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Chapter 1.
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Chapter 2.
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rec-to-ries \T1/cmtt/m/n/10.95 data/data8-3nil
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\T1/ptm/m/n/10.95 and \T1/cmtt/m/n/10.95 data/data8\T1/ptm/m/n/10.95 . The for-
mer con-tains the data re-lat-ing to 3-nilpotent semi-groups (see
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[9]
Chapter 3.
[10

] [11] [12] [13] [14] [15] [16]
Chapter 4.

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[]\T1/ptm/m/n/10.95 returns \T1/cmtt/m/n/10.95 true \T1/ptm/m/n/10.95 if [] is 
a semi-group from the li-brary, that is if it was cre-ated us-ing
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[][] \T1/ptm/m/n/10.95 is a rep-re-sen-ta-tion sat-is-fy-ing []
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\T1/ptm/m/n/10.95 and \T1/cmtt/m/n/10.95 IsMultiplicativeElement \T1/ptm/m/n/10
.95 (\T1/ptm/b/n/10.95 Reference: Is-Mul-ti-plica-tiveEle-ment\T1/ptm/m/n/10.95
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[]\T1/ptm/m/n/10.95 To cre-ate a semi-group with the mul-ti-pli-ca-tion ta-ble 
ob-tained by
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\T1/cmtt/m/n/10.95 RecoverMultiplicationTable([]) \T1/ptm/m/n/10.95 use the fun
c-tion \T1/cmtt/m/n/10.95 SmallSemigroup \T1/ptm/m/n/10.95 ([][]4.1.1[][]) with
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[36]
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[]\T1/ptm/m/n/10.95 The fol-low-ing func-tions have the same us-age but may re-
turn dif-fer-ent val-
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\T1/ptm/m/n/10.95 ues: \T1/cmtt/m/n/10.95 EnumeratorOfSmallSemigroups \T1/ptm/m
/n/10.95 ([][]4.5.2[][]), \T1/cmtt/m/n/10.95 AllSmallSemigroups \T1/ptm/m/n/10.
95 ([][]4.5.1[][]),
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\T1/cmtt/m/n/10.95 EnumeratorSortedOfSmallSemigroups \T1/ptm/m/n/10.95 ([][]4.5
.4[][]), \T1/cmtt/m/n/10.95 IdsOfSmallSemigroups \T1/ptm/m/n/10.95 ([][]4.5.7[]
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\T1/cmtt/m/n/10.95 IteratorOfSmallSemigroups \T1/ptm/m/n/10.95 ([][]4.5.11[][])
, \T1/cmtt/m/n/10.95 NrSmallSemigroups \T1/ptm/m/n/10.95 ([][]4.5.15[][]), \T1/
cmtt/m/n/10.95 OneSmallSemigroup
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[]\T1/ptm/m/n/10.95 For ex-am-ple, to ob-tain all the com-mu-ta-tive semi-group
s with [] idem-po-tents of sizes
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[] \T1/ptm/m/n/10.95 to [] use one of \T1/cmtt/m/n/10.95 EnumeratorOfSmallSemig
roups \T1/ptm/m/n/10.95 ([][]4.5.2[][]), \T1/cmtt/m/n/10.95 AllSmallSemigroups 
\T1/ptm/m/n/10.95 ([][]4.5.1[][]),
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\T1/cmtt/m/n/10.95 AllSmallSemigroups \T1/ptm/m/n/10.95 ([][]4.5.1[][]) re-turn
s a list of all such semi-groups,
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\T1/cmtt/m/n/10.95 EnumeratorOfSmallSemigroups \T1/ptm/m/n/10.95 ([][]4.5.2[][]
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[]\T1/cmtt/m/n/10.95 EnumeratorOfSmallSemigroups \T1/ptm/m/n/10.95 ([][]4.5.2[]
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[]\T1/ptm/m/n/10.95 If \T1/cmtt/m/n/10.95 arg[1] \T1/ptm/m/n/10.95 is a list of
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/ptm/m/n/10.95 re-turns
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\T1/ptm/m/n/10.95 an enu-mer-a-tor of all the small semi-groups \T1/cmtt/m/n/10
.95 S \T1/ptm/m/n/10.95 in the li-brary with \T1/cmtt/m/n/10.95 Size(S) in arg[
1] \T1/ptm/m/n/10.95 and
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[]\T1/ptm/m/n/10.95 If \T1/cmtt/m/n/10.95 arg[1] \T1/ptm/m/n/10.95 is an enu-me
r-a-tor or it-er-a-tor of small semi-groups, then
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[]\T1/ptm/m/n/10.95 returns a list of the func-tions and their val-ues that wer
e used to cre-ate the enu-mer-
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\T1/ptm/m/n/10.95 a-tor of small semi-groups []. If you only want the names of 
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[]\T1/ptm/m/n/10.95 If \T1/cmtt/m/n/10.95 arg[1] \T1/ptm/m/n/10.95 is a list of
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[]\T1/ptm/m/n/10.95 returns \T1/cmtt/m/n/10.95 true \T1/ptm/m/n/10.95 if [] is 
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[]\T1/ptm/m/n/10.95 returns \T1/cmtt/m/n/10.95 true \T1/ptm/m/n/10.95 if [] is 
an it-er-a-tor of small semi-groups cre-ated us-ing
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\T1/ptm/m/n/10.95 re-turns an it-er-a-tor of all the small semi-groups \T1/cmtt
/m/n/10.95 S \T1/ptm/m/n/10.95 in the li-brary with \T1/cmtt/m/n/10.95 S in arg
[1] \T1/ptm/m/n/10.95 and
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[]\T1/ptm/m/n/10.95 The func-tion re-turns a list of the sec-ond com-po-nents o
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\T1/ptm/m/n/10.95 of all the small semi-groups \T1/cmtt/m/n/10.95 S \T1/ptm/m/n
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95 in \T1/cmtt/m/n/10.95 arg[1] \T1/ptm/m/n/10.95 or \T1/cmtt/m/n/10.95 Size(S)
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