One pari command I am searching for is polynomials with the same properties as their cyclotomic polynomials, and finds them based on fixed coefficients in order.
({a, b}, x) would search for a polynomial with the same properties as the cyclotomic polynomial of x, with leading coefficients a, b, c for each higher degree.
For example:
({1, 4}, 5) should find all polynomials with the same number field properties as x^4+x^3+x^2+x+1 of the form x^4+4x^3+ax^2+bx+c. That is should output the solutions, if any {a, b, c} for the degrees 2, 1, 0.
I've scoured a whole column of polynomial commands and not one serves for this purpose.
