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Hi, I'm trying to implement the Baby Step Giant Step algorithm in the group of units of prime fields. I would like to generate the field provided one generator polynomial. But I need to calculate p^(-1) (where p is a polynomial), but can't find a function to do so. This is what I'm doing,

F. = GF(2)[]; R. = PolynomialRing(F) S.<x> = R.quotient(b^4+b+1)

Hi, I'm trying to implement the Baby Step Giant Step algorithm in the group of units of prime fields. I would like to generate the field provided one generator polynomial. But I need to calculate p^(-1) (where p is a polynomial), but can't find a function to do so. This is what I'm doing,

F.<a> = GF(2)[];
R. R.<b> = PolynomialRing(F)
S.<x> = R.quotient(b^4+b+1)
R.quotient(b^4+b+1)
  
m = sqrt(S.modulus().degree()); 
gamma = S.modulus();
alpha = x^3+1;x^3+1;