From: fateman@cs.berkeley.edu   
      
   On 6/17/2015 4:51 PM, clicliclic@freenet.de wrote:   
   >   
   ?   
   >   
   > Surely, a consistent solution to this problem would be to have Maxima   
   > itself query the user when in doubt: "There are two square roots. Which   
   > sqrt(cot(2*x)/cot(x)) did you have in mind?"   
      
   This is not particularly an integration problem, but a sqrt problem. Any   
   time a user types sqrt( ) she could be asked "do you want to specify a   
   particular branch, or would you like to continue computing with an   
   ambiguous specification, or would you like the system to choose one   
   branch based on some criterion?"   
      
   It is also not so easy to specify the choice.  How would you specify   
   sqrt(1-cos(x)^2) ?  The "positive one"  would be sin(x)  maybe??  But   
   sin(x) oscillates between pos and neg, so it is not "positive".   
   And what if was some complicated expression?   
      
   Better perhaps to leave  Root(...f(x), 2)   and keep it ambiguous, or   
   have a set { branch1, branch2} ?   
      
      
   Should a CAS have free will? How else can it choose?   
   RJF   
      
   PS the bug about %i and sign -- it can be tickled without using   
   integration.  Maxima CAN do the integral in exponential form,   
   but if one asks to re-express that answer in rectangular form (rectform() )   
   it has the same problem.   
      
      
      
      
   >   
   >>   
   >> This example does seem to identify a bug in Maxima, though.   
   >   
   > Martin.   
   >   
   > PS @ Waldek: you are asking a lot: I will try to answer at the end of   
   > the week :).   
   >   
      
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