From: fateman@cs.berkeley.edu   
      
   On 4/17/2017 9:52 AM, Nasser M. Abbasi wrote:   
   >   
   > On 4/17/2017 11:22 AM, clicliclic@freenet.de wrote:   
   >   
   >>>   
   >>> btw, on the ln(x^2)=2*ln(x) issue.   
   ...   
   Let us assume that you are a student in a class on   
     complex variables and you are asked on an exam,   
      
   where is  ln(x^2) equal to 2*ln(x)  ?   
      
   To get full points, you would probably have to   
   explain the regions in the complex plane   
   where the expressions are equal (e.g. real x, x>0),   
   where they differ,  and where they are not   
   defined.   
      
   A credible mathematical analysis computer system   
   should be able to answer this question at least   
   at the level of a beginning student in the subject.   
      
   A system that requires you to insert various commands   
   like assume(x>0)   or   combine / simplify / radcan /   
   in order to get a "yes"   or "no" that is correct,   
   is rather less than credible.   
      
   The text I used in grad school   
   (Carrier, Krook, Pearson) has many exercise   
   questions, almost none of which can be answered by our   
   CAS.   
      
   For example, p. 22 [CHAPTER ONE !]...   
      
   discuss the branch-cut and Riemann-surface situation for   
   each of the following functions ... h(z) = ln(1+sqrt(z^2+1)) ,,,   
      
   As I've said previously, answering such questions is   
   possible if they can be reduced to the (essentially algebraic)   
   questions that CAS  can already answer. That reduction   
   is, in general, not obvious.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)