info.6

6.   Other Programs.
The programs listed in this file are more experimental and less well
supported than those in Section 2 and 3.

The following two programs are an attempt at improving the performance of
nqrun for second cohomology groups for larger groups. They are awkward to use,
since they require a lot of preliminary work by the user, but they are worth it
in terms of time and space requirements for groups P which act to a fairly large
depth on the module M. Hopefully some more automatic method will be devised
eventually.
The idea is as follows. Find subgroups Q(1),...,Q(m) of P, for which
[M,Q(1),Q(2),...,Q(m)] = 0, where the Q(i) are as large as possible, and m is as
small as possible. (These two conditions conflict, of course). Then when the
Frattini module F(M) of P is computed, the conditions will be imposed on F(M)
at all depths l>=m, since [F(M),Q(1),...,Q(m)] must be in the kernel of all
P-homomorphisms F(M) -> P. The resultant  decrease in the size of F(M) can be
considerable, with consequent savings in time and space.
To use the programs, for each such set  of subgroups Q(1),...,Q(m) make a file
gpname.x?, where ?=a,b,c,... (So, for example, if 3 such systems are found for
the group l52, we make files l52.xa, l52.xb and l52.xc, and the programs note
that there is no file l52.xd in order to cease this phase of the processing.)
Similarly, for computing in the intersections, for each file gpname.sci, we
make files gpname.sciaxa, gpname.scibxa,... (one for each intersection Q in the
sci file), gpname.sciaxb, gpname.scibxb,.... and so on. For example, if
l52.sc2 contains 3 intersections, and we have 2 systems of subgroups of Q for
each of these, then we make files l52.sc2axa,l52.sc2bxa,l52.sc2cxa, and
l52.sc2axb,l52.sc2bxb,l52.sc2cxb.
The format of these files is as follows. Line 1 contains the number n(1) of
generators of Q(1) and m. Normally, the next n(1) lines contain the generators
of Q(1) (a minimal generating set is most efficient).  These consist of a string
of generators power pairs, preceded by total length.
For example, g(1)^3 * g(3)^2 * g(4) is written as
6 1 3 3 2 4 1
on a single line. The generators are the pcp generators of P or of the
appropriate intersection Q. An exception is when Q(1) is the whole of P or the
intersection Q. In this case, the number n(1) should be the full exponent of
the order of P or Q, and the list of generators MUST be omitted, since the
program can compute them itself.
     Next, if Q(2) is the same as Q(1), then the following line should contain
a single 0. If not, then it contains the number of generators n(2) of Q(2),
and if Q(2) is not the whole of P or Q, the list of generators follows as for
for Q(1). Similarly for Q(3), Q(4), ... Put a single 0 if Q(i+1)=Q(i).

(i) nq+chrun
Source files: nq+chd.c nq+chp.c nq+chfns.c matfns.c
Usage:    nq+chrun [-o] gpname [inf] [inf] ...
inf should take values sc, sc1, sc2, etc., one for each intersection file,
(but not for those containing g in N(P)).
This program is used to check that the subgroups Q(1),..,Q(m) in all of the
files described above really satisfy the required condition on their action on
P. It should always be used before nqrun+, since a mistake of this kind would
cause errors in the final answer.
First the files gpname.pgmat and gpname.pcp are used to compute the matrices
of all pcp generators of P (acting on M, not d(M)). The files gpname.inf are
then used to compute the matrices of the intersections Q.
If the -o option is used, then these matrices can be output to files
gpname.mats (for P itself) and gpname.infmats for intersection files. It
is a good idea to use the -o option BEFORE making any of the Q(i) files (in
which case the program computes the matrices only), since the matrices can
then be used to look for suitable sets of subgroups Q(i). It should then be
run again without the -o option to check the conditions on the Q(i).

(ii) nqrun+
Source files: nqd.c nqp1+.c nqp2.c nqp3+.c nqfns.c matfns.c
(Only two are different from nqrun. nqp3+.c contains the extra procedure that
 looks for and uses the intersection files, and nqp1+.c calls it in the
 procedure calcfm.)
Usage:  As for nqrun.
(If -1 is used, there is no difference from nqrun)
This is used in place of nqrun when the Q(i) files described above are present.

(ii)a nqrun+s
Source files: nqds.c nqp1+s.c nqp2s.c nqp3+s.c nqfnss.c matfns.c
As for nqrun+, but state saving procedures are used. (Local to Warwick system)
 

The following two programs are intended as converses of the programs to 
compute H^2 and extensions. Given an extension of a module M by H, where
P <= H <= G, they restrict the extension to P, and decide whether it splits,
or whether it is stable with respect to G. As input, they take the output of
extprun applied to the file gpname.hsg.er, where gpname.hsg is the strong-
generator file for H. If gpname.hsg.er is produced by corestricting stable
elements of H^2(P,M) in the usual way, then of course this extension will be
stable and usually nonsplit. Thus, for this purpose, they only provide an
additional check on everything.
If, in future, some other method should be found to produce the file, then
they would be useful.

(iii) respcrun
Source files: respcd.c respcp.c idextp.c pf.c matfns.c
(pf.c is a variation of permfns.c, with more use of pointers)

Usage: respcrun [-s] gpname [inf1]

Default: inf1 = sg
The following files are needed for input:
gpname.spc, gpname.inf1, gpname.inf1mat, gpname.cbmats, gpname.ep
(output of extprun), gpname.pcp.
(These are all produced by group and matrix theoretical programs)
      If -s is not called, gpname.ch2 is also required.
In this case, the program determines firstly if the extension splits, and
and secondly whether it is stable. It does this by computing the PCP for the
extension, and then identifying it using the information in gpname.ch2.
      If -s is called, then gpname.ch2 is not required, and the PCP for the
extension of M by P is output to a file gpname.eop, in the usual PCP format.
This is then used by splitrun to determine whether the extension splits, and
it should be quicker overall than the above method, since it does not
involve the prior use of nqrun.

(iv) splitrun
Source files: splitd.c splitp.c splitfns.c matfns.c
Usage: splitrun [inf1] [inf2]
Defaults: (probably always) inf1 = eop, inf2 = pgmat.

This program is similar in structure, time and space requirements to nqrun -1,
(which is much quicker than nqrun alone). Given a PCP for an extension E of M by
P, it lets this extension act on the dual module d(M) of M (with M acting
trivially on d(M). We now proceed to compute the p-multiplier of the semidirect
product of d(M) by E, as in the computation of H^1(E,M), with the difference
that we start by introducing a "key" generator G(1) say, with [d(b),b]=1, for
each element b of a basis of M, where d(b) is the corresponding element in the
dual basis of d(M). Then if G(1) gets eliminated, the extension does not split.
Otherwise it does.