1#SIXFORMAT  GapDocGAP
2HELPBOOKINFOSIXTMP := rec(
3encoding := "UTF-8",
4bookname := "RCWA",
5entries :=
6[ [ "Title page", ".", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" ],
7  [ "Abstract", ".-1", [ 0, 0, 1 ], 24, 2, "abstract", "X7AA6C5737B711C89" ],
8  [ "Copyright", ".-2", [ 0, 0, 2 ], 49, 2, "copyright", "X81488B807F2A1CF1" ]
9    , [ "Acknowledgements", ".-3", [ 0, 0, 3 ], 68, 2, "acknowledgements",
10      "X82A988D47DFAFCFA" ],
11  [ "Table of Contents", ".-4", [ 0, 0, 4 ], 80, 3, "table of contents",
12      "X8537FEB07AF2BEC8" ],
13  [ "\033[1X\033[33X\033[0;-2YAbout the RCWA Package\033[133X\033[101X", "1",
14      [ 1, 0, 0 ], 1, 5, "about the rcwa package", "X83A8C2927FAE2C23" ],
15  [
16      "\033[1X\033[33X\033[0;-2YResidue-Class-Wise Affine Mappings\033[133X\033[1\
1701X", "2", [ 2, 0, 0 ], 1, 7, "residue-class-wise affine mappings",
18      "X7FD73FCB8510050E" ],
19  [ "\033[1X\033[33X\033[0;-2YBasic definitions\033[133X\033[101X", "2.1",
20      [ 2, 1, 0 ], 12, 7, "basic definitions", "X78ED07E37FC2BD46" ],
21  [
22      "\033[1X\033[33X\033[0;-2YEntering residue-class-wise affine mappings\033[1\
2333X\033[101X", "2.2", [ 2, 2, 0 ], 56, 8,
24      "entering residue-class-wise affine mappings", "X86BC55648302D643" ],
25  [
26      "\033[1X\033[33X\033[0;-2YRcwaMapping (the general constructor)\033[133X\\
27033[101X", "2.2-5", [ 2, 2, 5 ], 304, 12,
28      "rcwamapping the general constructor", "X8799551B83644B37" ],
29  [
30      "\033[1X\033[33X\033[0;-2YBasic arithmetic for residue-class-wise affine ma\
31ppings\033[133X\033[101X", "2.3", [ 2, 3, 0 ], 481, 14,
32      "basic arithmetic for residue-class-wise affine mappings",
33      "X78E796B8824C4FC8" ],
34  [
35      "\033[1X\033[33X\033[0;-2YAttributes and properties of residue-class-wise a\
36ffine mappings\033[133X\033[101X", "2.4", [ 2, 4, 0 ], 605, 16,
37      "attributes and properties of residue-class-wise affine mappings",
38      "X7C16D22C7BD40FDC" ],
39  [
40      "\033[1X\033[33X\033[0;-2YFactoring residue-class-wise affine permutations\\
41033[133X\033[101X", "2.5", [ 2, 5, 0 ], 814, 20,
42      "factoring residue-class-wise affine permutations", "X8475F844869DD060"
43     ],
44  [
45      "\033[1X\033[33X\033[0;-2YExtracting roots of residue-class-wise affine map\
46pings\033[133X\033[101X", "2.6", [ 2, 6, 0 ], 1011, 23,
47      "extracting roots of residue-class-wise affine mappings",
48      "X8141065381B0942B" ],
49  [
50      "\033[1X\033[33X\033[0;-2YSpecial functions for non-bijective mappings\033[\
51133X\033[101X", "2.7", [ 2, 7, 0 ], 1043, 24,
52      "special functions for non-bijective mappings", "X8322C6848305EC4C" ],
53  [ "\033[1X\033[33X\033[0;-2YOn trajectories and cycles of residue-class-wise\
54 affine mappings\033[133X\033[101X", "2.8", [ 2, 8, 0 ], 1117, 25,
55      "on trajectories and cycles of residue-class-wise affine mappings",
56      "X7A34724386A2E9F3" ],
57  [
58      "\033[1X\033[33X\033[0;-2YTrajectory (methods for rcwa mappings)\033[133X\\
59033[101X", "2.8-1", [ 2, 8, 1 ], 1122, 25,
60      "trajectory methods for rcwa mappings", "X7C72174D7CCB6348" ],
61  [
62      "\033[1X\033[33X\033[0;-2YTrajectory (methods for rcwa mappings -- \033[21X\
63accumulated coefficients\033[121X\033[101X\027\033[1X\027)\033[133X\033[101X",
64      "2.8-2", [ 2, 8, 2 ], 1156, 25,
