[GAP Forum] algorithm used by GAP for OrbitsDomain(...) ?

[Alexander Hulpke]

>
Dear GAP-Forum,

Abishek wrote:

> I want to know the algorithm used by GAP when a call to OrbitsDomain 
> (...)
> function is made. The reference manual on page 396 only says that the
> OrbitsDomain operation is often faster than orbits. I want to know  
> how/why
> is it so.

OrbitsDomain *must* be given a domain which must be closed under the  
group operation.
Orbits takes only seed points for the orbits, the orbits can be much  
larger than the set of seed points.

`OrbitsDomain' can be faster as it can for example use an enumeration  
of the full domain and use bit lists to remember which points have  
been touched. `Orbits' instead must check all seed points whether  
they are contained in the orbits found so far.

The reason for having these two operations is that `Orbits' (with  
this syntax) was available in GAP3 and therefore has to be available  
for compatibility reasons. However now we realize that the syntax of  
`OrbitsDomain' in general permits a more efficient operation.

If you write new code I'd recommend you use `OrbitsDomain'.

Best wishes,

      Alexander Hulpke