XPost: comp.soft-sys.math.maple   
   From: &noreply@axelvogt.de   
      
   On 19.08.2015 20:19, Peter Luschny wrote:   
   > Hi Martin!   
   >   
   >> I expect the remainder to be handled in the same manner. But I don't see   
   >> why Derive should not fail to simplify similar expressions whose   
   >> trigonometric arguments involve larger denominators, as the rule to   
   >> handle SIN(3*pi/14) - SIN(pi/14) is not generic.   
   >   
   > I include some further examples (array of expressions).   
   >   
   > case 7:   
   >   
   > [(10/7)*x^4*cos((1/7)*Pi)+(2/7)*cos((1/7)*Pi)+(20/7)*x^2*cos((   
   /7)*Pi)-(20/7)*x^3*cos((1/7)*Pi)-(10/7)*x*cos((1/7)*Pi)-(20/7)*c   
   s((2/7)*Pi)*x^2-(10/7)*cos((2/7)*Pi)*x^4+(10/7)*x*cos((2/7)*Pi)-   
   2/7)*cos((2/7)*Pi)+(20/7)*cos((2/7)*Pi)*x^3+(10/7)*x^4*cos((   
   3/7)*Pi)+(2/7)*cos((3/7)*Pi)+(20/7)*x^2*cos((3/7)*Pi)-(20/7)*x^3   
   cos((3/7)*Pi)-(10/7)*x*cos((3/7)*Pi)-1/7+(5/7)*x-(10/7)*x^2+(10/   
   )*x^3-(5/7)*x^4+x^5,   
   > -(6/7)*x+(15/7)*x^2-(20/7)*x^3+(15/7)*x^4-(6/7)*x^5+x^6+(30/7)   
   cos((2/7)*Pi)*x^4-(12/7)*cos((2/7)*Pi)*x^5-(30/7)*x^4*cos((3/7)*   
   i)-(30/7)*x^4*cos((1/7)*Pi)-(2/7)*cos((3/7)*Pi)-(2/7)*cos((1/7)*   
   i)-(12/7)*x*cos((2/7)*Pi)+1/7+(2/7)*cos((2/7)*Pi)-(30/7)*x^   
   2*cos((3/7)*Pi)-(30/7)*x^2*cos((1/7)*Pi)+(40/7)*x^3*cos((1/7)*Pi   
   +(40/7)*x^3*cos((3/7)*Pi)+(12/7)*x*cos((3/7)*Pi)+(12/7)*x*cos((1   
   7)*Pi)+(12/7)*x^5*cos((3/7)*Pi)+(12/7)*x^5*cos((1/7)*Pi)-(40/7)*   
   os((2/7)*Pi)*x^3+(30/7)*cos((2/7)*Pi)*x^2];   
   >   
   > case 9:   
   >   
   > [x+((4/9)*I)*sin((1/9)*Pi)+((4/9)*I)*sin((2/9)*Pi)-(2/9)*cos((   
   /9)*Pi)-((4/9)*I)*sin((4/9)*Pi)+(2/9)*cos((1/9)*Pi)-(2/9)*cos((4/9)*Pi),   
   > (4/9)*x*cos((1/9)*Pi)-(2/9)*cos((1/9)*Pi)-(4/9)*cos((2/9)*Pi)*   
   +(2/9)*cos((2/9)*Pi)-(4/9)*x*cos((4/9)*Pi)+(2/9)*cos((4/9)*Pi)+(   
   8/9)*I)*x*sin((1/9)*Pi)-((8/9)*I)*sin((1/9)*Pi)+((8/9)*I)*x*sin(   
   2/9)*Pi)-((8/9)*I)*sin((2/9)*Pi)+((8/9)*I)*sin((4/9)*Pi)-((   
   8/9)*I)*x*sin((4/9)*Pi)+x^2,   
   > ((4/3)*I)*sin((2/9)*Pi)*x^2-((8/3)*I)*x*sin((1/9)*Pi)-((8/3)*I   
