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# 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;
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