Problems with complex numbers



Volker van Nek wrote:

> 
> (%i2) gfactor(%i*k^4 -2*k^3 -2*%i*k^2+2*k+%i);
> 
> (%o2) %i*(k-1)*(k+1)*(k+%i)^2
> 
> See ?gfactor
> 
> HTH
> 
> Volker van Nek

Thanks, i had missed this one. Now the following problem which was
in my computation:


niobe% maxima
(%i1) gfactor(sqrt(%i*k^4 -2*k^3 -2*%i*k^2+2*k+%i));
                                 2               2
(%o1)                 sqrt((%i (k  - 1) - 2 k) (k  - 1))
(%i2) radcan(%o1);
                                                 2
(%o2)           sqrt(k - 1) sqrt(k + 1) sqrt(%i k  - 2 k - %i)

(%i6) map(gfactor, sqrt(%i*k^4 -2*k^3 -2*%i*k^2+2*k+%i));
                                                      2
(%o6)                 sqrt(%i (k - 1) (k + 1) (k + %i) )
(%i7) radcan(%);
                                                 2
(%o7)           sqrt(k - 1) sqrt(k + 1) sqrt(%i k  - 2 k - %i)


This misses the opportunity to get (k+%i) sqrt(k^2-1) and to simplify (k+%i)
with other factors in the computation. In fact i had to help a lot of the
computation by hand to get the simple result at the end.

Of course this is non trivial, and i don't pretend that maple is good for
manipulations of square roots!




-- 
Michel Talon