File format for finitely presented groups in the STLP system
R. A. Parker and P. E. Holmes  01.09.07  Version 3.1

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A finitely presented group file shall consist of a sequence of integers
separated by whitespace.  Hence spaces and newlines can appear anywhere
within the file.

The file shall consist of a sequence of groups.

The information for each group is divided into "blimps".  Each  blimp
contains a specific piece of information and has a blimp  type, which
is a positive integer.  For each blimp, the first number is the blimp
type, and the second is the number of integers in the blimp, not
counting the type or the length.

The blimps shall be in increasing order of type, and no blimp type 
shall be present more than once. 

Blimps 0, 1 and 2 are essential.  Every file of this format must contain
Blimp 0 at the end, and every group in the file must have  Blimps 1 and
2 and 999.  The other blimps will be essential for some  of the programs
and not others, and can be created, updated, copied or deleted by the 
programs.

We use two presentations for each group.  These are the "external"
presentation and the "internal" one.  The external presentation is the
one that is given by the user, for example giving the group as a
2,3-group, while the internal  presentation is the one that is used by
the programs.  Both presentations must give isomorphic groups. None of
the programs in the main group analysis suite shall change blimps 1 or 
2. 

The maps between the two groups are given in blimps 4 and 5.  Let f4
and f5 be the two maps.  Then f4.f5 must take each internal generator to
a word in the interal generators that is equal modulo the relators in
blimp 6 (basic relators) and f5.f4 must take each external generator to
a word that is equal modulo the relators in blimp 2 (external
presentation).

Here are the descriptions of each blimp:

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0 - This is the "end of file" blimp.  It must follow the last group in
the file.  Hence the first integer after the start of the file, or after
the 999 blimp of a group is either 0 (no more groups) or 1 (name of next
group).
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1 - This blimp contains the "name" of the group, to be used by programs
to indicate which group this is.  The first integer is a globally
significant integer to indicate what sort of group this is.  Further
information for such types of groups may also be stored in the name.  
The name is a sequence of integers. 
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2 - This blimp holds the external presentation.  After the type and the
length, the next integer is the number ng of generators and then the
number nr of relators.  This is followed by nr relators each terminated
by a zero.
Each relator is therefore given as a sequence of integers from 1 to ng
or from -1 down to -ng, where each integer i is identified with the
i-th generator, and a negative integer -i identified with the inverse
of generator i.  The sequence is read as a word in those generators.
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3 - This blimp holds the internal generators and the inverse table.
The first integer shall be the number of generators g.  The set of
generators shall be closed under inversion, and the next g integers
shall be the inverse of each generator.  The generators shall be
numbered from 1 to g.
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4 - The map from the generating set of the internal presentation into 
the group generated by the external generators.  This blimp consists of
words of integers separated by zeroes.  These words give each internal
generator in turn as a word in the external generators and their 
inverses, where a negative integer -i represents the inverse of the
external generator i.
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5 - As blimp 4, but the map goes in the opposite direction, from the
external generators to the internal ones.  The ng words give the
external generators as words in the internal ones, and in this case
negative generators are not allowed since the internal generators are 
closed under inversion.  
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6 - This blimp gives the basic relators.  These are in terms of the 
internal generators.
The first integer in this blimp shall be the number of (basic) relators 
r.  There then follows r strings of generators each terminated by  0,
being the basic relators as words in the internal generators.  All
generators are positive. 
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100 - This blimp gives the "project".  It is (famous last words) a
temporary blimp to enable work to start on the second batch or programs
to do the triangle project.  It consists of four words.  The first must
be 1 to indicate a triangle group.  The remaining 3 words are then the 
smallest triangle relator whose inclusion in the external presentation 
has not been decided.
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999 - This blimp is the last blimp of a group.  It has no length, and
is immediately followed by a 1 (the name of the next group) or a 0 to
indicate that there are no more groups in the file
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