oldk1331@gmail.com schrieb:   
   >   
   > > PPS: What is the exact purpose of the FriCAS procedure named rootSimp?   
   >   
   > There was a bug in rootSimp got fixed after FriCAS 1.3.1.   
   > Now in trunk version,   
   >     y := 1/((p*sqrt(1 - x^2) - 1)*sqrt(p*sqrt(1 - x^2) - x^2))   
   >     unparse((rootSimp simplify eval(y,x=sin(x)))::INFORM)   
   > returns   
   >     1/((p*cos(x)+(-1))*(cos(x)^2+p*cos(x)+(-1))^(1/2))   
   >   
   > rootSimp should be recursive, as the documentation says:   
   >   
   >         rootSimp   : F -> F   
   >           ++ rootSimp(f) transforms every radical of the form   
   >           ++ \spad{(a * b^(q*n+r))^(1/n)} appearing in f into   
   >           ++ \spad{b^q * (a * b^r)^(1/n)}.   
   >           ++ This transformation is not in general valid for all   
   >           ++ complex numbers b.   
      
   Ah, a recent bug fix. I didn't expect this for so basic a functionality.   
   Thanks for the explanation.   
      
   >   
   > > Why didn't it "simplify" SQRT(COS(z)^2) in particular?   
   >   
   > Well, SQRT(p^2) not necessarily should be simplified to p,   
   > there are branch issues, and dependent algebraic kernels   
   > issues.  Radical roots simplication is a complex topic in   
   > FriCAS.  Would this suprise you: FriCAS don't   
   > "simplify(sqrt(2)*sqrt(3)-sqrt(6))" to 0!   
      
   Exactly, you use rootSimp in order to override restrictions from a fixed   
   branch assignment for single-valued exponentiation, or more generally   
   from the multivaluedness of certain FriCAS objects. Restrictions on   
   single-valued objects do not necessarily coincide with those on   
   multivalued ones. But since rootSimp already breaks both kinds of   
   restrictions (shudder), it may be a good idea to enhance it such that   
   SQRT(2)*SQRT(3) - SQRT(6) is indeed simplified to zero (yum-yum).   
      
   >   
   > BTW, may I respectfully ask you that why not install a   
   > (trunk version) FriCAS on your machine?   
   >   
   >     simplify   : F -> F   
   >       ++ simplify(f) performs the following simplifications on f:   
   \begin{items}   
   >       ++ \item 1. rewrites trigs and hyperbolic trigs in terms   
   >       ++ of \spad{sin} , \spad{cos}, \spad{sinh}, \spad{cosh}.   
   >       ++ \item 2. rewrites \spad{sin^2} and \spad{sinh^2} in terms   
   >       ++ of \spad{cos} and \spad{cosh},   
   >       ++ \item 3. rewrites \spad{exp(a)*exp(b)} as \spad{exp(a+b)}.   
   >       ++ \item 4. rewrites \spad{(a^(1/n))^m * (a^(1/s))^t} as a single   
   >       ++ power of a single radical of \spad{a}.   
   >       ++ \end{items}   
      
   Being 20+ years old, my machine presumably wouldn't be able to run it.   
   But if you have a Windows-98 executable of a few Megabytes size, I will   
   certainly give it a try. Text-only input/output would be entirely   
   satisfactory.   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
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