[newbie] problem with determining modulus of complex quantity

I think, factor is helping: http://maxima-online.org/?inc=r1525287778
Greetings from Austria
Johnny W.

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2013/11/21 Hugo Coolens <hugo.coolens at kuleuven.be>

> I defined the following function:
> calpgon(m,s):=product(1/(s+4*(cos((k*%pi)/(2*m+1)))^2),k,1,m);
>
> simplified it for the case m=3 like this:
> trigrat(calpgon(3,s));
>                                        1
> (%o2)                         -------------------
>                                3      2
>                               s  + 5 s  + 6 s + 1
>
>
> substituted s by i*omega like this
>
> s : %i*omega;
>
> tried to calculate the modulus of calpgon(3,i*omega) like this
> abs(trigrat(calpgon(3,s)));
>
> and got this:
>                     !         3                     2    !
>                     !%i (omega  - 6 omega) - 5 omega  + 1!
> (%o4)               --------------------------------------
>                            6           4           2
>                       omega  + 13 omega  + 26 omega  + 1
>
> however I hoped to get this "neater" form:
>                                      1
>                      --------------------------------
>                      sqrt(omega^6+13 omega^4 +26 omega^2+1)
>
> Can anyone here tell me how to make maxima go for the last expression?
>
> thanks in advance
> hugo
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