From: nma@12000.org   
      
   On 3/6/2018 6:13 PM, Richard Fateman wrote:   
   > In Maxima   
   >>   
   > f(n):= integrate(cos(x)* sin(x)^2*cos(n*x),x,0,2*%pi)$   
   >   
   > makelist(f(n),n,0,10);   
   >   
   > returns   
   >   
   >    [0,%pi/4,0,-%pi/4,0,0,0,0,0,0,0]   
   >   
   > There is a substantial difference in what you can compute for   
   > n being a particular integer, say 5,   and what you can compute   
   > for" n being some integer but I'm not going to tell you which one."   
   >   
   > If you insist on being vague, you elevate the problem from being   
   > rather ordinary algorithmic processing, to some kind of mathematical   
   > knowledge representation and theorem-proving scenario.   
   >   
   > This is generally something to be avoided.   
   >   
      
   I am really confused by this comment.   
      
   I am, as a CAS user, not being vague at all. I am simply using   
   a CAS commands, provided by the CAS maker to use.   
   Which is to do some computation under some assumptions.   
      
   You seem to blame the user for simply using what CAS provides   
   to use, then say this is something to be avoided.   
      
   This is like a car manufacturer building a car with big red   
   button which activates automatic speed control, then say to   
   customers who buy the car that one should avoid hitting the   
   button since it can cause problems.   
      
   >     In my experience, a CAS   
   > is more likely to work to rapidly solve particular example problems that   
   > will either refute or tend to confirm some hypothesis that you (a human)   
   > wish to test.   
   >   
   > e.g. a hypothesis that the determinant of a certain kind of nXn matrix   
   > has a particular formula  g(n) for all n.   
   > You try it for n=1,2,3.  guess at g(n).  see if it is confirmed for   
   > n=4,5.   If so, try to come up with a proof.   
   >   
   > Challenging a CAS  to compute a determinant for a matrix   
   > with specified entries   e(i,j)  whose   
   > size is "some integer n but I'm not going to tell you which one",   
   > requires rather different techniques.   
   >   
   > Consequently ---   
   > You should not be under the impression   
   >    that a CAS will figure out all the consequences   
   > of "assume n is a positive integer".   
   >   
   > By the way, this problem has almost nothing to do with integrals   
   > specifically.   
   >   
   > For example,  it is well known that you can divide one polynomial   
   > by another and get a quotient and remainder.   
   > if n is a positive integer, then  x^n+ 34 is a polynomial.   
   > Or is it?   
   > Sure, it is a polynomial but you don't know which one.   
   > So you can't divide.   
   >   
   > You also can't divide by n-3, which, as it happens, comes up in the symbolic   
   > answer to this integration   
   > problem.   
   >   
   > However,  The fact that you cannot reliably divide by n-3 is   
   > NOT  an integration problem.   
   >   
   >   
   >   
   > It is mathematical database representation consistency problem.   
   > If you want to address such issues, fine.  Stop calling it   
   > integration though.   
   >   
   > RJF   
   >   
   >   
      
   If using assumptions to be avoided when solving CAS problems,   
   then they should be removed from CAS systems, this is until the   
   CAS makers sort out these problems using them.   
      
   ps. I said before in this thread, this is not an integrate   
   problem per say, but related to using assumptions. I happend   
   to face the problem when using Integrate, that is all.   
      
   Thanks,   
   --Nasser   
   >   
   >   
   >> So I do not know how to tell Fricas to "assume" n is   
   >> a positive integer? Does FriCAS has assumptions other than   
   >> just saying  n: Integer or n: PositiveInteger and so on?   
   >>   
   >> I googled and not able to find this information about FriCAS.   
   >>   
   >> CAS will be limited if one can not use assumptions?   
   >>   
   >> The above integrate will only work if   
   >>   
   >> n : Symbol   
   >>   
   >> May be a FriCAS expert knows how to do this in Fricas.   
   >>   
   >> --Nasser   
   >>   
   >>   
   >   
      
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