Dear Forum, When a finite field is defined using an irreducible polynomial, there seems to be a problem finding the coefficients of the field's elements in the natural power bases. For example:
---------------------------------------- gap> x:=Indeterminate(GF(5),"x"); x gap> pol:=x^7+x^4+x^2-x+Z(5); x^7+x^4+x^2-x+Z(5) gap> F:=GF(GF(5),pol); <field of size 78125> gap> a:=RootOfDefiningPolynomial(F); (a) gap> t:=a^32; (Z(5)^2+Z(5)*a^2+Z(5)*a^3+Z(5)^2*a^5+a^6) ----------------------------------------- Even though "t" is displayed as a polynomial in "a", I do not know how to get hold of the corresponding coefficients, because the field "F" as a vector space does not have a basis: -------------------------------------------------------------------------------- gap>IsVectorSpace(F); true gap> b:=List([0..6],i->a^i); [ !Z(5)^0, (a), (a^2), (a^3), (a^4), (a^5), (a^6) ] gap> Basis(F,b); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 3rd choice method found for `PrimitiveRoot' on 1 arguments called from PrimitiveRoot( F ) called from Basis( V ) called from <function>( <arguments> ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> -------------------------------------------------------------------------------- Is there any way around this problem? Thank you, Anvita _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
