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b(PERMS)1742 1204 y Fy(B.)33 b(Fiedler)1140 1320 y(Alfred-Rosc)m(h-Str.)43 b(13,)32 b(D-04249)f(Leipzig)881 1436 y(email:)41 b(Bernd.Fiedler.Rosc)m(hStr.Leipzig@t-online.de)1692 1632 y(Marc)m(h,)34 b(1999)523 1989 y Fx(1)135 b(General)45 b(c)l(haracteristics)i(of)e Fw(PERMS)523 2171 y Fv(The)29 b(program)f(pac)n(k)-5 b(age)27 b Fu(PERMS)o Fv(,)j(v)n(ersion)e(2.1)g (\(15.1.1999\))2491 2141 y Ft(1)2555 2171 y Fv(is)h(a)g Fu(Mathematica)o Fv(-pac)n(k-)523 2271 y(age.)42 b(It)30 b(is)g(a)f(collection)g(of)h(to)r(ols)f(for)g(in)n(v)n(estigations)f (of)i(p)r(erm)n(utation)f(groups)f(and)i(for)523 2370 y(doing)19 b(calculations)g(in)i(the)f(represen)n(tation)e(theory)i(of) g(symmetric)f(groups.)33 b(These)20 b(to)r(ols)523 2470 y(can)32 b(b)r(e)g(used)h(together)e(with)h(the)h(full)g(p)r(o)n(w)n (er)e(of)h(the)g Fu(Mathematica)o Fv(-system.)50 b Fu(PERMS)523 2570 y Fv(runs)40 b(under)f Fu(Mathematica)53 b Fv(2.x)40 b([2)o(])g(and)g(3.x)g([3)o(].)74 b(It)41 b(w)n(orks)d(without)j 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y(con)n(tained)d(in)h(the)g(con)n(text)f Fs(Perms`)e Fv(since)j(all)f(sources)f(are)h(accessible.)648 3466 y(The)g(follo)n(wing)g(statistics)g(c)n(haracterize)e(the)j(\014les)g (of)g Fu(PERMS)o Fv(:)977 3758 y(\014les)p 1443 3787 4 100 v 379 w(n)n(um)n(b)r(er)p 1818 3787 V 99 w(name)p 2591 3787 V 714 w(b)n(yte)p 927 3791 2056 4 v 977 3860 a(source)e(co)r(de)p 1443 3890 4 100 v 291 w(29)p 1818 3890 V 2591 3890 V 914 w(354279)p 927 3894 2056 4 v 977 3963 a(data)p 1443 3993 4 100 v 589 w(3)p 1818 3993 V 2591 3993 V 1443 4093 V 1818 4093 V 1869 4063 a Fs(ftdata.m)p 2591 4093 V 463 w Fv(331766)p 1443 4193 V 1818 4193 V 1869 4163 a Fs(chartab.m)e Fv(\(small\))p 2591 4193 V 183 w(40221)p 1443 4292 V 1818 4292 V 1869 4262 a Fs(chartab.m)g Fv(\(full\))p 2591 4292 V 173 w(2324983)p 523 4345 1146 4 v 615 4399 a Fr(1)650 4422 y Fq(Some)50 b(examples)g(in)h(this)f(pap) r(er)h(w)n(ere)g(calculated)h(b)n(y)f(means)f(of)g Fp(PERMS)p Fq(,)57 b(v)n(ersion)50 b(2.1)523 4501 y(\(23.3.1998\).)71 b(The)36 b(ab)r(o)n(v)n(e)i(new)n(er)e(v)n(ersion)g(of)g Fp(PERMS)48 b Fq(is)36 b(iden)n(tical)g(with)h(this)f(older)g(v)n (ersion)g(up)523 4580 y(to)31 b(the)h(\014v)n(e)f(to)r(ols)g Fo(GenerateVTuples)p Fq(,)37 b Fo(MinimalGroupings)p Fq(,)f Fo(GroupingData)p Fq(,)g Fo(MakeInvFourierData)p Fq(,)523 4659 y Fo(DataInvFourierTransform)c Fq(whic)n(h)27 b(are)f(added)h(to)f Fp(PERMS)38 b Fq(1999.)h(No)26 b(other)g(to)r(ol)h (of)e Fp(PERMS)38 b Fq(calls)523 4738 y(these)26 b(\014v)n(e)f(to)r (ols.)34 b(Th)n(us)25 b(all)f(calculations)i(whic)n(h)f(do)g(not)g(use) g(one)g(of)g(these)h(\014v)n(e)f(to)r(ols)g(ha)n(v)n(e)g(the)h(same)523 4817 y(course)e(under)g(b)r(oth)h(v)n(ersions.)1934 5147 y Fv(1)p eop %%Page: 2 2 2 1 bop 523 614 a Fv(The)23 b(\014le)h Fs(ftdata.m)c Fv(con)n(tains)i(the)i(precomputed)f(data)f(for)h(the)h(discrete)e(F)-7 b(ourier)22 b(trans-)523 714 y(form.)41 b(Character)28 b(tables)h(are)f(stored)h(in)g(the)h(\014les)f Fs(chartab.m)p Fv(.)38 b(The)29 b(user)g(can)g(c)n(ho)r(ose)523 814 y(b)r(et)n(w)n(een)35 b(a)g(small)g(v)n(ersion)f(of)h Fs(chartab.m)d Fv(whic)n(h)j(con)n(tains)f(the)i(c)n(haracter)d(tables) i(of)523 913 y Fn(S)573 925 y Ft(2)611 913 y Fm(;)14 b(:)g(:)g(:)f(;)h Fn(S)845 925 y Ft(10)947 913 y Fv(and)32 b(a)f(long)g(v)n(ersion)f(of)i Fs(chartab.m)c Fv(comprises)i(the)i(c)n (haracter)e(tables)h(of)523 1013 y Fn(S)573 1025 y Ft(2)611 1013 y Fm(;)14 b(:)g(:)g(:)f(;)h Fn(S)845 1025 y Ft(17)916 1013 y Fv(.)35 b(W)-7 b(e)21 b(ha)n(v)n(e)f(observ)n(ed)g(the)i(follo)n (wing)e(costs)h(for)g(the)g(load)g(pro)r(cess)f(of)h Fu(PERMS)523 1112 y Fv(under)27 b(the)h(conditions)g(\(1\))f(in)h (Section)g Fl(??)p Fv(.)p Fl(??)p Fv(.)p 715 1337 2480 4 v 713 1437 4 100 v 1612 1437 V 2003 1437 V 2453 1407 a(memory)p 3193 1437 V 713 1537 V 1612 1537 V 1793 1507 a(time)p 2003 1537 V 227 w(for)f(loading)p 2619 1537 V 114 w(after)g(loading)p 3193 1537 V 715 1540 2480 4 v 713 1640 4 100 v 765 1610 a(with)h(small)f Fs(chartab.m)p 1612 1640 V 138 w Fv(33.66)f(s)p 2003 1640 V 140 w(1921708)f(b)n(yte)p 2619 1640 V 99 w(1721012)f(b)n(yte)p 3193 1640 V 713 1739 V 765 1709 a(with)k(full)g Fs(chartab.m)p 1612 1739 V 168 w Fv(236.44)e(s)p 2003 1739 V 99 w(13549484)e(b)n(yte)p 2619 1739 V 99 w(7915796)g(b)n(yte)p 3193 1739 V 715 1743 2480 4 v 523 1922 a(The)30 b(long)f(v)n(ersion)f(of)i Fs(chartab.m)c Fv(has)j(only)g(to)h(b)r(e)g(loaded)f(if)h(v)-5 b(alues)29 b(of)h(c)n(haracters)d(of)523 2022 y(symmetric)g(groups)g Fn(S)1246 2034 y Fk(r)1310 2022 y Fv(with)h Fm(r)e(>)d Fv(10)j(are)h(needed.)648 2121 y(W)-7 b(e)21 b(do)f(not)h(store)f(the)h (original)e(\014les)i Fs(chartab.m)c Fv(on)j(the)i(hard)e(disk)g(but)i (compressed)523 2221 y(\014les)h(whic)n(h)g(will)g(b)r(e)g (uncompressed)f(during)g(the)h(load)g(pro)r(cess.)34 b(Under)23 b(MS-Dos)f(w)n(e)h(use)523 2321 y Fs(pkzip/pkunzip)i Fv(to)30 b(this)g(end.)45 b(Only)29 b(the)i(use)f(of)g(suc)n(h)f(a)h (compression)e(utilit)n(y)j(has)f(to)523 