Database of the Transitive Groups of Degrees from 2 to 12

This database contains all the transitive groups of degrees from 2 to 12. It has been prepared by Greg Butler.

Each group is labelled according to its degree. For example, the label of the 3rd transitive group of degree 9 is 9, 3.

The groups are accessed through the following functions only.

TrnGroup(d, n)

This function returns the n-th group of degree d.

TrnNumberOfDegree(d)

This function returns the number of groups of degree d which are stored in the library.

TrnGroupSatisfying(f)

Given a boolean valued function f: GrpPerm --> BoolElt (which may either be an intrinsic function or a user defined function), return a group satisfying f(G). This function runs through all the stored groups, expanding each from the stored generators and applies the predicate f until it finds a suitable one. If no group is found, an error message is printed.

TrnGroupOfDegreeSatisfying(d, f)

As TrnGroupSatisfying(f), except it only runs through the groups of degree d.

TrnGroupsSatisfying(f)

As TrnGroupSatisfying(f), except a sequence of all such groups is returned.

TrnGroupsOfDegreeSatisfying(d, f)

As TrnGroupOfDegreeSatisfying(d, f), except a sequence of all such groups is returned.

TrnProcess()

Return a "process" for looping over all the stored groups. Initially it points to the first group (of degree 2).

TrnProcessOfDegree(d)

Return a "process" for looping over all the stored groups of degree d. Initially it points to the first group of degree d.

TrnGroupOfDegreeProcess()

Return a "process" for looping over all the stored groups of degree d where lo <= d <= hi. Initially it points to the first group of degree lo.

TrnProcessIsEmpty(P)

Return whether the process P currently points to a group.

TrnProcessGroup(P)

Given a process P which currently points to a group, return that group.

TrnProcessLabel(P)

Given a process P which currently points to a group, return the label d, n of the group.

TrnProcessNext(~P)

Given a process P which currently points to a group, modify it so that it points to the next group if there is one or make it empty if there is not.

Example

load trngps;
P := TrnProcessOfDegree(5);
while not TrnProcessIsEmpty(P) do
    G := TrnProcessGroup(P);
    ... do computations with G ...
    TrnProcessNext(~P);
end while;