> 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.   
      
   > 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!   
      
   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}   
      
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