Geoffrey Mess <geoff@math.ucla.edu> writes :

a)It should only be defined for prime values of the second variable.
b) Reduce( n, p) yields n*Z(p)^0, if n is an integer.
c) Reduce(a/b, p) yields a * ( b*Z(p)^0 )^(-1), if b is coprime to p.
d) Reduce should also apply to vectors and matrices with rational
entries, to functions that return vectors and matrices with rational
entries, and so on.

I haven't had the need to use such a function, but it is fairly straight
forward to implement one. Here's a quick attempt at it, you might want to
clean it up a little, especially the error handling part :

################################################################################
Reduce:=function(n,p) local a,b;
 # handle a non-prime second argument
 if not(IsPrime(p)) then
   Print("ERROR : p is not a prime \n");
   return;
 fi;
 # case when n is an integer
 if IsInt(n) then
   return n*Z(p)^0;
 fi;
 # case when n is rational
 if IsRat(n) then
   a:=Numerator(n);
   b:=Denominator(n);
   if Gcd(b,p)<>1 then
     Print("ERROR : b not coprime to p \n");
     return;
   fi;
   return a*(b*Z(p)^0 )^(-1);
 fi;
 # case when n is a vector
 if IsVector(n) then
  return List(n,x->Reduce(x,p));
 fi;
 # case when n is a matrix
 if IsMat(n) then
  return List(n,x->Reduce(x,p));
 fi;
return;
end;
################################################################################

for example :
gap> tw3;
[ [ 1, 0, 0, 0 ], [ 1, 1, -1, 0 ], [ 0, 0, 1, 0 ], [ -1, 0, 1, 1 ] ]

gap> Reduce(tw3,2);
[ [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2) ],
  [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0 ] ]

gap> Reduce(tw3/3,5);
[ [ Z(5), 0*Z(5), 0*Z(5), 0*Z(5) ], [ Z(5), Z(5), Z(5)^3, 0*Z(5) ],
  [ 0*Z(5), 0*Z(5), Z(5), 0*Z(5) ], [ Z(5)^3, 0*Z(5), Z(5), Z(5) ] ]

gap> Reduce(tw3[2],2);
[ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2) ]

Good luck,

Jacob.