Re: [Axiom-mail] create a function

[Martin Rubey]

Hi Cereja!

There is one "real" problem with your definition, and another one
that is trivial.

The "real" problem is that

         dx(x) == D(func,x)

cannot work.  (I'm guessing that you want to define a function that
returns the derivative of func evaluated at x.)  Actually, I'm not
sure what the interpreter would do with it in case it could compile
it.  I guess it would interpret it as a "rule", which is certainly
not what you had in mind.

The right way to do this is

         dx := D(func, x)
         m := eval(dx, x=P1.1)/(2*P1.2)

i.e., you define dx to be the derivative of func (i.e., dx is a
polynomial) and then you evaluate it using "eval".


The second, minor problem is that the interpreter is too stupid to
infer the types of m and ponto.  The workaround is to help the
interpreter by declaring them appropriately.

Below a function that seems to work.

Martin


AddPoints(func:POLY(INT),P1:LIST(INT),P2:LIST(INT)):LIST(FRAC(INT)) ==
   z:=1
   m: FRAC INT
   ponto: List FRAC INT
   if (P1.3 = 1) and (P2.3 = 1) then
      if (P1.1 < P2.1) then
         m:= (P2.2 - P1.2)/(P2.1 - P1.1)
      if (P2.1 < P1.1) then
         m:= (P1.2 - P2.2)/(P1.1 - P2.1)
      if (P1.1 = P2.1) and (P1.2 ~= P2.2) then
         z:=0
      if (P1.1 = P2.1) and (P1.2 = P2.2) then
         dx := D(func, x)
         m:= eval(dx, x=P1.1)/(2*P1.2)
      if (z = 1) then
         a := m^2
         xsoma := (-(P1.1 + P2.1 - a))
         ysoma := ((m*(xsoma-P1.1) + P1.2) * (-1))
         ponto := [xsoma,ysoma,z]
         ponto
      else
         [0,1,z]
   else
      if (P1.3 = 0) then
         ponto := P2
      else
         ponto := P1
      ponto