))+"x)")
      
  elif mode == 1: # Double r0
    # y(0) = B = y0
    # y1(0) = A + B*r0 = v0 -> A = v0 - y0*r0
    B_val = y0
    A_val = v0 - y0*p1
    print("A = "+str(round(A_val,2)))
    print("B = "+str(round(B_val,2)))
    print("SOL FINALE:")
    print("("+str(round(A_val,2))+"x + "+str(round(B_val,2))+")")
    print("* exp("+str(round(p1,2))+"x)")

  elif mode == 2: # Complexe alpha, beta
    # y(0) = A = y0
    # y1(0) = A*alpha + B*beta = v0
    # B = (v0 - A*alpha)/beta
    A_val = y0
    if p2 != 0:
      B_val = (v0 - A_val*p1)/p2
      print("A = "+str(round(A_val,2)))
      print("B = "+str(round(B_val,2)))
      print("SOL FINALE:")
      print("exp("+str(round(p1,2))+"x) * ...")
      print("("+str(round(A_val,2))+"cos("+str(round(p2,2))+"x)")
      print("+"+str(round(B_val,2))+"sin("+str(round(p2,2))+"x))")
  
  input("EXE pour Menu...")

def osc_physique():
  print("--- OSCILLATEURS ---")
  print("x2 + w0^2 x = f(t)")
  print("C est une ED Ordre 2 !")
  print("Avec a=1, b=0, c=w0^2")
  print("")
  print("1. SOL HOMOGENE (Regime Libre)")
  print("Delta toujours negatif (-4w0^2)")
  print("xh(t) = A*cos(w0t) + B*sin(w0t)")
  print("")
  print("2. SOL PARTICULIERE (Force)")
  print("- Si f(t)=F (Cst): xp = F/w0^2")
  print("- Si f(t)=cos(wt) (Sinus):")
  print("  Si w != w0: xp = C*cos(wt)")
  print("  Si w = w0 (RESONANCE):")
  print("  xp(t) = C * t * sin(wt)")
  print("")
  print("3. SOL GENERALE")
  print("x(t) = xh(t) + xp(t)")
  print("Utiliser cond init x(0), v(0)")
  print("pour trouver A et B.")
  print("ASTUCE: Utilise le Menu 2")
  print("avec a=1, b=0, c=w0^2")
  input("EXE pour Menu...")

def integr():
  print("--- INTEGRALES ---")
  print("1. METHODE GENERALE")
  print("- Faire un Dessin du domaine")
  print("- Ecrire bornes (ex: 0 a R)")
  print("- Integrale dedans vers dehors")
  print("")
  print("2. COORD POLAIRES (2D)")
  print("x=r*cos(th)  y=r*sin(th)")
  print("dx dy deviens r dr dth")
  print("!! NE PAS OUBLIER LE r !!")
  print("")
  print("3. COORD CYLINDRIQUES (3D)")
  print("Ajout de z. dV = r dr dth dz")
  input("EXE pour Menu...")

def menu():
  while True:
    print("")
    print("=== MENU ULTIMATE ===")
    print("1. Methodo ED Ordre 1")
    print("2. SOLVEUR ED Ordre 2")
    print("3. Oscillateurs (Phys)")
    print("4. Integrales")
    print("5. Quitter")
    c = input("Choix? ")
    if c=="1": ed1_methode()
    elif c=="2": ed2_ultimate()
    elif c=="3": osc_physique()
    elif c=="4": integr()
    elif c=="5": break

menu()