65      "trajectory methods for rcwa mappings -- accumulated coefficients",
66      "X7FFD09837E934853" ],
67  [
68      "\033[1X\033[33X\033[0;-2YIncreasingOn & DecreasingOn (for an rcwa mapping)\
69\033[133X\033[101X", "2.8-3", [ 2, 8, 3 ], 1185, 26,
70      "increasingon & decreasingon for an rcwa mapping", "X7E0244A386744185" ]
71    ,
72  [
73      "\033[1X\033[33X\033[0;-2YSources & Sinks (of an rcwa mapping)\033[133X\\
74033[101X", "2.8-8", [ 2, 8, 8 ], 1295, 28,
75      "sources & sinks of an rcwa mapping", "X81DBA2D58526BE7E" ],
76  [
77      "\033[1X\033[33X\033[0;-2YSaving memory -- the sparse representation of rcw\
78a mappings\033[133X\033[101X", "2.9", [ 2, 9, 0 ], 1415, 30,
79      "saving memory -- the sparse representation of rcwa mappings",
80      "X86F0E0D17E6A9663" ],
81  [
82      "\033[1X\033[33X\033[0;-2YThe categories and families of rcwa mappings\033[\
83133X\033[101X", "2.10", [ 2, 10, 0 ], 1499, 31,
84      "the categories and families of rcwa mappings", "X83FA71DD842377F0" ],
85  [ "\033[1X\033[33X\033[0;-2YResidue-Class-Wise Affine Groups\033[133X\033[10\
861X", "3", [ 3, 0, 0 ], 1, 32, "residue-class-wise affine groups",
87      "X874A3BB684F0639A" ],
88  [
89      "\033[1X\033[33X\033[0;-2YConstructing residue-class-wise affine groups\\
90033[133X\033[101X", "3.1", [ 3, 1, 0 ], 7, 32,
91      "constructing residue-class-wise affine groups", "X81242A6586A604A3" ],
92  [ "\033[1X\033[33X\033[0;-2YWreathProduct (for an rcwa group over Z, with a \
93permutation group or (\342\204\244,+))\033[133X\033[101X", "3.1-3",
94      [ 3, 1, 3 ], 86, 33,
95      "wreathproduct for an rcwa group over z with a permutation group or a\
96\204\244 +", "X80D13D2A7AD73C2C" ],
97  [
98      "\033[1X\033[33X\033[0;-2YRestriction (of an rcwa mapping or -group, by an \
99injective rcwa mapping)\033[133X\033[101X", "3.1-6", [ 3, 1, 6 ], 214, 35,
100      "restriction of an rcwa mapping or -group by an injective rcwa mapping",
101      "X852EF2C079E4D7FF" ],
102  [
103      "\033[1X\033[33X\033[0;-2YInduction (of an rcwa mapping or -group, by an in\
104jective rcwa mapping)\033[133X\033[101X", "3.1-7", [ 3, 1, 7 ], 242, 36,
105      "induction of an rcwa mapping or -group by an injective rcwa mapping",
106      "X82171D7287CBED95" ],
107  [
108      "\033[1X\033[33X\033[0;-2YBasic routines for investigating residue-class-wi\
109se affine groups\033[133X\033[101X", "3.2", [ 3, 2, 0 ], 395, 38,
110      "basic routines for investigating residue-class-wise affine groups",
111      "X80C042BE82EE0F9A" ],
112  [
113      "\033[1X\033[33X\033[0;-2YThe natural action of an rcwa group on the underl\
114ying ring\033[133X\033[101X", "3.3", [ 3, 3, 0 ], 675, 43,
115      "the natural action of an rcwa group on the underlying ring",
116      "X8151BE577FFDCE87" ],
117  [
118      "\033[1X\033[33X\033[0;-2YOrbit (for an rcwa group and either a point or a \
119set)\033[133X\033[101X", "3.3-1", [ 3, 3, 1 ], 797, 45,
120      "orbit for an rcwa group and either a point or a set",
121      "X7C046BE97EE53692" ],
122  [
123      "\033[1X\033[33X\033[0;-2YShortOrbits (for rcwa groups) & ShortCycles (for \
124rcwa permutations)\033[133X\033[101X", "3.3-4", [ 3, 3, 4 ], 925, 47,
125      "shortorbits for rcwa groups & shortcycles for rcwa permutations",
126      "X78F145197F63A25D" ],