2420 y(b)r(e)e(mo)r(di\014ed)g (if)g(a)f(transfer)g(of)h Fu(PERMS)40 b Fv(to)28 b(an)f(other)g(op)r (erating)f(system)i(is)f(in)n(tended.)648 2520 y(W)-7 b(e)31 b(ha)n(v)n(e)f(made)h(man)n(y)f(e\013orts)g(to)h(get)g(a)g(high) g(w)n(orking)e(sp)r(eed)i(of)g Fu(PERMS)o Fv(.)47 b(Since)523 2620 y Fu(Mathematica)37 b Fv(uses)23 b(an)h(extensiv)n(e)f(set)h(of)f (rules)h(to)f(ev)-5 b(aluate)24 b(a)f(giv)n(en)g(expression,)g(it)i (can)523 2719 y(happ)r(en)g(that)f Fu(Mathematica)37 b Fv(mak)n(es)24 b(unnecessary)f(attempts)h(to)h(c)n(hange)e(an)h (expression)523 2819 y(b)n(y)30 b(means)h(of)f(rules)g(whic)n(h)h(can)f (b)r(e)i(neglected)e(or)g(ha)n(v)n(e)f(no)i(e\013ect)g(in)g(the)g(giv)n (en)f(situa-)523 2918 y(tion.)48 b(The)31 b(reduction)g(of)g(the)g(n)n (um)n(b)r(er)g(of)g(suc)n(h)g(sup)r(er\015uous)f(attempts)i(of)f(ev)-5 b(aluation)523 3018 y(is)24 b(an)h(imp)r(ortan)n(t)f(factor)f(to)i (increase)e(the)i(sp)r(eed)f(of)h(a)f(program.)34 b(T)-7 b(o)24 b(ac)n(hiev)n(e)f(suc)n(h)h(a)g(re-)523 3118 y(duction,)j(w)n(e) f(ha)n(v)n(e)g(found)h(out)f(b)n(y)g(the)h Fu(Mathematica)o Fv(-to)r(ol)f Fs(TraceDialog)c Fv(whic)n(h)27 b(single)523 3217 y(steps)k(ev)n(ery)f Fu(PERMS)o Fv(-to)r(ol)h(carries)f(out)h (during)g(a)g(run.)48 b(Then)31 b(w)n(e)g(ha)n(v)n(e)f(mo)r(di\014ed)i (the)523 3317 y(implemen)n(tations)24 b(of)g(the)h Fu(PERMS)o Fv(-to)r(ols)e(to)i(eliminate)f(unnecessary)f(ev)-5 b(aluation)23 b(steps.)648 3417 y(W)-7 b(e)23 b(ha)n(v)n(e)g(k)n(ept)g(to)g(a)h (great)e(exten)n(t)h(the)h(principle)g(to)f(omit)h(an)n(y)e(tests)i(of) f(the)h(correct-)523 3516 y(ness)32 b(of)f(the)i(input)f(for)g(the)g Fu(PERMS)o Fv(-to)r(ols.)49 b(Th)n(us)32 b(a)f(user)g(has)h(to)g(mak)n (e)f(sure)g(himself)523 3616 y(whether)f(the)h(input)g(ful\014ls)g(all) f(conditions)g(required)f(b)n(y)h(a)g(to)r(ol.)45 b(Ho)n(w)n(ev)n(er,) 29 b(this)i(prin-)523 3715 y(ciple)j(also)f(in)n(v)n(olv)n(es)g(the)h (adv)-5 b(an)n(tage)33 b(that)h(the)h(use)f(of)g(a)g Fu(PERMS)o Fv(-to)r(ol)f(in)i(a)e(program)523 3815 y(pac)n(k)-5 b(age)19 b(whic)n(h)i(calls)f(v)n(ery)f(often)i(this)g(to)r(ol)g(ha)n (v)n(e)e(more)h(fa)n(v)n(ourable)e(costs)i(in)h(calculation)523 3915 y(time.)648 4014 y Fu(PERMS)36 b Fv(uses)24 b(o)n(wn)f(data)h(t)n (yp)r(es)g(or)f(t)n(yp)r(es)h(of)g(expressions)e(iden)n(ti\014ed)i(b)n (y)g(the)g(follo)n(w-)523 4114 y(ing)j(heads:)1934 5147 y(2)p eop %%Page: 3 3 3 2 bop 973 601 a Fv(head)278 b(expression)p 923 634 2064 4 v 973 704 a Fs(GLoop)229 b Fv(lo)r(op)27 b(in)h(a)f(Ca)n(yley)f (graph)973 804 y Fs(GWord)229 b Fv(w)n(ord)26 b(de\014ned)i(b)n(y)f(a)g (path)h(of)g(a)f(Ca)n(yley)f(graph)973 903 y Fs(HoldList)97 b Fv(list)27 b(of)h(elemen)n(ts)973 1003 y Fs(Parti)229 b Fv(partition)27 b(of)g(a)g(natural)g(n)n(um)n(b)r(er)973 1103 y Fs(Perm)273 b Fv(p)r(erm)n(utation)973 1202 y Fs(Tableau)141 b Fv(Y)-7 b(oung)27 b(frame)g(or)g(Y)-7 b(oung)27 b(tableau)973 1302 y Fs(TabRow)185 b Fv(ro)n(w)26 b(of)h(a)h(Y)-7 b(oung)27 b(tableau)973 1401 y Fs(Type)273 b Fv(t)n(yp)r(e)27 b(of)h(a)f(natural)g(n)n(um)n(b)r(er)523 1611 y(T)-7 b(o)24 b(all)g(these)h(heads)f(the)h(attribute)g Fs(HoldAll)c Fv(is)k(assigned.)34 b(This)25 b(attribute)g(causes)e (that)523 1711 y(no)j(sub)r(expression)g(of)g(an)g(expression)f(with)i (one)g(of)f(the)h(ab)r(o)n(v)n(e)e(heads)h(is)g(automatically)523 1810 y(ev)-5 b(aluated)28 b(b)n(y)g Fu(Mathematica)n Fv(.)39 b(An)28 b(ev)-5 b(aluation)28 b(of)f(suc)n(h)h(sub)r (expressions)f(is)h(carried)e(out)523 1910 y(only)37 b(then)g(if)g(it)h(is)f(required)e(b)n(y)i(an)g(instruction)f(of)h Fu(PERMS)o Fv(.)65 b(This)37 b(helps)g(to)g(a)n(v)n(oid)523 2009 y(unnecessary)26 b(ev)-5 b(aluations.)648 2109 y(The)22 b(use)g(of)g(the)h(ab)r(o)n(v)n(e)d(o)n(wn)i(data)g(t)n(yp)r(es)g(had)g (a)g(further)g(fa)n(v)n(ourable)e(e\013ect.)35 b Fu(PERMS)523 2209 y Fv(turned)41 b(out)f(to)h(b)r(e)g(insensitiv)n(e)f(to)h(mo)r (di\014cations)f(in)g Fu(Mathematica)54 b Fv(3.x)40 b(whic)n(h)g(are) 523 2308 y(not)33 b(compatible)f(with)h(the)g(standard)f(of)g Fu(Mathematica)46 b Fv(2.x)32 b(\(see)g([3,)i(pp.1413-1414]\).)523 2408 y Fu(Mathematica)g Fv(can)22 b(ev)-5 b(aluate)21 b(these)h(data)f(t)n(yp)r(es)h(only)f(b)n(y)h(means)f(of)h(rules)f (from)g Fu(PERMS)o Fv(.)523 2508 y(W)-7 b(e)42 b(ha)n(v)n(e)e(not)i (disco)n(v)n(ered)d(up)j(to)f(no)n(w)g(a)g(rule)g(of)h Fu(PERMS)54 b Fv(whic)n(h)41 b(do)r(es)g(not)h(w)n(ork)523 2607 y(correct)18 b(under)i Fu(Mathematica)32 b Fv(3.x.)i(Our)19 b(program)e(do)r(es)i(not)h(use)f(an)n(y)g Fu(Mathematica)o Fv(-to)r(ol)523 2707 y(from)26 b(the)g(list)h(in)f([3,)g (pp.1413-1414].)33 b(An)26 b(in)n(v)n(estigation)f(\(b)n(y)h(means)g (of)g Fs(TraceDialog)p Fv(\))523 2806 y(whether)e(unnecessary)e(ev)-5 b(aluations)24 b(again)e(arise)h(under)h Fu(Mathematica)37 b Fv(3.x)23 b(has)h(not)g(y)n(et)523 2906 y(b)r(een)k(carried)e(out)i (for)f(all)g(to)r(ols)g(of)h Fu(PERMS)o Fv(.)523 3181 y Fx(2)135 b(A)44 b(list)i(of)f(to)t(ols)h(of)f Fw(PERMS)523 3362 y Fv(\(i\))28 b(T)-7 b(o)r(ols)27 b(for)g(the)h(in)n(v)n 