Generate all the monic polynomials up to degree n with coefficients in Zp(p prime number) field and find all the irriducible polynomials
My code.
def POLYNOMIAL_OBTAINED_BY_RECURSION(p,n):
R=Zmod(p)
Z.<x>=PolynomialRing(R)
All=[]
if n==1:
h=[]
for i in range(0,p):
pol=x+i
h.append(pol)
return(pol)
All.append(Set(h))
else :
h=[]
for i in range(0,p):
Pol=POLYNOMIAL_OBTAINED_BY_RECURSION(p,n-1)+i*(x^(n-1))+x^n
h.append(Pol)
return(Pol)
All.append(Set(h))
return(All)
def MYSIEVE(n,All)
for d in range(1,floor(n/2)+1):
for j in range(d+1,n+1):
for polinomio1 in All[j]:
for polinomio2 in All[d]:
if polinomio1%polinomio2==0:
k={polinomio1}
All[j].difference(k)
return(All)
def project(p,n):
if not(is_prime(p)):
print('p is not prime',p)
R=Zmod(p)
Z.<x>=PolynomialRing(R)
All=[]
All=POLYNOMIAL_OBTAINED_BY_RECURSION(p,n)
All=MYSIEVE(n,All)
return(All)
What is your question ?