127  [
128      "\033[1X\033[33X\033[0;-2YShortResidueClassOrbits & ShortResidueClassCycles\
129\033[133X\033[101X", "3.3-5", [ 3, 3, 5 ], 980, 48,
130      "shortresidueclassorbits & shortresidueclasscycles",
131      "X80D18D0778A96C16" ],
132  [
133      "\033[1X\033[33X\033[0;-2YBall (for group, element and radius or group, poi\
134nt, radius and action)\033[133X\033[101X", "3.3-9", [ 3, 3, 9 ], 1144, 51,
135      "ball for group element and radius or group point radius and action",
136      "X8735855587CC029F" ],
137  [
138      "\033[1X\033[33X\033[0;-2YSpecial attributes of tame residue-class-wise aff\
139ine groups\033[133X\033[101X", "3.4", [ 3, 4, 0 ], 1384, 55,
140      "special attributes of tame residue-class-wise affine groups",
141      "X781CBEFA7F39B58D" ],
142  [
143      "\033[1X\033[33X\033[0;-2YRespectedPartition (of a tame rcwa group or -perm\
144utation)\033[133X\033[101X", "3.4-1", [ 3, 4, 1 ], 1396, 55,
145      "respectedpartition of a tame rcwa group or -permutation",
146      "X7F523A6B87825AB8" ],
147  [
148      "\033[1X\033[33X\033[0;-2YActionOnRespectedPartition & KernelOfActionOnResp\
149ectedPartition\033[133X\033[101X", "3.4-2", [ 3, 4, 2 ], 1430, 56,
150      "actiononrespectedpartition & kernelofactiononrespectedpartition",
151      "X831ADC1584DE6113" ],
152  [
153      "\033[1X\033[33X\033[0;-2YGenerating pseudo-random elements of RCWA(R) and \
154CT(R)\033[133X\033[101X", "3.5", [ 3, 5, 0 ], 1492, 57,
155      "generating pseudo-random elements of rcwa r and ct r",
156      "X81941A247942FB99" ],
157  [
158      "\033[1X\033[33X\033[0;-2YThe categories of residue-class-wise affine group\
159s\033[133X\033[101X", "3.6", [ 3, 6, 0 ], 1540, 58,
160      "the categories of residue-class-wise affine groups",
161      "X86327F6C83D09798" ],
162  [
163      "\033[1X\033[33X\033[0;-2YResidue-Class-Wise Affine Monoids\033[133X\033[10\
1641X", "4", [ 4, 0, 0 ], 1, 59, "residue-class-wise affine monoids",
165      "X81C90F7C7BA25BDF" ],
166  [
167      "\033[1X\033[33X\033[0;-2YConstructing residue-class-wise affine monoids\\
168033[133X\033[101X", "4.1", [ 4, 1, 0 ], 8, 59,
169      "constructing residue-class-wise affine monoids", "X83D42E26849D5580" ],
170  [ "\033[1X\033[33X\033[0;-2YComputing with residue-class-wise affine monoids\
171\033[133X\033[101X", "4.2", [ 4, 2, 0 ], 78, 60,
172      "computing with residue-class-wise affine monoids", "X8759954F7EB1A658"
173     ],
174  [
175      "\033[1X\033[33X\033[0;-2YBall (for monoid, element and radius or monoid, p\
176oint, radius and action)\033[133X\033[101X", "4.2-2", [ 4, 2, 2 ], 165, 62,
177      "ball for monoid element and radius or monoid point radius and action",
178      "X787848137DF1C245" ],
179  [
180      "\033[1X\033[33X\033[0;-2YResidue-Class-Wise Affine Mappings, Groups and Mo\
181noids over \033[22X\342\204\244^2\033[122X\033[101X\027\033[1X\027\033[133X\
182\033[101X", "5", [ 5, 0, 0 ], 1, 63,
183      "residue-class-wise affine mappings groups and monoids over a\204\244^2"
184        , "X788EB00B82897762" ],
185  [
186      "\033[1X\033[33X\033[0;-2YThe definition of residue-class-wise affine mappi\
187ngs of \033[22X\342\204\244^d\033[122X\033[101X\027\033[1X\027\033[133X\033[10\
1881X", "5.1", [ 5, 1, 0 ], 22, 63,
189      "the definition of residue-class-wise affine mappings of a\204\244^d",