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Fc(1)2889 3807 y Fm(;)14 b(:)g(:)g(:)g(;)g(n) 3124 3819 y Fk(i)3147 3827 y Fg(s)3183 3807 y Fv(\))38 b(is)f(a)731 3906 y(giv)n(en)26 b(subtuple.)235 4072 y Fs(MinimalGrouping:)35 b Fv(Let)26 b Fn(f)p Fm(i)1192 4084 y Ft(1)1228 4072 y Fm(;)14 b(:)g(:)g(:)g(;)g(i)1442 4084 y Fk(r)1478 4072 y Fn(g)25 b Fv(b)r(e)h(a)f(sequence)g(of)g (natural)g(n)n(um)n(b)r(ers)g(that)h(represen)n(ts)e(a)731 4172 y(v)n(ector)e(tuple)j Fm(b)d Fv(=)h(\()p Fm(n)1413 4184 y Fk(i)1436 4192 y Fc(1)1473 4172 y Fm(;)14 b(:)g(:)g(:)g(;)g(n) 1708 4184 y Fk(i)1731 4192 y Fg(r)1769 4172 y Fv(\))23 b Fn(2)g(B)1960 4142 y Fk(r)2020 4172 y Fv(of)h(basis)f(v)n(ectors)f (of)i(a)g(\014nite-dimensional)731 4272 y(v)n(ector)32 b(space)g Fm(V)19 b Fv(.)54 b(The)34 b(to)r(ol)f(determines)g(that)h(n) n(um)n(b)r(er)f(sequence)f Fn(f)p Fm(j)3053 4284 y Ft(1)3090 4272 y Fm(;)14 b(:)g(:)g(:)g(;)g(j)3309 4284 y Fk(r)3346 4272 y Fn(g)731 4371 y Fv(whic)n(h)31 b(corresp)r(onds)f(to)i(the)g (smallest)f(grouping)g(\()p Fm(n)2441 4383 y Fk(j)2468 4391 y Fc(1)2505 4371 y Fm(;)14 b(:)g(:)g(:)f(;)h(n)2739 4383 y Fk(j)2766 4391 y Fg(r)2804 4371 y Fv(\))30 b(=)g Fn(h)p Fm(\025)p Fv(;)14 b Fm(w)3137 4383 y Fk(i)3166 4371 y Fn(i)32 b Fv(of)g Fm(b)p Fv(.)731 4471 y(F)-7 b(urthermore,)37 b(the)g(to)r(ols)f(calculates)g(the)h(grouping)e (partition)h Fm(\025)i Fv(=)g Fm(b)3094 4441 y Fh(`)3175 4471 y Fv(and)f(a)731 4570 y(p)r(erm)n(utation)27 b Fm(p)g Fv(whic)n(h)h(ful\014ls)g Fm(b)23 b Fv(=)f Fm(p)p Fn(h)p Fm(\025)p Fv(;)14 b Fm(w)2101 4582 y Fk(i)2130 4570 y Fn(i)p Fv(.)p 523 4644 1146 4 v 615 4698 a Fr(3)650 4722 y Fq(Only)25 b(a)h(part)g(of)f(the)h(follo)n(wing)f(group)h(ring)f (elemen)n(ts)h(are)f(Lie)h(idemp)r(oten)n(ts)g(or)f(prop)r(ortional)h (to)523 4800 y(Lie)h(idemp)r(oten)n(ts.)41 b(W)-6 b(e)28 b(ha)n(v)n(e)g(used)g(the)f(substring)g Fo(Lie)h Fq(in)f(all)f(names)g (of)h(these)h(to)r(ols)f(so)g(that)h(a)f(user)523 4879 y(can)d(easily)g(\014nd)g(them)f(b)n(y)h(means)f(of)h(the)g(help)g (system)f(of)h Fp(Mathematica)35 b Fq(en)n(tering)25 b Fo(?Lie*)p Fq(.)1914 5147 y Fv(11)p eop %%Page: 12 12 12 11 bop 235 614 a Fs(GroupingData)37 b Fv(Let)25 b Fn(B)1001 626 y Fk(b)1030 634 y Fc(0)1091 614 y Fv(b)r(e)h(a)f(set)g (of)g(v)n(ector)f(tuples)h(represen)n(ted)f(b)n(y)h(\014nite)g(n)n(um)n (b)r(er)g(sequences)731 714 y(\(see)g Fs(GenerateVTuples)p Fv(\).)30 b(The)c(to)r(ol)f(determines)h(the)g(sets)f(\003)2753 726 y Fk(b)2782 734 y Fc(0)2844 714 y Fv(and)g Fn(M)3103 726 y Fk(b)3132 734 y Fc(0)3165 