[Maxima] Problems with complex numbers

Michel Talon talon at lpthe.jussieu.fr
Thu Mar 26 11:55:08 CDT 2009

```Hello,

maxima has difficulties factoring polynomials on the complex field.
As an example, compare the following maple and maxima computation:

niobe% maple
|\^/|     Maple 9 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc.
2003
<____ ____>  Waterloo Maple Inc.
|       Type ? for help.
> factor(I*k^4 -2*k^3 -2*I*k^2+2*k+I);
2
(k - 1) (k + 1) (k + I)  I

> quit
bytes used=978068, alloc=851812, time=0.05

niobe% maxima
(%i1) algebraic:true;
(%o1)                                true
(%i2)  factor(%i*k^4 -2*k^3 -2*%i*k^2+2*k+%i);
2
(%o2)                 (k - 1) (k + 1) (%i k  - 2 k - %i)
(%i3)  factor(%i*k^4 -2*k^3 -2*%i*k^2+2*k+%i,b^2+1);
2
(%o3)                    %i (k - 1) (k + 1) (k + %i)

Note that it is necessary to specify that the computation is in the field of
b^2+1 to get the answer. Moreover in many cases, b is returned in place
of %i and many simplifications are missed.

Is there any way to get more efficient computations?

Thanks you very much

--
Michel Talon

```