190      "X781907CA785CC7AC" ],
191  [
192      "\033[1X\033[33X\033[0;-2YEntering residue-class-wise affine mappings of \\
193033[22X\342\204\244^2\033[122X\033[101X\027\033[1X\027\033[133X\033[101X",
194      "5.2", [ 5, 2, 0 ], 44, 64,
195      "entering residue-class-wise affine mappings of a\204\244^2",
196      "X7A39FCF08030AB9B" ],
197  [
198      "\033[1X\033[33X\033[0;-2YRcwaMapping (the general constructor; methods for\
199 \033[22X\342\204\244^2\033[122X\033[101X\027\033[1X\027)\033[133X\033[101X",
200      "5.2-1", [ 5, 2, 1 ], 52, 64,
201      "rcwamapping the general constructor methods for a\204\244^2",
202      "X790649618012C606" ],
203  [
204      "\033[1X\033[33X\033[0;-2YClassTransposition (for \033[22X\342\204\244^2\\
205033[122X\033[101X\027\033[1X\027)\033[133X\033[101X", "5.2-2", [ 5, 2, 2 ],
206      201, 66, "classtransposition for a\204\244^2", "X7B450EE17B465E02" ],
207  [
208      "\033[1X\033[33X\033[0;-2YClassRotation (for \033[22X\342\204\244^2\033[122\
209X\033[101X\027\033[1X\027)\033[133X\033[101X", "5.2-3", [ 5, 2, 3 ], 267, 67,
210      "classrotation for a\204\244^2", "X828438127DDAEBB4" ],
211  [
212      "\033[1X\033[33X\033[0;-2YClassShift (for \033[22X\342\204\244^2\033[122X\\
213033[101X\027\033[1X\027)\033[133X\033[101X", "5.2-4", [ 5, 2, 4 ], 304, 68,
214      "classshift for a\204\244^2", "X7A14A8F48247E651" ],
215  [
216      "\033[1X\033[33X\033[0;-2YMethods for residue-class-wise affine mappings of\
217 \033[22X\342\204\244^2\033[122X\033[101X\027\033[1X\027\033[133X\033[101X",
218      "5.3", [ 5, 3, 0 ], 342, 69,
219      "methods for residue-class-wise affine mappings of a\204\244^2",
220      "X8531E39785FFF8A7" ],
221  [
222      "\033[1X\033[33X\033[0;-2YMethods for residue-class-wise affine groups and \
223-monoids over \033[22X\342\204\244^2\033[122X\033[101X\027\033[1X\027\033[133X\
224\033[101X", "5.4", [ 5, 4, 0 ], 407, 70,
225      "methods for residue-class-wise affine groups and -monoids over a\204\
226\244^2", "X83A1752F7BE9CE85" ],
227  [
228      "\033[1X\033[33X\033[0;-2YIsomorphismRcwaGroup (Embeddings of SL(2,\342\\
229204\244) and GL(2,\342\204\244))\033[133X\033[101X", "5.4-1", [ 5, 4, 1 ],
230      424, 70,
231      "isomorphismrcwagroup embeddings of sl 2 a\204\244 and gl 2 a\204\244",
232      "X79A8F9AD7E839862" ],
233  [ "\033[1X\033[33X\033[0;-2YDrawGrid\033[133X\033[101X", "5.4-2",
234      [ 5, 4, 2 ], 469, 71, "drawgrid", "X812135EB87527F01" ],
235  [
236      "\033[1X\033[33X\033[0;-2YDatabases of Residue-Class-Wise Affine Groups and\
237 -Mappings\033[133X\033[101X", "6", [ 6, 0, 0 ], 1, 72,
238      "databases of residue-class-wise affine groups and -mappings",
239      "X81BA344979567342" ],
240  [ "\033[1X\033[33X\033[0;-2YThe collection of examples\033[133X\033[101X",
241      "6.1", [ 6, 1, 0 ], 8, 72, "the collection of examples",
242      "X86CCBF017A746F50" ],
243  [ "\033[1X\033[33X\033[0;-2YDatabases of rcwa groups\033[133X\033[101X",
244      "6.2", [ 6, 2, 0 ], 45, 73, "databases of rcwa groups",
245      "X85DD85DF87DE47C9" ],
246  [ "\033[1X\033[33X\033[0;-2YDatabases of rcwa mappings\033[133X\033[101X",
247      "6.3", [ 6, 3, 0 ], 404, 79, "databases of rcwa mappings",
248      "X78A1A8E587C7FFD5" ],
249  [ "\033[1X\033[33X\033[0;-2YExamples\033[133X\033[101X", "7", [ 7, 0, 0 ],
