Computation of d(f(x,y))

In this section we will compute d(f(x,y)) using the addition and multiplication rules for a p-derivation in order to come up with a result that involves d of the basic elements of f(x,y), ie x, y, c1, etc. The final result is named df. Note that the assumption that d(-1)=0 is included here in this section and will carry over into the next one. We also apply the fact that (-1)^p = -1 here.

> d(-1):=0;

> d(x^2):= multp(x,x);

> d(x^3):= multp(x,x^2);

> d(y^2):= multp(y,y);

> d(-x^3):= multp(-1,x^3);

> d(-x):= multp(-1,x);

> d(-x*c1):=multp(-x,c1);

> d(-c2):=multp(-1,c2);

> d(y^2-x^3):=addp(y^2,-x^3);

> d(-x*c1-c2):=addp(-x*c1,-c2);

> f(x,y);

> dftemp:=addp(y^2-x^3,-x*c1-c2);

> df:=subs((-1)^p = -1,simplify(dftemp,power,symbolic));