   *x*sin((2/9)*Pi)-((4/3)*I)*sin((4/9)*Pi)+((8/3)*I)*x*sin((4/9)*P   
   )+((4/3)*I)*x^2*sin((1/9)*Pi)-((4/3)*I)*x^2*sin((4/9)*Pi)+((4/3)   
   I)*sin((2/9)*Pi)+((4/3)*I)*sin((1/9)*Pi)-(2/3)*x*cos((1/9)*   
   Pi)+(2/3)*x^2*cos((1/9)*Pi)+(2/3)*cos((2/9)*Pi)*x-(2/3)*cos((2/9   
   *Pi)*x^2+(2/3)*x*cos((4/9)*Pi)-(2/3)*x^2*cos((4/9)*Pi)+x^3,   
   > ((16/3)*I)*x*sin((1/9)*Pi)+((16/9)*I)*x^3*sin((1/9)*Pi)-((16/3   
   *I)*x*sin((4/9)*Pi)-((16/3)*I)*x^2*sin((1/9)*Pi)+((16/3)*I)*x^2*   
   in((4/9)*Pi)-((16/9)*I)*x^3*sin((4/9)*Pi)-((16/3)*I)*sin((2/9)*P   
   )*x^2+((16/9)*I)*sin((2/9)*Pi)*x^3+((16/3)*I)*x*sin((2/9)*   
   Pi)+((16/9)*I)*sin((4/9)*Pi)-((16/9)*I)*sin((2/9)*Pi)-((16/9)*I)   
   sin((1/9)*Pi)+(8/9)*x^3*cos((1/9)*Pi)-(2/9)*cos((1/9)*Pi)-(4/3)*   
   ^2*cos((1/9)*Pi)+(4/3)*cos((2/9)*Pi)*x^2+(2/9)*cos((2/9)*Pi)-(8/   
   )*cos((2/9)*Pi)*x^3+(4/3)*x^2*cos((4/9)*Pi)+(2/9)*cos((4/9)*   
   Pi)-(8/9)*x^3*cos((4/9)*Pi)+x^4,   
   > x^5-(10/9)*cos((2/9)*Pi)*x^4+(20/9)*cos((2/9)*Pi)*x^3-(10/9)*x   
   cos((1/9)*Pi)+(10/9)*x*cos((4/9)*Pi)+(10/9)*cos((2/9)*Pi)*x+(20/   
   )*x^3*cos((4/9)*Pi)-(20/9)*x^3*cos((1/9)*Pi)-(2/9)*cos((2/9)*Pi)   
   ((20/9)*I)*sin((2/9)*Pi)-((20/9)*I)*sin((4/9)*Pi)+((20/9)*I)   
   *sin((1/9)*Pi)-((80/9)*I)*sin((2/9)*Pi)*x^3+((20/9)*I)*sin((2/9)   
   Pi)*x^4-((20/9)*I)*x^4*sin((4/9)*Pi)+((20/9)*I)*x^4*sin((1/9)*Pi   
   +((40/3)*I)*sin((2/9)*Pi)*x^2-((40/3)*I)*x^2*sin((4/9)*Pi)+((40/   
   )*I)*x^2*sin((1/9)*Pi)+((80/9)*I)*x^3*sin((4/9)*Pi)-((80/9)*   
   I)*x^3*sin((1/9)*Pi)-((80/9)*I)*x*sin((2/9)*Pi)+((80/9)*I)*x*sin   
   (4/9)*Pi)-((80/9)*I)*x*sin((1/9)*Pi)+(10/9)*x^4*cos((1/9)*Pi)-(1   
   /9)*x^4*cos((4/9)*Pi)+(2/9)*cos((1/9)*Pi)-(2/9)*cos((4/9)*Pi)];   
   >   
   > case 11:   
   >   
   > [-1/11+x+(2/11)*cos((5/11)*Pi)+(2/11)*cos((1/11)*Pi)+(2/11)*co   
   ((3/11)*Pi)-(2/11)*cos((4/11)*Pi)-(2/11)*cos((2/11)*Pi),   
   > -(2/11)*cos((1/11)*Pi)+(4/11)*x*cos((1/11)*Pi)+(2/11)*cos((2/1   
   )*Pi)-(4/11)*cos((2/11)*Pi)*x-(2/11)*cos((3/11)*Pi)+(4/11)*x*cos   
   (3/11)*Pi)+(2/11)*cos((4/11)*Pi)-(4/11)*x*cos((4/11)*Pi)-(2/11)*   