250      1, 81, "examples", "X7A489A5D79DA9E5C" ],
251  [ "\033[1X\033[33X\033[0;-2YThompson's group V\033[133X\033[101X", "7.1",
252      [ 7, 1, 0 ], 23, 81, "thompsons group v", "X84A058CF7C65A908" ],
253  [
254      "\033[1X\033[33X\033[0;-2YFactoring Collatz' permutation of the integers\\
255033[133X\033[101X", "7.2", [ 7, 2, 0 ], 197, 84,
256      "factoring collatz permutation of the integers", "X86C2BAE3876985A6" ],
257  [ "\033[1X\033[33X\033[0;-2YThe \033[22X3n+1\033[122X\033[101X\027\033[1X\
258\027 group\033[133X\033[101X", "7.3", [ 7, 3, 0 ], 301, 86, "the 3n+1 group",
259      "X811919107D5DAAC1" ],
260  [
261      "\033[1X\033[33X\033[0;-2YA group with huge finite orbits\033[133X\033[101X\
262", "7.4", [ 7, 4, 0 ], 728, 93, "a group with huge finite orbits",
263      "X7DCFDC797FF213C5" ],
264  [
265      "\033[1X\033[33X\033[0;-2YA group which acts 4-transitively on the positive\
266 integers\033[133X\033[101X", "7.5", [ 7, 5, 0 ], 941, 97,
267      "a group which acts 4-transitively on the positive integers",
268      "X7968C1DF7EF0BD8E" ],
269  [
270      "\033[1X\033[33X\033[0;-2YA group which acts 3-transitively, but not 4-tran\
271sitively on \342\204\244\033[133X\033[101X", "7.6", [ 7, 6, 0 ], 1390, 105,
272      "a group which acts 3-transitively but not 4-transitively on a\204\244",
273      "X85C529088050BEA3" ],
274  [
275      "\033[1X\033[33X\033[0;-2YAn rcwa mapping which seems to be contracting, bu\
276t very slow\033[133X\033[101X", "7.7", [ 7, 7, 0 ], 1586, 108,
277      "an rcwa mapping which seems to be contracting but very slow",
278      "X878499AF7889FD9E" ],
279  [
280      "\033[1X\033[33X\033[0;-2YChecking a result by P. Andaloro\033[133X\033[101\
281X", "7.8", [ 7, 8, 0 ], 1677, 110, "checking a result by p. andaloro",
282      "X84A915BA833E0BDE" ],
283  [
284      "\033[1X\033[33X\033[0;-2YTwo examples by Matthews and Leigh\033[133X\033[1\
28501X", "7.9", [ 7, 9, 0 ], 1723, 111, "two examples by matthews and leigh",
286      "X7E8CD9B67ED78735" ],
287  [ "\033[1X\033[33X\033[0;-2YOrders of commutators\033[133X\033[101X",
288      "7.10", [ 7, 10, 0 ], 1839, 113, "orders of commutators",
289      "X854E9F65817E4F63" ],
290  [
291      "\033[1X\033[33X\033[0;-2YAn infinite subgroup of CT(GF(2)[x]) with many to\
292rsion elements\033[133X\033[101X", "7.11", [ 7, 11, 0 ], 1916, 114,
293      "an infinite subgroup of ct gf 2 [x] with many torsion elements",
294      "X7F085B867D799293" ],
295  [
296      "\033[1X\033[33X\033[0;-2YAn abelian rcwa group over a polynomial ring\033[\
297133X\033[101X", "7.12", [ 7, 12, 0 ], 2071, 117,
298      "an abelian rcwa group over a polynomial ring", "X7A8605E680F664BF" ],
299  [ "\033[1X\033[33X\033[0;-2YChecking for solvability\033[133X\033[101X",
300      "7.13", [ 7, 13, 0 ], 2172, 119, "checking for solvability",
301      "X78DFE4B4821E07A6" ],
302  [
303      "\033[1X\033[33X\033[0;-2YSome examples over (semi)localizations of the int\
304egers\033[133X\033[101X", "7.14", [ 7, 14, 0 ], 2224, 120,
305      "some examples over semi localizations of the integers",
306      "X783D54DC7A646273" ],
307  [
308      "\033[1X\033[33X\033[0;-2YTwisting 257-cycles into an rcwa mapping with mod\
309ulus 32\033[133X\033[101X", "7.15", [ 7, 15, 0 ], 2356, 122,
310      "twisting 257-cycles into an rcwa mapping with modulus 32",
