// given f a quadratic function defined over PolynomialRing(FiniteField(2,n)), it returns true if f is APN, false otherwise 
IsAPNdeg2:= function(f) 
R<x>:=Parent(f);
F:=BaseRing(R);
n:=Degree(F);
E:=Basis(F);
for a in F do 
if a ne 0 then
           m:=Matrix(GF(Characteristic(F)),[Eltseq(Evaluate(f,x)-Evaluate(f,x+a)+Evaluate(f,a)):x in E]);
            if Rank(m) ne (n-1) then return false;
            end if; 
    end if;
 end for;
return  true;
end function;