[GAP Forum] op and nops commands?

[Hulpke,Alexander]

Dea Forum,

Tim Kohl asked

> On Dec 2, 2019, at 9:17 PM, tkohl at math.bu.edu wrote:
> 
> 
> Dear forum members.
> 
> In Maple, there are commands nops() and op() which allow
> one to 'pick apart' expressions, such as polynomials for example,


These Maple functions are the interface to Maples internal data type (which is probably a tree structure for algebraic expressions).
> 
> i.e. nops(expr) is the number of terms of expr
>     op(1,expr) is the first term of expr
> 
> although how nops() evaluates the number of terms is a bit subtle.
> 
> Anyway, I was just wondering if GAP has similar commands?

GAP has similar commands (the most generic being ExtRepOfObject), though the storage is different and thus interface routines are different.
> 
> I am trying to sort (and pull apart) words in fp groups which are,
> of course, polynomials.

Probably you want LetterRepAssocWord. Note that the elements of fp groups wrap words in the free group, thus one needs to call UnderlyingElement first:

gap> f:=FreeGroup("a","b");;
gap> g:=f/ParseRelators(f,"a2,b3,(ab)5");
<fp group on the generators [ a, b ]>
gap> s:=SylowSubgroup(g,2);;
gap> w:=GeneratorsOfGroup(s)[2];
b*a*b^-1*a*b*a^-1*b^-1*a^-1*b
gap> LetterRepAssocWord(UnderlyingElement(w));
[ 2, 1, -2, 1, 2, -1, -2, -1, 2 ]


Regards,

   Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke