Casting t_POL to t_FFELT?

[Aleksandr Lenin <aleksandr.lenin@cyber.ee>]

Hello

I noticed that the string repreentation of the t_FFELT (finite field)
elements is exactly identical to the polynomial.

Consider a field F_{137^2} defined by polynomial x^2 + x + 1 that is
irreducible over F_137. Consider an element of F_{137^2} 136x + 136,
which is a 3-rd order root of unity in this field.

When I obtain 136x + 136 as the result of FF_sqrtn() call, its type is
t_FFELT. Then I write it to a string representation as 136x + 136. At
this point, the information about the finite field is lost. When I try
to read this value back read it back as gp_read_str("136x + 136"), the
program does not recognize that this value was once an element of a
finite field, and gives me a polynomial instead (t_POL).

I closely inspected the PARI library manual, but could not find any
meaningful method to convert a t_POL back into t_FFELT. Is there any? I
ended up with a weird code reconstructing a t_FFELT coefficientwise from
the coefficients of the corresponding t_POL, but this code looks ugly
and I think there must be a better way of doing it.

-- 
With kind regards,
Aleksandr Lenin