/usr/share/pyshared/pyromaths/classes/Polynome.py is in pyromaths 11.05.1b2-0ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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if __name__=="__main__":
import sys,os
sys.path.append(os.path.join('..'))
from .Racine import simplifie_racine, RacineDegre2, sqrt
from .Fractions import Fractions
import re
from ..outils.Affichage import pTeX, TeX, radicalTeX, fTeX, Fractions, tTeX
class Polynome:
'''Classe de polynôme pour le lycee'''
def __init__(self, liste_coeff, var = "x"):
self.var = var # Lettre pour la var
liste_reduite={}
if isinstance(liste_coeff,str):
liste_coeff=str_Polynome(liste_coeff,var)
elif isinstance(liste_coeff,list):
liste_coeff=dict((i,liste_coeff[i])for i in range(len(liste_coeff)))
elif isinstance(liste_coeff,int) or isinstance(liste_coeff,Fractions.Fractions) or isinstance(liste_coeff,float):
liste_coeff={0:liste_coeff}
for i in liste_coeff.iterkeys():
if liste_coeff[i] != 0:
liste_reduite[i]=liste_coeff[i]+Fractions.Fractions(0, 1)
if liste_reduite=={} or liste_coeff==[]:
liste_reduite={0:0}
self.dictio = liste_reduite
self.puiss = liste_reduite.keys()
self.puiss.sort(reverse=True)
self.deg=self.degre()
self.degre_max=max(0,self.deg)
def __len__(self):
return max(0,self.deg)+1
def degre(self):
degre=float("-inf")
for i in self.dictio.iterkeys():
if i > degre and self.dictio[i] !=0:
degre=i
return degre
def __getitem__(self,i):
'''P[i] renvoie le coefficient de rang i'''
return self.dictio.get(i,0)
def __str__(self):
'''renvoie une str pour un affichage python'''
return self.TeX(var=self.var)
def TeX(self,var='',display=True,parenthese=False):
'''renvoie une chaine de caractere imprimant les fractions dans TeX'''
if var=='':
var=self.var
exposants = []+self.puiss
premier = 1
string=''
if display:
fractex="\\dfrac"
else:
fractex="\\frac"
for exposant in exposants :
if premier:
if self[exposant]==1 and exposant!=0:
string=''
elif self[exposant]==-1 and exposant!=0:
string='-'
else:
string=TeX(self[exposant])
premier=0
elif self[exposant] != 1:
if self.dictio[exposant] == -1:
string += '-'
else:
string+=tTeX(self[exposant])
else:
string+="+"
if exposant == 1:
terme = var
elif (exposant == 0) and ((self[exposant] == 1) or (self[exposant] == -1)):
terme = '1'
elif exposant == 0:
terme = ''
else:
terme = var + u'^' + str(exposant)
string+=terme
if parenthese and (len(self.puiss)>1 or self[self.degre_max]<0):
return "\\left("+string+"\\right)"
else:
return string
def __add__(self, other):
if isinstance(other,int) or isinstance(other,float) or isinstance(other,Fractions.Fractions) or isinstance(other,RacineDegre2):
return self+Polynome({0:other},var=self.var)
result={0:0}
liste1=self.puiss
liste2=other.puiss
for i in liste1 :
s=self.dictio.get(i)+other.dictio.get(i,0)
if s!=0:
result[i]=s
for i in liste2:
if i not in liste1:
result[i]=other.dictio[i]
return Polynome(result,var=self.var)
def __mul__(self, other):
if isinstance(other,Polynome):
result=Polynome({0:0},var=self.var)
for i in self.dictio.iterkeys():
for j in other.dictio.iterkeys():
exposant=i+j
coefficient=self.dictio[i]*other.dictio[j]
result = result + Polynome({exposant:coefficient},var=self.var)
return result
else:
return self*Polynome(other)
def __ne__(self,other):
return not(self == other)
def __eq__(self,other):
if (isinstance(other,int) or isinstance(other,Fractions.Fractions) or isinstance(other,float)):
if self.degre_max==0 and self[0]==other:
return True
else:
return False
elif self.var==other.var and self.dictio==other.dictio:
return True
else:
return False
def __pow__(self, other):
if isinstance(other,int) and other>=0:
result=Polynome({0:1},self.var)
for i in xrange(other):
result*=self
return result
def __radd__(self, other):
if isinstance(other,int) or isinstance(other,float) or isinstance(other,Fractions.Fractions):
return self+Polynome({0:other},var=self.var)
return self + other
def __sub__(self, other):
return self + (-other)
def __rsub__(self, other):
return -(self - other)
def __neg__(self):
return self * Polynome({0:-1},var=self.var)
def __rmul__(self,nombre):
