There is a program gfactor which is supposed to factor
over the gaussian integers, which is equivalent to
factor(....,i^2-1).
Computing zeros is not the same as factoring, unless you
(a) have only one variable and
(b) do not mind getting approximations.
For many purposes you can and should use rootfinding,
but this alternative is not mentioned in most CAS discussions
because so much effort has been put into exact rational
factoring, even up to the present. It would make the
work of all those theoreticians just a bit less relevant,
and who needs that.
RJF
Janos Blazi wrote:
> Am Sun, 19 Oct 2003 09:05:29 -0700 hat Richard Fateman
> <fateman@cs.berkeley.edu> geschrieben:
>
>> try
>>
>> factor(x^2-5, a^2-5). The second argument specifies that you
>> are adjoining a root of a^2-5=0 to the algebraic field.
>
>
> I should expect that Maxima (or for that matter, any CAS) should
> factor in the algebraic closure of Q and Q[i]. But Maxima does not,
> neither does Maple, though both packages calculate the zeroes in these
> fields. What is the reason for this? Is not factoring and finding
> zeroes essentially the same (at least in subfields of C that have
> characteristic 0)?
>