test000.in

# test000.in - Colin Ramsay - 15 Mar 99
#
# An example of the trivial group from p18 of Coxeter & Moser (3rd edn).

Mess:10000;

Gr: r,s;
Rel: rs^2=s^3r, sr^2=r^3s;

# The book does this in 6; we manage 7!

Gen: r;
Fel:1;  No:0;
End;

# This (ie, 27) is the best I can find over the trivial subgroup.

Gen: ;
Fel:1;
Aep:7;

# A winning presentation is ...

Rel: srrSRRR, RSSSrss;
Diagnostics:2;
End;

# An explicit defn sequence; pri coincs are 9=5 & 18=26.
# We seem to need these, but we can shave it down to t=23.

Gr: r,s;
Rel: rs^2=s^3r, sr^2=r^3s;
Gen:
 r R,  			# 2
 rr RR,  		# 3
 rrr RRR,  		# 4
 rrrs SRRR,  		# 5
 rrrsR rSRRR,  		# 6
 rrrsRR rrSRRR,		# 7
 S s,  			# 8
 SS ss,  		# 9
 SSR rss,  		# 10
 SSRs Srss,  		# 11
 SSRss SSrss,  		# 12
 SSRsss SSSrss,		# 13
 rs SR,  		# 14
 rS sR,  		# 15
# rrs SRR,  		# 16
# rrS sRR,  		# 17
 rrrr RRRR,  		# 18
 rrrS sRRR,  		# 19
# rrrsr RSRRR, 		# 20
# rrrss SSRRR,  	# 21
 rrrsRs SrSRRR,  	# 22
 rrrsRS srSRRR,  	# 23
 rrrsRSS ssrSRRR,	# 24
 rrrSR rsRRR,  		# 25
 rSr RsR,  		# 26
 SSRS srss;  		# 27

AsIs:1;
No:0;       		# Since done _before_ first DD!
Di:0;
End;

# Looking at the coinc words, and `priming' the system to look for them,
#   shows that rrr & rS are good (aep gives t=25).
# This yields the run (with 16=8, 14=19 & 22=23), which we can take down
#   to t=22.

Gen:
 r R,  		# 2
 rr RR,  	# 3
 rrr RRR,  	# 4
 rS sR,  	# 5
 R r,  		# 6
 RS sr,  	# 7
 RSr Rsr,  	# 8
 RSrr RRsr,  	# 9
 s S,  		# 10
 sr RS,  	# 11
 srS sRS,  	# 12
 srSS ssRS,  	# 13
 srSSR rssRS,  	# 14
 srSSRs SrssRS,	# 15
# rs SR,  	# 16 !
# rrs SRR,  	# 17
# rrS sRR,  	# 18
 rrrs SRRR,  	# 19
 rrrS sRRR,  	# 20
 rrrSR rsRRR,  	# 21
 rrrr RRRR,  	# 22
 rSr RsR,  	# 23
 srSSRR rrssRS,	# 24
 srSSRRs SrrssRS; # 25

End;
Stat;