Dear Francisco, dear DERIVIANS,
Seems to be a bug!
I found out that the problem is buried in the subexpression
SIN(PI/(2ˇn + 1))/COS(2/(2ˇn + 1))
Applying stepwise simplification for n > 2 leads to 0 ^ n --> +- inf.
But if you rewrite the expression substituting the denominator with
sqrt(1 - SIN(2/(2ˇn + 1))^2)
then everything is ok - having set the Mode Trigonometry > Expand > Sines.
Trying now stepwise simplification you will recognize just another
procedure.
Don't know why.
Regards
Josef
Maybe that Albert Rich is checking the mail and he could be the only one to
lift the secret!!??
1-5 July 2014, Krems, Austria
www.time2014.org
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-----Ursprüngliche Nachricht-----
Von: DERIVE computer algebra system [mailto:[log in to unmask]] Im
Auftrag von Francisco Marcelo Fern ández
Gesendet: Dienstag, 5. November 2013 08:45
An: [log in to unmask]
Betreff: Bug in Derive subst
Dear derivians,
I found this unpleasant behaviour of Derive 5 and Derive 6. Perhaps someone
can explain it.
SUBST((SIN(pi/(2*n+1))/COS(2/(2*n+1)))^(-2*(2*n+1)/(2*n+3)),n,2)
;Simp(#1')
((7500*SQRT(5)-12500)^(1/7)/10+(60-20*SQRT(5))^(1/7)/2)*COS(4/5)/COS(2/5)^(4
/~
7)+((7500*SQRT(5)-12500)^(1/7)/10+(60-20*SQRT(5))^(1/7)/2)/COS(2/5)^(4/7)
SUBST((SIN(pi/(2*n+1))/COS(2/(2*n+1)))^(-2*(2*n+1)/(2*n+3)),n,3)
;Simp(#3)
(1,0)
SUBST((SIN(pi/(2*n+1))/COS(2/(2*n+1)))^(-2*(2*n+1)/(2*n+3)),n,4)
;Simp(#5)
(1,0)
APPROX(SUBST((SIN(pi/(2*n+1))/COS(2/(2*n+1)))^(-2*(2*n+1)/(2*n+3)),n,4))
;Simp(#7)
5.556064454
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