GAP Manual: 18.8. IntFFE

IntFFE( z )

IntFFE returns the integer corresponding to the element z, which must lie in a finite prime field. That is IntFFE returns the smallest nonnegative integer i such that i * z^ 0 = z.

The correspondence between elements from a finite prime field of characteristic p and the integers between 0 and p-1 is defined by choosing Z(p) the smallest primitive root mod p (see PrimitiveRootMod).

    gap> IntFFE( Z(13) );
    2
    gap> PrimitiveRootMod( 13 );
    2
    gap> IntFFE( Z(409) );
    21
    gap> IntFFE( Z(409)^116 );
    311
    gap> 21^116 mod 409;
    311