return self*Polynome({0:nombre})
def __div__(self,other):
if isinstance(other,int):
return Fractions.Fractions(1,other)*self
elif isinstance(other,Fractions.Fractions) or isinstance(other,float)or isinstance(other,RacineDegre2):
return (1/other)*self
else:
quotient=Polynome({},var=self.var)
reste=self
diviseur_degre=other.deg
while diviseur_degre <= reste.deg:
ajout_quotient_deg=reste.deg-diviseur_degre
facteur= reste.dictio[reste.deg]/other.dictio[other.deg]
ajout_quotient=Polynome({ajout_quotient_deg:facteur},var=self.var)
quotient=quotient+ajout_quotient
soustrait_reste=ajout_quotient*other
reste=reste-soustrait_reste
return quotient,reste
def simplifie(self):
result={}
for i in self.puiss:
if isinstance(self[i],(Fractions.Fractions,RacineDegre2)):
result[i]=self[i].simplifie()
else:
result[i]=self[i]
return Polynome(result)
def __call__(self,x,):
'''renvoie la Fraction ou l'int P(x)'''
if x==float("inf") or x==float("-inf"):
if self.degre_max==0:
return self[0]
elif self.deg%2==0:
return self[self.deg]*float("inf")
else:
return self[self.deg]*x
elif isinstance(x,str):
return self.TeX(var=x)
else:
result=0
for i in self.dictio.iterkeys():
result= result+self[i]*x**i
if isinstance(result,Fractions.Fractions):
result=result.simplifie()
if result.denominateur==1:
return result.numerateur
else:
return result
def racine_evidente(self,liste=[-2,-1,0,1,2]):
listerac=[]
for i in liste:
if self(i)==0:
listerac=listerac+[i]
return listerac
def factorise(self,TeX=False,racines=[0,-1,1,2,-2]):
facteurs=[Polynome({0:self.dictio[self.deg]},var=self.var)]
developpe,reste=self/facteurs[0]
for r in racines:
while developpe(r)==0:
rac=-r
developpe,reste = developpe/Polynome({1:1,0:rac},var=self.var)
facteurs=facteurs+[Polynome({1:1,0:rac})]
if TeX:
stringTeX=""
if not(facteurs[0]==Polynome({0:1},var=self.var)):
stringTeX+=facteurs[0].TeX()
for i in facteurs[1:]:
if i[0]!=0:
stringTeX+="\\left("+i.TeX()+"\\right) \\times "
else:
stringTeX+=i.TeX()+" \\times "
if developpe==Polynome({0:1},var=self.var):
return stringTeX[:-7]
else:
return stringTeX+"\\left("+developpe.TeX()+"\\right)"
else:
return facteurs + [developpe]
def derive(self):
result={}
for i in self.dictio.iterkeys():
if i == 0:
result[0]=0
else:
result[i-1]=int(i)*self[i]
return Polynome(result,self.var)
def primitive(self):
result={}
for i in self.dictio.iterkeys():
result[i+1]=Fractions.Fractions(1,int(i+1))*self.dictio[i]
return Polynome(result,self.var)
def str_Polynome(string,var='x'):
'''str -> dict'''
#TODO reconnaitre les coefficients fractionnaires
resultat = []
termes = {}
separeplus = (string).split("+")
for element in separeplus:
temp = []
temp = element.split("-")
for bis in temp:
resultat.append(bis)
if temp.index(bis) != len(temp)-1:
resultat.append(-1)
if separeplus.index(element) != len(separeplus)-1:
resultat.append(1)
if '' in resultat:
resultat.remove('')
for element in resultat:
index = resultat.index(element)
if index > 0:
coeff = resultat[index-1]
else:
coeff = 1
if (element not in [-1, 1]):
if element==var:
termes[1]=(coeff)
else:
a = re.findall('\d+(?:\.\d*)?', element)
if (len(a) == 1) and (not re.findall('\^', element)) and (re.findall(var, element)):
termes[1]=coeff * Fractions.Fractions(eval(a[0]))
elif (len(a) == 1) and (re.findall(var, element)):
termes[int(a[0])]=coeff * 1
elif (len(a) == 1):
termes[0]=coeff * Fractions.Fractions(eval(a[0]))
else:
termes[int(a[1])]=coeff * Fractions.Fractions(eval(a[0]))
return termes
if __name__=="__main__":
from TEST.imprimetest import *
X=Polynome("x")
P=Polynome({2:4,1:8,0:1,3:0})
## Q=Polynome({2:-4,0:-1,1:8})
## R=Polynome({3:1,2:1,1:-2})
## D=Polynome({1:1,0:2})
## F=Polynome("x-4")
## FF=Polynome("x^2-3")
## Divi=FF*F+7
## FR=Polynome({3:Fractions(2,3),2:Fractions(2,3),1:Fractions(-4,3)})
## print "P=", P
## print "Q=", Q
## print "R=", R
## print "FR=",FR
## R_facteur=R.factorise()
## print "R=",R.factorise(TeX=True)
## #TeX_division(R,D)
## print Divi*Polynome("x^3")-28*X
## #imprime_TeX(TeX_division(Divi*Polynome("x^3")-28*X,F*X))
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