311      "X846D7D087861E0AC" ],
312  [
313      "\033[1X\033[33X\033[0;-2YThe behaviour of the moduli of powers\033[133X\\
314033[101X", "7.16", [ 7, 16, 0 ], 2445, 124,
315      "the behaviour of the moduli of powers", "X78D5DC93845CA6A0" ],
316  [
317      "\033[1X\033[33X\033[0;-2YImages and preimages under the Collatz mapping\\
318033[133X\033[101X", "7.17", [ 7, 17, 0 ], 2509, 125,
319      "images and preimages under the collatz mapping", "X855A3CD88459958B" ],
320  [ "\033[1X\033[33X\033[0;-2YAn extension of the Collatz mapping T to a permu\
321tation of \033[22X\342\204\244^2\033[122X\033[101X\027\033[1X\027\033[133X\033\
322[101X", "7.18", [ 7, 18, 0 ], 2616, 127,
323      "an extension of the collatz mapping t to a permutation of a\204\244^2",
324      "X84B6A498838A5509" ],
325  [
326      "\033[1X\033[33X\033[0;-2YFinite quotients of Grigorchuk groups\033[133X\\
327033[101X", "7.19", [ 7, 19, 0 ], 2788, 130,
328      "finite quotients of grigorchuk groups", "X81EB8D397898C6B2" ],
329  [
330      "\033[1X\033[33X\033[0;-2YForward orbits of a monoid with 2 generators\033[\
331133X\033[101X", "7.20", [ 7, 20, 0 ], 2873, 131,
332      "forward orbits of a monoid with 2 generators", "X7DD9502F80364631" ],
333  [ "\033[1X\033[33X\033[0;-2YThe free group of rank 2 and the modular group P\
334SL(2,\342\204\244)\033[133X\033[101X", "7.21", [ 7, 21, 0 ], 2957, 132,
335      "the free group of rank 2 and the modular group psl 2 a\204\244",
336      "X815800ED820C6ECF" ],
337  [
338      "\033[1X\033[33X\033[0;-2YThe Algorithms Implemented in RCWA\033[133X\033[1\
33901X", "8", [ 8, 0, 0 ], 1, 135, "the algorithms implemented in rcwa",
340      "X79EA0B717B045756" ],
341  [
342      "\033[1X\033[33X\033[0;-2YInstallation and Auxiliary Functions\033[133X\\
343033[101X", "9", [ 9, 0, 0 ], 1, 150, "installation and auxiliary functions",
344      "X859F6BF88754E5CC" ],
345  [ "\033[1X\033[33X\033[0;-2YRequirements\033[133X\033[101X", "9.1",
346      [ 9, 1, 0 ], 4, 150, "requirements", "X85A08CF187A6D986" ],
347  [ "\033[1X\033[33X\033[0;-2YInstallation\033[133X\033[101X", "9.2",
348      [ 9, 2, 0 ], 15, 150, "installation", "X8360C04082558A12" ],
349  [ "\033[1X\033[33X\033[0;-2YBuilding the manual\033[133X\033[101X", "9.3",
350      [ 9, 3, 0 ], 23, 150, "building the manual", "X854E65D281B80D3B" ],
351  [ "\033[1X\033[33X\033[0;-2YThe testing routines\033[133X\033[101X", "9.4",
352      [ 9, 4, 0 ], 39, 151, "the testing routines", "X865D6A49826B92EC" ],
353  [ "\033[1X\033[33X\033[0;-2YThe Info class of the package\033[133X\033[101X"
354        , "9.5", [ 9, 5, 0 ], 83, 151, "the info class of the package",
355      "X7A31FA44791E93C5" ],
356  [ "Bibliography", "bib", [ "Bib", 0, 0 ], 1, 152, "bibliography",
357      "X7A6F98FD85F02BFE" ],
358  [ "References", "bib", [ "Bib", 0, 0 ], 1, 152, "references",
359      "X7A6F98FD85F02BFE" ],
360  [ "Index", "ind", [ "Ind", 0, 0 ], 1, 154, "index", "X83A0356F839C696F" ],
361  [ "Collatz conjecture", "1.", [ 1, 0, 0 ], 1, 5, "collatz conjecture",
362      "X83A8C2927FAE2C23" ],
363  [ "Collatz mapping", "1.", [ 1, 0, 0 ], 1, 5, "collatz mapping",
364      "X83A8C2927FAE2C23" ],
365  [ "rcwa mapping definition", "2.1", [ 2, 1, 0 ], 12, 7,
366      "rcwa mapping definition", "X78ED07E37FC2BD46" ],
