I need to determine the minimal polynomial for a quotient in (1).


(1) B = C / A


C is known as a root of a 36th degree polynomial and A is known as a root of a 24th degree polynomial.


However I have not been able to succeed in recovering the coefficients nor the degree of the polynomial for B.


Any suggestions? I have tried to use GP-Pari's algdep(number,power) command, but so far with little success, even though I know the decimal value of B to 10,018 digits.


Thanks for your help.


Randall


P.S. This is a repost after a suggestion


After working with the resultant method, I was able to successfully recover a 144th degree polynomial whose highest power term has the expected square coefficient. This polynomial was one of 3 polynomials factored from a 864th degree polynomial originally obtained.


I guessed 72nd degree, but it would have taken too long using GP-Pari's algdep(number,144) to recover the polynomial.


Thanks for your suggestions, I now have a valuable tool to help me work with algebraic vectors in R3.



Question on determining the minimal polynomial for an algebraic quotient
Let $F$ be the polynomial for $A$, let $G$ be the polynomial for $C$. Consider the resultant of $x^{24}F(y/x)$ and 
$G(y)$. This will be a polynomial whose roots are all the numbers of the form $\gamma/\alpha$, where $\gamma$ (resp., $\alpha$) runs through the roots of $G$ (resp., $F$). The resultant is the determinant of a $60\times60$ matrix. 