726 y Fk(;\025)3254 714 y Fv(and)731 814 y(returns)1095 904 y Ff(n)1150 929 y(\010)1199 996 y Fm(\025;)14 b Fn(f)p Fv(\()p Fn(h)p Fm(\025)p Fv(;)g Fm(w)1534 1008 y Fk(i)1563 996 y Fn(i)p Fm(;)g(a)1676 1011 y Fh(h)p Fk(\025)p Ft(;)p Fk(w)1809 1019 y Fg(i)1835 1011 y Fh(i)1866 996 y Fv(\))23 b Fn(j)h(h)p Fm(\025)p Fv(;)14 b Fm(w)2144 1008 y Fk(i)2172 996 y Fn(i)24 b(2)f(M)2406 1008 y Fk(b)2435 1016 y Fc(0)2467 1008 y Fk(;\025)2531 996 y Fn(g)2573 929 y Ff(\011)2644 901 y(\014)2644 951 y(\014)2644 1000 y(\014)2694 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Fv(\()p Fm(A)p Fv(\))34 b(for)g(a)f(giv)n(en)g(matrix)g Fm(A)h Fv(and)g(a)731 2175 y(giv)n(en)17 b(p)r(erm)n(utation)i(set)f Fm(M)28 b Fv(using)18 b(a)g(data)g(set)h Fs(data)e Fv(whic)n(h)h(is)h (generatet)f(b)n(y)g(means)731 2275 y(of)g Fs(MakeInvFourierDa)o(ta)12 b Fv(from)18 b Fm(M)9 b Fv(.)33 b(The)19 b(use)f(of)g(the)h(pair)f Fs(MakeInvFourierDa)o(ta)731 2374 y Fv(and)g Fs(DataInvFourierTr)o(an)o (sfo)o(rm)12 b Fv(w)n(orks)k(quic)n(k)n(er)h(than)i Fs (InvFourierTransf)o(or)o(m)731 2474 y Fv(if)45 b(pro)5 b(j)974 2494 y Fk(M)1048 2474 y Fv(\()p Fm(D)r Fn(j)1174 2486 y Fa(a)1209 2495 y Fg(\025)1252 2474 y Fv(\))1284 2444 y Fh(\000)p Ft(1)1373 2474 y Fv(\()p Fm(A)p Fv(\))46 b(has)e(to)h(b)r(e)g(calculated)f(for)g(man)n(y)g(matrices)g Fm(A)h Fv(since)731 2574 y Fs(InvFourierTrans)o(for)o(m)35 b Fv(rep)r(eatedly)41 b(determines)g(the)h(elemen)n(ts)f(of)g Fs(data)f Fv(for)731 2673 y(ev)n(ery)26 b(matrix)h Fm(A)p Fv(.)523 2948 y Fx(References)523 3130 y Fv([1])41 b(G.)35 b(Butler.)59 b Fi(F)-6 b(undamental)36 b(A)n(lgorithms)h(for)h (Permutation)e(Gr)l(oups)p Fv(,)h(v)n(olume)e(559)652 3229 y(of)28 b Fi(L)l(e)l(ctur)l(e)h(Notes)h(in)g(Computer)h(Scienc)l (e)p Fv(.)38 b(Springer-V)-7 b(erlag,)26 b(Berlin,)i(Heidelb)r(erg,)652 3329 y(New)g(Y)-7 b(ork,)27 b(1991.)523 3495 y([2])41 b(Stephen)35 b(W)-7 b(olfram.)54 b Fi(Mathematic)l(a)p Fv(.)k(Addison-W)-7 b(esley)g(,)35 b(Bonn,)g(M)r(\177)-44 b(unc)n(hen,)35 b(P)n(aris,)652 3595 y(Reading,)27 b(Mass.,)g(2.)g (edition,)h(1992.)35 b(In)28 b(German.)523 3761 y([3])41 b(Stephen)50 b(W)-7 b(olfram.)102 b Fi(Das)50 b(Mathematic)l(a-Buch)p Fv(.)104 b(Addison-W)-7 b(esley-Longman,)652 3860 y(Bonn,)40 b(Reading,)f(Mass.,)g(Menlo)f(P)n(ark,)g(Cal.,)h(New)f(Y)-7 b(ork,)39 b(Harlo)n(w,)g(Don)e(Mills,)652 3960 y(Sydney)-7 b(,)28 b(Mexico)f(Cit)n(y)-7 b(,)28 b(Madrid,)f(Amsterdam,)g(3.)g (edition,)h(1997.)1914 5147 y(14)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF