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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346%!PS-Adobe-2.0
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(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(23)203
1600 y(B.7)80 b Fr(beg[in])53 b(/)e(end)h(/)g(start)h(;)90
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(24)203 1780 y(B.8)80
b Fr(bye)52 b(/)f(exit)i(/)e(q[uit])i(;)39 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(24)203 1960 y(B.9)80
b Fr(cc)51 b(/)h(coset)h(coinc[idence])h(:)e(<int>)g(;)65
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)
138 b(24)203 2140 y(B.10)31 b Fr(c[factor])53 b(/)f(ct[)g(factor])h(:)f
([<int>])h(;)90 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g
(.)g(.)g(.)138 b(24)203 2320 y(B.11)31 b Fr(check)52
b(/)g(redo)g(;)91 b Fx(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)
138 b(24)203 2500 y(B.12)31 b Fr(com[paction])54 b(:)e([0..100])h(;)65
b Fx(.)50 b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f
(.)h(.)g(.)g(.)g(.)g(.)138 b(24)203 2681 y(B.13)31 b
Fr(cont[inue])54 b(;)39 b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g
(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)
g(.)g(.)g(.)138 b(25)203 2861 y(B.14)31 b Fr(cy[cles])53
b(;)65 b Fx(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)
138 b(25)203 3041 y(B.15)31 b Fr(ded)52 b(mo[de])h(/)e(dmod[e])i(:)f
([0..4])h(;)65 b Fx(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f
(.)h(.)g(.)g(.)g(.)g(.)138 b(25)203 3221 y(B.16)31 b
Fr(ded)52 b(si[ze])h(/)e(dsiz[e])i(:)f([0/1..])h(;)90
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g
(.)138 b(26)203 3401 y(B.17)31 b Fr(def[ault])53 b(;)91
b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(26)203 3581 y(B.18)31 b Fr(del)52 b(gen[erators])i(/)e(ds)g(:)f(<int)
h(list>)h(;)39 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g
(.)g(.)g(.)138 b(26)203 3761 y(B.19)31 b Fr(del)52 b(rel[ators])i(/)d
(dr)h(:)g(<int)g(list>)g(;)65 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(26)203 3941 y(B.20)31
b Fr(d[ump])53 b(:)e([0/1/2[,0/1]])k(;)39 b Fx(.)50 b(.)g(.)g(.)g(.)g
(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)
138 b(26)203 4121 y(B.21)31 b Fr(easy)52 b(;)39 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f
(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(27)203 4301 y(B.22)31 b Fr(echo)52 b(:)g([0/1])g(;)91
b Fx(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(27)203 4481 y(B.23)31 b Fr(enum[eration])54 b(/)e(group)h(name)f(:)f
(<string>)j(;)39 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)
g(.)138 b(27)203 4661 y(B.24)31 b Fr(fel[sch])53 b(:)f([0/1])g(;)39
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(27)203
4841 y(B.25)31 b Fr(f[factor])53 b(/)f(fi[ll)g(factor])i(:)d([0/1..])i
(;)65 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(27)203 5021 y(B.26)31 b Fr(gen[erators])54 b(/)e(subgroup)h
(gen[erators])87 b Fx(:)33 b(<w)m(ord)g(list>)e(;)83
b(.)50 b(.)g(.)g(.)g(.)g(.)138 b(28)203 5201 y(B.27)31
b Fr(gr[oup)53 b(generators]:)h([<letter)f(list>)g(/)f(<int>])g(;)40
b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(28)203
5381 y(B.28)31 b Fr(group)52 b(relators)i(/)d(rel[ators])j(:)e
(<relation)h(list>)g(;)91 b Fx(.)49 b(.)h(.)g(.)g(.)g(.)g(.)138
b(28)203 5561 y(B.29)31 b Fr(hard)52 b(;)39 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f
(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(29)1815 6054 y(iv)p eop
%%Page: 5 5
5 4 bop 203 340 a Fx(B.30)31 b Fr(h[elp])53 b(;)90 b
Fx(.)50 b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f
(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(29)203 520 y(B.31)31 b Fr(hlt)52 b(;)90 b Fx(.)50 b(.)g(.)g(.)g(.)g
(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)
g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(29)203
700 y(B.32)31 b Fr(ho[le)52 b(limit])h(:)f([-1/0..100])i(;)65
b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g
(.)g(.)g(.)g(.)138 b(29)203 880 y(B.33)31 b Fr(look[ahead])54
b(:)d([0/1..4])j(;)39 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(29)203 1060 y(B.34)31 b Fr(loop[)52 b(limit])h(:)f([0/1..])h(;)39
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(30)203 1240 y(B.35)31
b Fr(max[)52 b(cosets])h(:)f([0/2..])h(;)39 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h
(.)g(.)g(.)g(.)g(.)138 b(30)203 1420 y(B.36)31 b Fr(mend[elsohn])54
b(:)e([0/1])g(;)65 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(30)203 1600 y(B.37)31 b Fr(mess[ages])54 b(/)d(mon[itor])j(:)d
([<int>])i(;)65 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g
(.)g(.)g(.)g(.)138 b(31)203 1780 y(B.38)31 b Fr(mo[de])53
b(;)90 b Fx(.)50 b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)
g(.)138 b(32)203 1960 y(B.39)31 b Fr(nc)51 b(/)h(normal[)h(closure])h
(:)d([0/1])i(;)65 b Fx(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(32)203 2140 y(B.40)31
b Fr(no[)52 b(relators)h(in)f(subgroup])i(:)d([-1/0/1..])j(;)65
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(32)203 2320 y(B.41)31 b Fr(oo)51 b(/)h(order[)h(option])g(:)f(<int>)g
(;)91 b Fx(.)50 b(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h
(.)g(.)g(.)g(.)g(.)138 b(33)203 2500 y(B.42)31 b Fr(opt[ions])53
b(;)91 b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f
(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(33)203 2681 y(B.43)31 b Fr(par[ameters])54 b(;)91 b
Fx(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(33)203 2861 y(B.44)31 b Fr(path[)52 b(compression])j(:)c([0/1])i(;)65
b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g
(.)g(.)g(.)g(.)138 b(33)203 3041 y(B.45)31 b Fr(pd)51
b(mo[de])i(/)f(pmod[e])h(:)f([0/1..3])h(;)90 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(34)203 3221 y(B.46)31 b Fr(pd)51 b(si[ze])i(/)f(psiz[e])h(:)f
([0/2/4/8/...])i(;)65 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g
(.)g(.)g(.)g(.)138 b(34)203 3401 y(B.47)31 b Fr(print)52
b(det[ails])i(/)d(sr)h(:)g([0/1..5])h(;)39 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(34)203 3581 y(B.48)31 b Fr(pr[int)53 b(table])f(:)g
([[-]<int>[,<int>[,<int>]])q(])57 b(;)91 b Fx(.)50 b(.)g(.)f(.)h(.)g(.)
g(.)g(.)g(.)138 b(34)203 3761 y(B.49)31 b Fr(pure)52
b(c[t])g(;)91 b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)
g(.)138 b(35)203 3941 y(B.50)31 b Fr(pure)52 b(r[t])g(;)91
b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(35)203 4121 y(B.51)31 b Fr(rc)51 b(/)h(random)h(coinc[idences]:)i
(<int>[,<int>])g(;)65 b Fx(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(35)203 4301 y(B.52)31 b Fr(rec[over])53 b(/)f(contig[uous])i(;)91
b Fx(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h
(.)g(.)g(.)g(.)g(.)138 b(35)203 4481 y(B.53)31 b Fr(rep)52
b(:)f(1..7[,<int>])k(;)90 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h
(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(35)203 4661 y(B.54)31 b Fr(restart)53 b(;)39 b Fx(.)50
b(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(36)203 4841 y(B.55)31 b Fr(r[factor])53 b(/)f(rt[)g(factor])h(:)f
([<int>])h(;)90 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g
(.)g(.)g(.)138 b(36)203 5021 y(B.56)31 b Fr(row[)52 b(filling])h(:)f
([0/1])h(;)90 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(36)203
5201 y(B.57)31 b Fr(sc)51 b(/)h(stabil[ising)i(cosets])g(:)d(<int>)i(;)
90 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)
138 b(36)203 5381 y(B.58)31 b Fr(sims)52 b(:)g(1/3/5/7/9)h(;)39
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(37)203
5561 y(B.59)31 b Fr(st[andard)53 b(table])g(;)39 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(37)1829 6054
y(v)p eop
%%Page: 6 6
6 5 bop 203 340 a Fx(B.60)31 b Fr(stat[istics])54 b(/)e(stats)g(;)65
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(37)203 520 y(B.61)31
b Fr(style)52 b(;)65 b Fx(.)50 b(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)
g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f
(.)h(.)g(.)g(.)g(.)g(.)138 b(37)203 700 y(B.62)31 b Fr(subg[roup)53
b(name])g(:)e(<string>)j(;)65 b Fx(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(37)203
880 y(B.63)31 b Fr(sys[tem])53 b(:)f(<string>)h(;)39
b Fx(.)50 b(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(38)203 1060
y(B.64)31 b Fr(text)52 b(:)g(<string>)h(;)90 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g
(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138 b(38)203 1240
y(B.65)31 b Fr(ti[me)52 b(limit])h(:)f([-1/0/1..])i(;)39
b Fx(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h
(.)g(.)g(.)g(.)g(.)138 b(38)203 1420 y(B.66)31 b Fr(tw)51
b(/)h(trace[)h(word])f(:)g(<int>,<word>)i(;)65 b Fx(.)50
b(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(38)203 1600 y(B.67)31 b Fr(wo[rkspace])54 b(:)d([<int>[k/m/g]])k(;)40
b Fx(.)50 b(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g
(.)g(.)g(.)138 b(38)203 1780 y(B.68)31 b Fr(#)51 b(...)h(<newline>)42
b Fx(.)49 b(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(39)57 1960 y Fu(C)65 b(State)38 b(mac)m(hine)e(details)2287
b(40)57 2140 y(D)60 b(Abbreviations)2648 b(47)57 2320
y(References)2959 b(51)1815 6054 y Fx(vi)p eop
%%Page: 7 7
7 6 bop 1370 793 a Fv(List)54 b(of)g(\014gures)203 1139
y Fx(C.1)79 b(The)33 b(R/C)g(st)m(yle)i(.)50 b(.)g(.)f(.)h(.)g(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)
f(.)h(.)g(.)g(.)g(.)g(.)138 b(40)203 1319 y(C.2)79 b(The)33
b(R*)f(st)m(yle)d(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)
g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g
(.)g(.)138 b(41)203 1499 y(C.3)79 b(The)33 b(Cr)g(st)m(yle)41
b(.)50 b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)
g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(42)203 1679 y(C.4)79 b(The)33 b(C)g(st)m(yle)79 b(.)50
b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(43)203 1859 y(C.5)79 b(The)33 b(Rc)g(st)m(yle)h(.)50
b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
b(44)203 2039 y(C.6)79 b(The)33 b(R)g(st)m(yle)77 b(.)50
b(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g
(.)g(.)g(.)g(.)g(.)g(.)g(.)g(.)f(.)h(.)g(.)g(.)g(.)g(.)138
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4043 y(redo.)169 4276 y Fu(B.14)112 b Fr(cy[cles])53
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3145 y(giv)m(en)f(are,)i(in)d(order:)52 b Fr(a)p Fx(,)37
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(\014lled)g(\(sub)5 b(ject)37 b(to)f(the)g(v)-5 b(alue)35
b(of)42 b Fr(fi)p Fx(\).)54 b(If)36 b(the)g(argumen)m(t)57
921 y(is)30 b Fr(1)p Fx(,)h(they)g(are)g(\014lled)e(immediately)-8
b(,)28 b(and)i(if)g(it)f(is)h Fr(2)p Fx(,)h(the)g(consequen)m(t)i
(deduction)e(is)f(also)f(made)57 1047 y(immediately)i(\(of)j(course,)j
(these)e(are)g(also)e(put)i(on)g(the)f(deduction)h(stac)m(k\).)51
b(If)34 b(the)h(argumen)m(t)57 1174 y(is)f Fr(3)p Fx(,)h(then)g(the)g
(gaps)g(are)f(noted)h(in)e(the)i(preferred)h(de\014nition)d(queue.)51
b(Pro)m(vided)35 b(a)f(liv)m(e)f(suc)m(h)57 1300 y(gap)28
b(surviv)m(es)i(\(and)f(no)f(coincidence)h(o)s(ccurs,)h(whic)m(h)f
(causes)h(the)f(queue)h(to)e(b)s(e)g(discarded\))h(the)57
1427 y(next)40 b(coset)f(will)e(b)s(e)i(de\014ned)h(to)e(\014ll)f(the)j
(oldest)e(gap)g(of)h(length)f(one.)62 b(The)40 b(default)e(v)-5
b(alue)38 b(is)57 1553 y(either)h Fr(0)g Fx(or)g Fr(3)p
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f(3.2\).)63 b(If)39 b(y)m(ou)h(w)m(an)m(t)g(to)57 1679
y(kno)m(w)34 b(more)e(details,)f(read)i(the)g(co)s(de.)169
1913 y Fu(B.46)112 b Fr(pd)52 b(si[ze])h(/)e(psiz[e])i(:)f
([0/2/4/8/...])j(;)57 2114 y Fx(The)29 b(preferred)h(de\014nition)d
(queue)j(is)e(implemen)m(ted)f(as)h(a)g(ring,)h(dropping)e(earliest)h
(en)m(tries.)42 b(Its)57 2241 y(size)c Fm(must)48 b Fx(b)s(e)39
b(2)687 2205 y Fj(n)717 2241 y Fx(,)h(for)d(some)h Fq(n)g(>)f
Fx(0.)60 b(An)39 b(argumen)m(t)f(of)44 b Fr(0)39 b Fx(selects)g(the)g
(default)e(size)i(of)e(256.)57 2367 y(Eac)m(h)32 b(queue)h(slot)d(tak)m
(es)i(t)m(w)m(o)g(w)m(ords)g(\(i.e.,)f(8)g(b)m(ytes\),)i(and)e(the)g
(queue)i(can)e(store)h(up)f(to)g(2)3441 2331 y Fj(n)3507
2367 y Fk(\000)19 b Fx(1)57 2494 y(en)m(tries.)169 2727
y Fu(B.47)112 b Fr(print)53 b(det[ails])g(/)f(sr)g(:)f([0/1..5])j(;)57
2929 y Fx(This)43 b(command)f(prin)m(ts)h(out)g(details)f(of)h(the)h
(curren)m(t)g(presen)m(tation)g(and)f(parameters.)75
b(No)57 3055 y(argumen)m(t,)34 b(or)g(an)g(argumen)m(t)g(of)41
b Fr(0)p Fx(,)34 b(prin)m(ts)h(out)f(the)g(group)g Fs(&)g
Fx(subgroup)h(name,)f(the)g(group's)57 3182 y(relators)21
b(and)h(the)g(subgroup's)h(generators.)40 b(If)22 b(the)g(argumen)m(t)g
(is)f Fr(1)p Fx(,)j(then)f(the)f(group)f(generators)57
3308 y(and)28 b(the)g(curren)m(t)g(setting)f(of)h(the)f(en)m(umeration)
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b(\(This)57 3434 y(prin)m(tout)37 b(is)f(the)i(same)e(as)i(that)e(pro)s
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(on.\))57 3561 y(Argumen)m(ts)23 b(of)29 b Fr(2)23 b
Fx({)g Fr(5)g Fx(prin)m(t)f(out)h(the)g(curren)m(t)h(v)-5
b(alues)22 b(of)30 b Fr(enum)p Fx(,)c Fr(rel)p Fx(,)f
Fr(subg)f Fs(&)e Fr(gen)p Fx(,)k(resp)s(ectiv)m(ely)-8
b(.)57 3687 y(See)33 b(App)s(endix)g(A)g(for)f(some)h(examples.)57
3867 y Fi(Notes:)51 b Fx(The)37 b(output)g(is)f(prin)m(ted)h(out)g(in)f
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3994 y(a)d(previous)h(run)f(can)h(b)s(e)f(used)i(to)d(replicate)h(the)g
(run.)49 b(Note)35 b(that,)f(due)h(to)f(the)h(defaulting)d(of)57
4120 y(some)j(parameters)h(and)g(the)f(sp)s(ecial)g(meaning)f(attac)m
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4246 y(to)j(b)s(e)g(tak)m(en)h(in)e(in)m(terpreting)h(the)g
(parameters.)60 b(If)38 b(y)m(ou)h(wish)f(to)g Fm(exactly)46
b Fx(duplicate)38 b(a)f(run,)57 4373 y(y)m(ou)c(should)g(use)g(the)g
(output)g(of)39 b Fr(sr)33 b Fm(after)43 b Fx(the)33
b(run)g(completes.)169 4606 y Fu(B.48)112 b Fr(pr[int)53
b(table])g(:)e([[-]<int>[,<int>[,<int>])q(]])57 b(;)57
4808 y Fx(Compact)37 b(the)g(table,)h(and)f(then)g(prin)m(t)g(it)f(out)
h(from)e(the)j(\014rst)f(to)g(the)g(second)i(argumen)m(t,)f(in)57
4934 y(steps)44 b(of)e(the)h(third)f(argumen)m(t.)73
b(If)42 b(the)h(\014rst)g(argumen)m(t)f(is)g(negativ)m(e,)k(then)d(the)
g(orders)g(\(if)57 5061 y(a)m(v)-5 b(ailable\))42 b(and)j(represen)m
(tativ)m(es)i(of)d(the)h(cosets)h(are)e(prin)m(ted)h(also.)79
b(The)45 b(third)f(argumen)m(t)57 5187 y(defaults)i(to)g(one.)85
b(The)48 b(one-argumen)m(t)e(form)f(is)h(equiv)-5 b(alen)m(t)46
b(to)g(the)h(t)m(w)m(o-argumen)m(t)f(form)57 5313 y(with)e(a)g(\014rst)
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b(form)f(prin)m(ts)i(the)g(en)m(tire)f(table,)g(without)g(orders)i(or)e
(represen)m(tativ)m(es.)1806 6054 y(34)p eop
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35 42 bop 169 340 a Fu(B.49)112 b Fr(pure)52 b(c[t])h(;)57
542 y Fx(Sets)31 b(the)f(strategy)g(to)f(basic)h(C-st)m(yle)g(\(coset)h
(table)e(based\))h({)g(no)f(compaction,)g(no)h(gap-\014lling,)57
668 y(no)i(relators)g(in)g(subgroup;)h(see)h(Section)f(3.2.)169
902 y Fu(B.50)112 b Fr(pure)52 b(r[t])h(;)57 1103 y Fx(Sets)38
b(the)f(strategy)g(to)g(basic)f(R-st)m(yle)h(\(relator)e(based\))j({)f
(no)f(Mendelsohn,)j(no)e(compaction,)57 1230 y(no)32
b(lo)s(ok)-5 b(ahead,)32 b(no)g(ro)m(w-\014lling;)e(see)k(Section)e
(3.2.)169 1463 y Fu(B.51)112 b Fr(rc)52 b(/)f(random)i(coinc[idences]:)
j(<int>[,<int>])e(;)57 1665 y Fx(This)36 b(option)e(attempts)i(to)f
(\014nd)h(non)m(trivial)e(subgroups)i(with)g(index)g(a)f(m)m(ultiple)e
(of)i(the)h(\014rst)57 1791 y(argumen)m(t)e(b)m(y)i(rep)s(eatedly)e
(putting)g(random)g(cosets)i(coinciden)m(t)e(with)g(coset)h(#1)g(and)g
(seeing)57 1918 y(what)44 b(happ)s(ens.)78 b(If)43 b(the)h(\014rst)g
(argumen)m(t)g(is)f Fr(0)h Fx(an)m(y)g Fm(non-trivial)53
b Fx(\014nite)43 b(index)h(is)f(accepted,)57 2044 y(while)34
b(if)g(it's)g Fr(1)h Fm(any)44 b Fx(\014nite)35 b(index)g(will)d(do.)51
b(The)36 b(starting)e(coset)h(table)g(m)m(ust)g(b)s(e)g(non-empt)m(y)-8
b(,)57 2170 y(but)41 b(should)g(not)f(b)s(e)h(complete.)67
b(The)42 b(second)g(argumen)m(t)e(puts)i(a)e(limit)d(on)k(the)g(n)m(um)
m(b)s(er)g(of)57 2297 y(attempts,)30 b(with)e(a)h(default)g(of)f(eigh)m
(t.)42 b(F)-8 b(or)29 b(eac)m(h)h(attempt,)f(w)m(e)h(rep)s(eatedly)g
(add)f(random)f(coset)57 2423 y(represen)m(tativ)m(es)36
b(to)d(the)g(subgroup)h(and)g(redo)f(the)h(en)m(umeration.)45
b(If)34 b(the)f(table)g(b)s(ecomes)h(to)s(o)57 2550 y(small,)i(the)i
(attempt)f(is)g(ab)s(orted,)h(the)g(original)c(subgroup)k(generators)g
(restored,)h(the)f(CT)g(is)57 2676 y(recalculated,)29
b(and)h(another)f(attempt)f(made.)42 b(If)30 b(an)f(attempt)f
(succeeds,)33 b(then)d(the)f(new)h(set)g(of)57 2802 y(subgroup)j
(generators)g(is)f(retained.)57 2982 y Fi(Gur)n(u)e(Notes:)39
b Fx(\(i\))25 b(A)h(coset)h(can)f(ha)m(v)m(e)h(man)m(y)e(di\013eren)m
(t)h(represen)m(tativ)m(es.)44 b(Consider)26 b(running)57
3109 y Fr(st)39 b Fx(b)s(efore)g Fr(rc)p Fx(,)i(to)d(canonicise)h(the)g
(table)f(and)h(the)g(represen)m(tativ)m(es.)64 b(This)39
b(mak)m(es)h(the)f(reps)57 3235 y(minimal;)29 b(sadly)-8
b(,)33 b(ho)m(w)m(ev)m(er,)i(it)d(will)e(only)i(do)h(so)g(for)f(the)h
(\014rst)h(of)e(a)g(series)i(of)e(attempts.)44 b(\(ii\))31
b(If)57 3362 y(a)j(series)g(of)g(attempts)f(to)h(\014nd)g(a)g(subgroup)
g(fails,)f(consider)h(running)g(the)g(en)m(umeration)f(with)57
3488 y(di\013eren)m(t)43 b(parameters.)73 b(Although)41
b Fr(rc)i Fx(is)f(random,)i(it)e(is)g(alw)m(a)m(ys)h(w)m(orking)f(with)
g(the)h(same)57 3614 y(coset)34 b(table;)f(c)m(hanging)g(the)g
(parameters)h(will)d(giv)m(e)i(a)g(di\013eren)m(t)g(table)g(and)g
(hence)i(a)e(di\013eren)m(t)57 3741 y(set)g(of)f(reps.)169
3974 y Fu(B.52)112 b Fr(rec[over])54 b(/)d(contig[uous])k(;)57
4176 y Fx(In)m(v)m(ok)m(es)39 b(the)e(compaction)e(routine)g(on)i(the)f
(table)g(to)g(reco)m(v)m(er)i(the)e(space)i(used)f(b)m(y)g(an)m(y)g
