ffmaprel

Function: ffmaprel
Section: number_theoretical
C-Name: ffmaprel
Prototype: GG
Help: ffmaprel(m, x): given a (partial) map m between two finite fields,
 express x as an algebraic element over the codomain of m in a way which
 is compatible with m.
 The function is applied recursively to the component of vectors, matrices and
 polynomials.
Doc: given a (partial) map $m$ between two finite fields, express $x$ as an
 algebraic element over the codomain of $m$ in a way which is compatible
 with $m$.
 The function is applied recursively to the component of vectors,
 matrices and polynomials.
 \bprog
 ? a = ffgen([3,5],'a);
 ? b = ffgen([3,10],'b);
 ? m = ffembed(a, b);
 ? mi= ffinvmap(m);
 ? R = ffmaprel(mi,b)
 %5 = Mod(b,b^2+(a+1)*b+(a^2+2*a+2))
 @eprog
 In particular, this function can be used to compute the relative minimal
 polynomial, norm and trace:
 \bprog
 ? minpoly(R)
 %6 = x^2+(a+1)*x+(a^2+2*a+2)
 ? trace(R)
 %7 = 2*a+2
 ? norm(R)
 %8 = a^2+2*a+2
 @eprog