none Rouben Rostamian schrieb:   
   >   
   > [...]   
   >   
   > Let's look at a simpler case:   
   > restart;   
   > > kernelopts(version);   
   >            Maple 2017.3, X86 64 LINUX, Sep 27 2017, Build ID 1265877   
   >   
   > > int(cos(n*x), x=0..2*Pi, allsolutions) assuming n::integer;   
   >                             { 2 Pi          n = 0   
   >                             {   
   >                             {  0          otherwise   
   >   
   > That's good. But this one doesn't work -- the n=0 case should give 2 Pi:   
   > > int(exp(n*I*x), x=0..2*Pi, allsolutions) assuming n::integer;   
   >                                        0   
      
   Again, Derive 6.10 fails for n Integer, but not for n Real, and works   
   for explicit n = 0:   
      
   n :epsilon Integer   
      
   INT(EXP(n*#i*x), x, 0, 2*pi)   
      
   0   
      
   n :epsilon Real   
      
   INT(EXP(n*#i*x), x, 0, 2*pi)   
      
   - (-1)^((4*n + 1)/2)/n + #i/n   
      
   n := 0   
      
   INT(EXP(n*#i*x), x, 0, 2*pi)   
      
   2*pi   
      
   The origin of the problem for Integer n is exhibited by stepwise   
   evaluation:   
      
   n:epsilonInteger   
      
   INT(EXP(n*#i*x),x,0,2*pi)   
      
   " e^(y*#i) -> COS(y)+#i*SIN(y) "   
      
   INT(COS(n*x)+#i*SIN(n*x),x,0,2*pi)   
      
   " INT(F(x)+#i*G(x),x,a,b) -> INT(F(x),x,a,b)+#i*INT(G(x),x,a,b) "   
      
   INT(COS(n*x),x,0,2*pi)+#i*INT(SIN(n*x),x,0,2*pi)   
      
   " INT(F(x),x,a,b) -> SUBST_DIFF(INT(F(x),x),x,a,b) "   
      
   SUBST_DIFF(INT(COS(n*x),x),x,0,2*pi)+#i*INT(SIN(n*x),x,0,2*pi)   
      
   " INT(COS(a*x+b),x) -> SIN(a*x+b)/a "   
      
   SUBST_DIFF(SIN(n*x)/n,x,0,2*pi)+#i*INT(SIN(n*x),x,0,2*pi)   
      
   " SUBST_DIFF(F(x),x,a,b) -> F(b)-F(a) "   
      
   #i*INT(SIN(n*x),x,0,2*pi)   
      
   " INT(F(x),x,a,b) -> INT(F(x)+F(a+b-x),x,a,b)/2 "   
      
   #i*INT(0,x,0,2*pi)   
      
   " INT(0,x,a,b) -> 0 "   
      
   0   
      
   How could three independent developers commit the same blunder?   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)