David Holmgren wrote:
>
> Hi - I wouldn't call using expand and factor a waste of time; it doesn't
> take that much effort to go through one or two more steps on the road to a
> solution. I use expand, factor, etc. all the time. Cheers, Dave H.
>
While it is possible to use expand and factor, for the computer system
to take these steps on its own might be risky. For example, expanding
(x+1)^100000 is really not a great idea. By the way, using ratsimp
or ratexpand may be a lot faster than using expand.
Factoring can also be quite expensive.
As for x^2+1=0 being solved in other domains (e.g. in a
finite field)... it may seem to a mathematician that the
choice of real/ complex / etc / etc. is arbitrary. But
to an engineer, physicist, chemist, biologist, economist,
.... the choice not arbitrary at all.
Complex is right, 99.999% of the time.
The goal of the
computer algebra systems like Macsyma, Maple, Mathematica..
are primarily to support applied mathematics, not
pure math. There are other systems with more specialized
objectives that are efficient in (for example) group
theory calculations or number theory calculations.
While one can do arithmetic in a finite field in Macsyma
by setting modulus:2 or modulus:13 etc,
the support for this is spotty. The Axiom system
is/was much better for this. But that may be related
to the fact that its current owner, NAG, is dropping
support for it.
RJF