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il dérive tel un radeau

from math import *

#----------------------
#Polynome
#----------------------
def r_coefs(expression,debug=False):
    coefs = []
    termes = []

    car = ["0","1","2","3","4","5","6","7","8","9","-","+","(",")","*","^","/","x","X",""," "]
    etat,caractere=check(expression,car)

    if etat == False:
        print("caractère invalide :",caractere)
        print("Les caractères autorisés sont :",car)
        return None


    poly = nettoyage(expression)

    if debug :
        print("---Polynome---")
        print("")
        print("Le polynome est :")
        print(poly)

    #recherche du plus grand exposant
    exp_max = 0
    for i,elt in enumerate(poly):
        if elt == "x" and poly[i+1] != "+" and poly[i+1] != "-":
            if exp_max < int(poly[i+1]):
                exp_max = int(poly[i+1])
    if debug :
        print("Polynome de degrès",exp_max)

    exposants = list(range(exp_max+1))
    del exposants[0]
    exposants.reverse() #liste des exposants pour ordonner la liste des coefs

    #recherche des coeeficients
    for i,elt in enumerate(poly):
        if elt =="-" or elt =="+":
            nb = elt
            for j in poly[i+1:]:
                if j == "+" or j=="-":
                    break  #j'aime pas les breaks mais la flm
                else :
                    nb += j


            termes.append(nb)

    #Mis en ordre des coefs
    for i in exposants:
        n = "x{}".format(i)

        if n in poly:
            for j in termes:
                if n in j :
                    coefs.append(j[:-2])
        else:
            coefs.append(0)

    if debug :
        print("les termes de ce polynome sont :", termes)
        print("Et ses coefficients (utiles) sont :",coefs)

    
    return coefs


#----------------------
#Utilitaires
#----------------------


def nettoyage(arg):
    '''
    :param arg: Chaine à "nétoyer" (normaliser)
    :return: revoie la chaines libile par l'analyseur de syntaxe
    '''
    arg = arg.replace(" ","")
    arg = arg.replace("^","")
    arg = arg.replace("*","")
    arg = arg.replace("**","")
    arg = arg.lower()

    if arg[0] != '-':
        arg ='+' + arg
    arg="".join(arg)
    sortie=""

    #débug temporaire
    if arg[-1] =="x":
        arg += "+0"

    #ajout du 1x
    for i,j in enumerate(arg):
        if (j == "x" and ( arg[i-1] == "+" or arg[i-1] == "-")):
            sortie += "1"+j+"1"
        elif j=="x" and ( arg[i+1] == "+" or arg[i+1] == "-"):
            sortie += j+"1"
        else :
            sortie += j

    sortie = sortie.replace(" ","")
    return sortie


def check(expression,liste):
    '''
    :param expression: Expression à vérfier
    :param liste: Liste des caractères valides
    :return: Vrai si l'expression est bonne et Faux si un caractère est invalide
    '''
    for i in expression:
        if i not in liste:
            return (False,i)

    return True,None

print(r_coefs("10x5-4x"))