367  [ "rcwa group definition", "2.1", [ 2, 1, 0 ], 12, 7,
368      "rcwa group definition", "X78ED07E37FC2BD46" ],
369  [ "modulus definition", "2.1", [ 2, 1, 0 ], 12, 7, "modulus definition",
370      "X78ED07E37FC2BD46" ],
371  [ "rcwa mapping modulus", "2.1", [ 2, 1, 0 ], 12, 7, "rcwa mapping modulus",
372      "X78ED07E37FC2BD46" ],
373  [ "multiplier definition", "2.1", [ 2, 1, 0 ], 12, 7,
374      "multiplier definition", "X78ED07E37FC2BD46" ],
375  [ "rcwa mapping multiplier", "2.1", [ 2, 1, 0 ], 12, 7,
376      "rcwa mapping multiplier", "X78ED07E37FC2BD46" ],
377  [ "divisor definition", "2.1", [ 2, 1, 0 ], 12, 7, "divisor definition",
378      "X78ED07E37FC2BD46" ],
379  [ "rcwa mapping divisor", "2.1", [ 2, 1, 0 ], 12, 7, "rcwa mapping divisor",
380      "X78ED07E37FC2BD46" ],
381  [ "tame rcwa mapping", "2.1", [ 2, 1, 0 ], 12, 7, "tame rcwa mapping",
382      "X78ED07E37FC2BD46" ],
383  [ "tame rcwa group", "2.1", [ 2, 1, 0 ], 12, 7, "tame rcwa group",
384      "X78ED07E37FC2BD46" ],
385  [ "wild rcwa mapping", "2.1", [ 2, 1, 0 ], 12, 7, "wild rcwa mapping",
386      "X78ED07E37FC2BD46" ],
387  [ "wild rcwa group", "2.1", [ 2, 1, 0 ], 12, 7, "wild rcwa group",
388      "X78ED07E37FC2BD46" ],
389  [ "rcwa mapping tame", "2.1", [ 2, 1, 0 ], 12, 7, "rcwa mapping tame",
390      "X78ED07E37FC2BD46" ],
391  [ "rcwa group tame", "2.1", [ 2, 1, 0 ], 12, 7, "rcwa group tame",
392      "X78ED07E37FC2BD46" ],
393  [ "rcwa mapping wild", "2.1", [ 2, 1, 0 ], 12, 7, "rcwa mapping wild",
394      "X78ED07E37FC2BD46" ],
395  [ "rcwa group wild", "2.1", [ 2, 1, 0 ], 12, 7, "rcwa group wild",
396      "X78ED07E37FC2BD46" ],
397  [ "\033[2XClassShift\033[102X r, m", "2.2-1", [ 2, 2, 1 ], 117, 9,
398      "classshift r m", "X86B611BD7EED62A1" ],
399  [ "\033[2XClassShift\033[102X cl", "2.2-1", [ 2, 2, 1 ], 117, 9,
400      "classshift cl", "X86B611BD7EED62A1" ],
401  [ "\033[2XClassReflection\033[102X r, m", "2.2-2", [ 2, 2, 2 ], 143, 9,
402      "classreflection r m", "X7896C5417E3692B4" ],
403  [ "\033[2XClassReflection\033[102X cl", "2.2-2", [ 2, 2, 2 ], 143, 9,
404      "classreflection cl", "X7896C5417E3692B4" ],
405  [ "\033[2XClassTransposition\033[102X r1, m1, r2, m2", "2.2-3",
406      [ 2, 2, 3 ], 170, 10, "classtransposition r1 m1 r2 m2",
407      "X8716A75F7DD1C46B" ],
408  [ "\033[2XClassTransposition\033[102X cl1, cl2", "2.2-3", [ 2, 2, 3 ], 170,
409      10, "classtransposition cl1 cl2", "X8716A75F7DD1C46B" ],
410  [ "\033[10XTransposedClasses\033[110X of a class transposition", "2.2-3",
411      [ 2, 2, 3 ], 170, 10, "transposedclasses of a class transposition",
412      "X8716A75F7DD1C46B" ],
413  [ "\033[10XClassPairs\033[110X m", "2.2-3", [ 2, 2, 3 ], 170, 10,
414      "classpairs m", "X8716A75F7DD1C46B" ],
415  [ "\033[10XNrClassPairs\033[110X m", "2.2-3", [ 2, 2, 3 ], 170, 10,
416      "nrclasspairs m", "X8716A75F7DD1C46B" ],
417  [ "\033[10XExtRepOfObj\033[110X for a class transposition", "2.2-3",
418      [ 2, 2, 3 ], 170, 10, "extrepofobj for a class transposition",
419      "X8716A75F7DD1C46B" ],
420  [
421      "\033[10XSplittedClassTransposition\033[110X for a class transposition and \
422a number of factors", "2.2-3", [ 2, 2, 3 ], 170, 10,
423      "splittedclasstransposition for a class transposition and a number of fa\
424ctors", "X8716A75F7DD1C46B" ],
