CAS command question

[parisse]

To Arno K: I want to stress that English is not my native language, my first post was not intented to be rude, it was just factual.
To the subject: I think you can make a parallel with RPN : when people first use a RPN calculator they must learn a little how it works. This is the same for CAS, except the rules are different, in RPN you have much more control over evaluation than in algebraic mode ... but it's much harder to program (and maintain a program). For that reason, you shouldn't try to go against the system (even if you can quote arguments) because at some point your expression will be evaluated.
Here is a CAS program that extracts the information of any inequation condition for a simplex program

Code:


linecond(ex,vars):=begin
  local k1,k2,oper;
  oper:=ex[1];
  ex:=left(ex)-right(ex);
  k1:=diff(ex,vars); 
  k2:=diff(k1,vars); // check that ex is linear w.r.t. vars
  if k2!=0*k2 then return "error" end;
  k2:=normal(ex-k1*vars); // constant part of the inequation
  return [append(k1,k2),oper];
end;

For example l,o:=linecond(x+y<=4,[x,y]) will return [-1,-1,4] in l and '>=' in o. You would get the same with 4>=x+y or 4-x>=y which means you give the user more freedom to enter the conditions, and you the programmer have less cases to consider since oper can only be > or >= (or maybe = too). Note also that the parser will detect syntax errors unlike when the user enter conditions as strings.
I really believe that it is worth the effort to learn a little bit how CAS work because you can make more powerful programs.