   os((5/11)*Pi)+(4/11)*x*cos((5/11)*Pi)+1/11-(2/11)*x+x^2,   
   > (2/11)*cos((1/11)*Pi)+(6/11)*x^2*cos((1/11)*Pi)-(6/11)*x*cos((   
   /11)*Pi)-(6/11)*cos((2/11)*Pi)*x^2-(2/11)*cos((2/11)*Pi)+(6/11)*   
   os((2/11)*Pi)*x+(2/11)*cos((3/11)*Pi)+(6/11)*x^2*cos((3/11)*Pi)-   
   6/11)*x*cos((3/11)*Pi)-(6/11)*x^2*cos((4/11)*Pi)-(2/11)*cos(   
   (4/11)*Pi)+(6/11)*x*cos((4/11)*Pi)+(2/11)*cos((5/11)*Pi)+(6/11)*   
   ^2*cos((5/11)*Pi)-(6/11)*x*cos((5/11)*Pi)-1/11+(3/11)*x-(3/11)*x^2+x^3,   
   > -(4/11)*x+(6/11)*x^2-(4/11)*x^3+x^4-(8/11)*cos((2/11)*Pi)*x^3+   
   12/11)*cos((2/11)*Pi)*x^2-(8/11)*cos((2/11)*Pi)*x-(12/11)*x^2*co   
   ((5/11)*Pi)+(12/11)*x^2*cos((4/11)*Pi)-(12/11)*x^2*cos((1/11)*Pi   
   -(12/11)*x^2*cos((3/11)*Pi)-(2/11)*cos((5/11)*Pi)-(2/11)*   
   cos((1/11)*Pi)-(2/11)*cos((3/11)*Pi)+(2/11)*cos((4/11)*Pi)+(8/11   
   *x^3*cos((1/11)*Pi)+(8/11)*x^3*cos((3/11)*Pi)+(8/11)*x^3*cos((5/   
   1)*Pi)-(8/11)*x^3*cos((4/11)*Pi)+1/11+(2/11)*cos((2/11)*Pi)-(8/1   
   )*x*cos((4/11)*Pi)+(8/11)*x*cos((3/11)*Pi)+(8/11)*x*cos((1/   
   11)*Pi)+(8/11)*x*cos((5/11)*Pi),   
   > (5/11)*x-(10/11)*x^2+(10/11)*x^3-(5/11)*x^4+x^5+(20/11)*cos((2   
   11)*Pi)*x^3-(20/11)*cos((2/11)*Pi)*x^2+(10/11)*cos((2/11)*Pi)*x-   
   10/11)*cos((2/11)*Pi)*x^4+(20/11)*x^2*cos((5/11)*Pi)-(20/11)*x^2   
   cos((4/11)*Pi)+(20/11)*x^2*cos((1/11)*Pi)+(20/11)*x^2*cos((   
   3/11)*Pi)+(2/11)*cos((5/11)*Pi)+(2/11)*cos((1/11)*Pi)+(2/11)*cos   
   (3/11)*Pi)-(2/11)*cos((4/11)*Pi)-(20/11)*x^3*cos((1/11)*Pi)-(20/   
   1)*x^3*cos((3/11)*Pi)-(20/11)*x^3*cos((5/11)*Pi)+(20/11)*x^3*cos   
   (4/11)*Pi)-(2/11)*cos((2/11)*Pi)-1/11+(10/11)*x^4*cos((5/11)   
   *Pi)-(10/11)*x^4*cos((4/11)*Pi)+(10/11)*x^4*cos((3/11)*Pi)+(10/1   
   )*x^4*cos((1/11)*Pi)+(10/11)*x*cos((4/11)*Pi)-(10/11)*x*cos((3/1   
   )*Pi)-(10/11)*x*cos((1/11)*Pi)-(10/11)*x*cos((5/11)*Pi)];   
   >   
   > Can Rubi handle them?   
   >   
   > And: what is the _general_ reduction strategy?   
   >   
      
   Maple does it, using convert(%, RootOf): simplify(%); gives the monomials x^k   
      
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