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\deflang1031\pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}reset():
\par {\pntext\f1\'b7\tab}F2:=Dom::GaloisField(2):
\par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 F256:=Dom::GaloisField(2,8,x^8+x^4+x^3+x+1):
\par R:=Dom::AlgebraicExtension( F2, x^8+1 ):
\par // The definition of R is illegal since x^8+1 is not irreducible
\par // but maybe it works for our purpose... [It does!]
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}// add missing features:
\par \pard\li600\ri1\fi-300\plain\f3\fs22\cf1 F256::element:=proc(n)
\par   local N,i;
\par begin
\par   N:=numlib::g_adic(n mod F256::size,F256::characteristic);
\par   _plus( F256(N[i]) * F256(F256::variable)^(i-1) $ i=1..nops(N) )
\par end_proc:
\par R::element:=proc(n)
\par   local N,i;
\par begin
\par   N:=numlib::g_adic(n mod 256,R::characteristic);
\par   _plus( R(N[i]) * R(R::variable)^(i-1) $ i=1..nops(N) )
\par end_proc:
\par R::elementNumber:=proc(n)
\par begin
\par   evalp(mapcoeffs(
\par          subsop(extop(n,1),3=Expr),
\par          _mod,
\par          R::characteristic ),
\par    R::variable = R::characteristic);
\par end_proc:
\par //random(0..255)(); F256::element(%); F256::elementNumber(%);
\par //random(0..255)(); R::element(%); R::elementNumber(%);
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}F256(x^3+x);
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\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}F256::element(17);
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\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}F256::elementNumber( F256(x^3+x) );
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\par \pard\li50\ri2\plain\f3\fs22\cf2\protect 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs22\cf1 {\pntext\f1\'b7\tab}
\par }