(dead)57 4302 y(cosets.)43 b(A)28 b Fr(CO)g Fx(message)g(line)e(is)h
(prin)m(ted)g(if)g(an)m(y)h(cosets)h(w)m(ere)f(reco)m(v)m(ered,)j(and)d
(a)f Fr(co)h Fx(line)e(if)g(none)57 4429 y(w)m(ere.)44
b(This)30 b(routine)f(is)g(called)f(automatically)e(if)j(the)h
Fr(cy)p Fx(,)h Fr(nc)p Fx(,)f Fr(pr)g Fx(or)g Fr(st)g
Fx(options)f(are)g(in)m(v)m(ok)m(ed.)169 4662 y Fu(B.53)112
b Fr(rep)52 b(:)g(1..7[,<int>])i(;)57 4864 y Fx(The)39
b Fr(rep)f Fx(\(random)f(equiv)-5 b(alen)m(t)37 b(presen)m(tations\))i
(option)d(complemen)m(ts)i(the)g Fr(aep)g Fx(option.)58
b(It)57 4990 y(generates)28 b(and)e(tests)i(some)e(random)g(equiv)-5
b(alen)m(t)26 b(presen)m(tations.)43 b(The)27 b(mandatory)f(argumen)m
(t)57 5117 y(acts)j(as)f(for)g Fr(aep)p Fx(,)i(while)d(the)i(optional)d
(second)j(argumen)m(t)f(sets)i(the)e(n)m(um)m(b)s(er)h(of)f(presen)m
(tations,)57 5243 y(with)k(a)g(default)g(of)g(eigh)m(t.)57
5423 y(The)40 b(routine)e(\014rst)h(turns)h Fr(asis)g
Fx(on)f(and)f Fr(mess)i Fx(o\013,)g(and)f(then)h(generates)g(and)f
(tests)h(the)f(re-)57 5549 y(quested)45 b(equiv)-5 b(alen)m(t)43
b(presen)m(tations.)75 b(F)-8 b(or)42 b(eac)m(h)i(presen)m(tation)g
(the)f(relators)f(used)i(and)f(the)1806 6054 y(35)p eop
%%Page: 36 44
36 43 bop 57 340 a Fx(summary)27 b(result)g(line)f(is)h(prin)m(ted.)42
b Fr(asis)28 b Fs(&)f Fr(mess)h Fx(are)g(no)m(w)g(restored)g(to)f
(their)g(original)d(v)-5 b(alues,)57 467 y(and)33 b(the)g(system)g(is)f
(ready)i(for)e(further)g(commands.)57 647 y Fi(Notes:)75
b Fx(The)49 b(relator)f(in)m(v)m(ersions)h Fs(&)f Fx(rotations)f(are)i
(`gen)m(uinely')g(random.)91 b(The)49 b(relator)57 773
y(p)s(erm)m(uting)36 b(is)g(a)h(little)d(bit)i(of)g(a)h(kludge,)h(with)
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899 y(to)41 b(impro)m(v)m(e)f(with)h(successiv)m(e)i(presen)m(tations.)
70 b(When)42 b(the)f Fr(rep)h Fx(command)d(completes,)k(the)57
1026 y(presen)m(tation)33 b(activ)m(e)g(is)f(the)h Fm(last)42
b Fx(one)33 b(generated.)57 1206 y Fi(Gur)n(u)46 b(Note:)59
b Fx(It)40 b(migh)m(t)g(app)s(ear)g(that)g(neglecting)g(to)g(restore)h
(the)g(original)c(presen)m(tation)57 1332 y(is)45 b(an)h(error.)84
b(In)46 b(fact,)j(it)c(is)g(a)h(useful)g(feature!)84
b(Supp)s(ose)47 b(that)e(the)i(space)g(of)e(equiv)-5
b(alen)m(t)57 1459 y(presen)m(tations)43 b(is)g(to)s(o)e(large)h(to)g
(exhaustiv)m(ely)h(test.)75 b(As)43 b(noted)g(in)e(the)i(en)m(try)h
(for)e Fr(aep)p Fx(,)k(w)m(e)57 1585 y(can)34 b(start)g(up)h(m)m
(ultiple)c(copies)k(of)40 b Fr(aep)35 b Fx(at)f(random)f(p)s(oin)m(ts)h
(in)f(the)i(searc)m(h-space.)50 b(Man)m(ually)57 1712
y(generating)44 b(`random')f(equiv)-5 b(alen)m(t)44 b(presen)m(tations)
i(to)e(serv)m(e)i(as)e(starting-p)s(oin)m(ts)f(is)h(tedious)57
1838 y(and)37 b(error-prone.)56 b(The)38 b Fr(rep)g Fx(option)e(pro)m
(vides)i(a)e(simple)g(solution;)h(simply)f(run)h Fr(rep)h
Fx(b)s(efore)57 1964 y Fr(aep)p Fx(!)169 2198 y Fu(B.54)112
b Fr(restart)53 b(;)57 2399 y Fx(An)47 b(old)e(option,)k(included)d
(for)g(bac)m(kw)m(ard)i(compatibilit)m(y)-8 b(.)81 b(Use)47
b(the)g Fr(check/redo)i Fx(option)57 2526 y(instead.)h(Pre-)p
Fo(A)m(CE)36 b Fx(3.001)e(scripts)i(ma)m(y)e(con)m(tain)h(this)f
(option,)h(whic)m(h)g(is)f(quietly)h(ignored)f(b)m(y)57
2652 y Fo(A)m(CE)g Fx(3.001.)169 2886 y Fu(B.55)112 b
Fr(r[factor])54 b(/)d(rt[)h(factor])h(:)f([<int>])h(;)57
3087 y Fx(The)33 b(v)-5 b(alue)32 b(of)f(this)h(parameter)g(sets)h(the)
g(`blo)s(c)m(king)e(factor')h(for)g(R-st)m(yle)g(de\014nitions;)f
(i.e.,)h(the)57 3214 y(n)m(um)m(b)s(er)25 b(of)g(cosets)h(applied)e(to)
h(all)d(the)k(relators)e(during)g(eac)m(h)i(pass)g(through)f(the)g(en)m
(umerator's)57 3340 y(main)32 b(lo)s(op.)45 b(The)35
b(absolute)e(v)-5 b(alue)34 b(of)40 b Fr(<int>)35 b Fx(is)e(the)h(v)-5
b(alue)33 b(used.)48 b(The)35 b(en)m(umeration)e(st)m(yle)h(is)57
3467 y(selected)g(b)m(y)f(the)g(v)-5 b(alues)33 b(of)f(the)h
Fr(ct)g Fs(&)f Fr(rt)h Fx(parameters;)g(see)g(Section)g(3.1.)169
3700 y Fu(B.56)112 b Fr(row[)52 b(filling])i(:)d([0/1])i(;)57
3902 y Fx(When)41 b(making)e(HL)-8 b(T-st)m(yle)40 b(de\014nitions,)i
(it)d(is)g(normal)f(to)i(scan)h(eac)m(h)g(ro)m(w)f(of)g(the)g(table)g
(af-)57 4028 y(ter)g(its)f(coset)i(has)f(b)s(een)g(applied)f(to)g(all)f
(relators,)j(and)f(mak)m(e)g(de\014nitions)f(to)g(\014ll)g(an)m(y)h
(holes)57 4154 y(encoun)m(tered.)65 b(F)-8 b(ailure)37
b(to)i(do)g(so)h(can)f(cause)h(ev)m(en)h(simple)d(en)m(umerations)h(to)
f(o)m(v)m(er\015o)m(w;)45 b(see)57 4281 y(Section)32
b(A.3.)44 b(T)-8 b(o)32 b(turn)h(ro)m(w)g(\014lling)d(o\013,)j(use)g
Fr(row:0)p Fx(.)169 4514 y Fu(B.57)112 b Fr(sc)52 b(/)f(stabil[ising)k
(cosets])e(:)f(<int>)g(;)57 4716 y Fx(This)24 b(option)f(tak)m(es)i
(the)f(curren)m(t)h(table)e(\(whic)m(h)h(ma)m(y)g(or)f(ma)m(y)h(not)f
(b)s(e)h(complete\),)h(and)f(lo)s(oks)f(for)57 4842 y(\(the)34
b(requested)i(n)m(um)m(b)s(er)e(of)7 b(\))33 b(cosets)i(whic)m(h)f
(`stabilise')f(the)h(subgroup.)47 b(A)34 b(coset)g Fq(c)g
Fx(stabilises)57 4969 y(the)g(subgroup)h Fk(h)p Fq(w)760
4984 y Fp(1)799 4969 y Fq(;)17 b(:)g(:)g(:)f(;)h(w)1088
4984 y Fj(s)1124 4969 y Fk(i)33 b Fx(if)g Fq(cw)1399
4984 y Fj(j)1465 4969 y Fx(=)d Fq(c)k Fx(for)f(all)f(1)d
Fk(\024)i Fq(j)36 b Fk(\024)30 b Fq(s)p Fx(.)47 b(If)34
b Fr(<int>)d Fq(>)f Fx(0,)k(the)g(\014rst)h Fr(<int>)57
5095 y Fx(stabilising)f(cosets)39 b(found)e(are)h(prin)m(ted.)57
b(If)37 b Fr(<int>)g Fx(=)f(0,)i(all)d(of)i(the)h(stabilising)c
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b(are)c(prin)m(ted.)60 b(If)37 b Fr(<int>)h Fq(<)f Fx(0,)i(the)f
(\014rst)h Fk(j)p Fr(<int>)q Fk(j)e Fx(stabilising)e(cosets,)57
5348 y(plus)d(their)h(represen)m(tativ)m(es,)i(are)d(prin)m(ted.)1806
6054 y(36)p eop
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@endspecial 57 5230 V 1806 6054 a(46)p eop
%%Page: 47 55
47 54 bop 1505 758 a Fz(Appendix)45 b(D)1359 1033 y Fv(Abbreviations)57
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