factor(x^4+1) and partfrac(1/(x^4+1))

[rombva]

(10-23-2019 08:36 AM)parisse Wrote:  

(10-23-2019 04:05 AM)rombva Wrote:  How to find out the elements for algebraic extensions that provide factorization?

With solve.

factor(x^4+1,lvar(cSolve(x^4+1=0,x))) works fine.

For some polynomyals factor(f(x),lvar(cSolve(f(x)=0,x))) does nothing, for example, factor(x^7+2,lvar(cSolve(x^7+2=0,x))).

For some polynomyals factor(f(x),lvar(cSolve(f(x)=0,x))) doesn't return complete factorization, for example, factor(x^7+1,lvar(cSolve(x^7+1=0,x))).

For other polynomials the result contains a rootof([[][]]), for example, factor(x^5+2,lvar(cSolve(x^5+2=0,x))).

How to find out the elements for algebraic extensions that provide factorization? How to get factorization for these cases?