[Axiom-math] Re: Help facility, Finite Fields in Axiom

[Martin Rubey]

Dear McAndrew,

> G16:=Dom::GaloisField(2,4,x^4+x+1);
> m1:=matrix(4,4,(i,j)->G16::random());
> m2:=matrix(4,4,(i,j)->G16::random());
> m1*m2;
> 
> and of course I can perform arithmetic in the field G16:
> 
> G16((x^3+x)/(x^3+x^2+1));
> G16((x^2+1)^9);

translates to

G16 := FF(2,4) 
-- FF is the abbreviation for FiniteField
m1 := matrix([[random()$G16 for i in 1..4] for j in 1..4])
m2 := matrix([[random()$G16 for i in 1..4] for j in 1..4])
m1*m2

x:=primitiveElement()$G16
(x^3+x)/(x^3+x^2+1)
(x^2+1)^9

I don't really know how it would be possible to specify the generator. But it
certainly can be done. 

-------------------------------------------------------------------------------

> I've been looking at Maxima lately, and have now started on axiom.  So
> here are three very simple questions:
> 
> 1) What online help is available from the axiom prompt?  In every other
> CAS I've tried (Maple, MuPAD, Maxima, plus numerical software such as
> Matlab, scilab, octave), a command such as
> 
> ? sin
> 
> or
> 
> help sin
> 
> will bring up either information about the sine function, or a small
> menu of related functions (arcsin etc.)
> 
> Such help is invaluable for my learning of a system.

You really should use HyperDoc for this task. For your example:

select "Browse" at the top level of HyperDoc

enter "sin"

select "Operations"

select "Descriptions" to obtain descriptions of all operations called "sin"
or
       "Origins"      to obtain a list of domains, packages, categories where
                      an operation called "sin" is defined. Chances are very
                      high that you get related functions this way, too. In the
                      running example, one of the hits is
                      "TrigonometricFunctionCategory", as it should be.

If HyperDoc does not help, I recommend you to ask on address@hidden I
volunteer to answer your questions personally as fast as possible, since it is
maybe my fault that you try to get along with Axiom :-)

By the way, I forgot an important "help" facility I often use:

)wh th foo

spits out a list of all things containing foo in its name. So, you'd probably
interested in typing

)wh th finite

(unfortunately, )wh th galois returns misleading entries...)


Personally, I would not recommend using 

)di op

or 

)sh

to a novice user.

Martin