425  [ "\033[2XClassRotation\033[102X r, m, u", "2.2-4", [ 2, 2, 4 ], 251, 11,
426      "classrotation r m u", "X87EB8C1C87F78A17" ],
427  [ "\033[2XClassRotation\033[102X cl, u", "2.2-4", [ 2, 2, 4 ], 251, 11,
428      "classrotation cl u", "X87EB8C1C87F78A17" ],
429  [ "\033[10XRotationFactor\033[110X of a class rotation", "2.2-4",
430      [ 2, 2, 4 ], 251, 11, "rotationfactor of a class rotation",
431      "X87EB8C1C87F78A17" ],
432  [ "\033[10XIsClassShift\033[110X for an rcwa mapping", "2.2-4",
433      [ 2, 2, 4 ], 251, 11, "isclassshift for an rcwa mapping",
434      "X87EB8C1C87F78A17" ],
435  [ "\033[10XIsClassReflection\033[110X for an rcwa mapping", "2.2-4",
436      [ 2, 2, 4 ], 251, 11, "isclassreflection for an rcwa mapping",
437      "X87EB8C1C87F78A17" ],
438  [ "\033[10XIsClassRotation\033[110X for an rcwa mapping", "2.2-4",
439      [ 2, 2, 4 ], 251, 11, "isclassrotation for an rcwa mapping",
440      "X87EB8C1C87F78A17" ],
441  [ "\033[10XIsClassTransposition\033[110X for an rcwa mapping", "2.2-4",
442      [ 2, 2, 4 ], 251, 11, "isclasstransposition for an rcwa mapping",
443      "X87EB8C1C87F78A17" ],
444  [ "\033[10XIsGeneralizedClassTransposition\033[110X for an rcwa mapping",
445      "2.2-4", [ 2, 2, 4 ], 251, 11,
446      "isgeneralizedclasstransposition for an rcwa mapping",
447      "X87EB8C1C87F78A17" ],
448  [ "\033[2XRcwaMapping\033[102X by ring, modulus and list of coefficients",
449      "2.2-5", [ 2, 2, 5 ], 304, 12,
450      "rcwamapping by ring modulus and list of coefficients",
451      "X8799551B83644B37" ],
452  [ "\033[2XRcwaMapping\033[102X by ring and list of coefficients", "2.2-5",
453      [ 2, 2, 5 ], 304, 12, "rcwamapping by ring and list of coefficients",
454      "X8799551B83644B37" ],
455  [ "\033[2XRcwaMapping\033[102X by list of coefficients", "2.2-5",
456      [ 2, 2, 5 ], 304, 12, "rcwamapping by list of coefficients",
457      "X8799551B83644B37" ],
458  [ "\033[2XRcwaMapping\033[102X by permutation and range", "2.2-5",
459      [ 2, 2, 5 ], 304, 12, "rcwamapping by permutation and range",
460      "X8799551B83644B37" ],
461  [ "\033[2XRcwaMapping\033[102X by modulus and list of values", "2.2-5",
462      [ 2, 2, 5 ], 304, 12, "rcwamapping by modulus and list of values",
463      "X8799551B83644B37" ],
464  [
465      "\033[2XRcwaMapping\033[102X by set of non-invertible primes and list of co\
466efficients", "2.2-5", [ 2, 2, 5 ], 304, 12,
467      "rcwamapping by set of non-invertible primes and list of coefficients",
468      "X8799551B83644B37" ],
469  [
470      "\033[2XRcwaMapping\033[102X by finite field size, modulus and list of coef\
471ficients", "2.2-5", [ 2, 2, 5 ], 304, 12,
472      "rcwamapping by finite field size modulus and list of coefficients",
473      "X8799551B83644B37" ],
474  [
475      "\033[2XRcwaMapping\033[102X by two partitions of a ring into residue class\
476es", "2.2-5", [ 2, 2, 5 ], 304, 12,
477      "rcwamapping by two partitions of a ring into residue classes",
478      "X8799551B83644B37" ],
479  [ "\033[2XRcwaMapping\033[102X by residue class cycles", "2.2-5",
480      [ 2, 2, 5 ], 304, 12, "rcwamapping by residue class cycles",
481      "X8799551B83644B37" ],
482  [ "\033[2XRcwaMapping\033[102X by arithmetical expression", "2.2-5",
483      [ 2, 2, 5 ], 304, 12, "rcwamapping by arithmetical expression",
484      "X8799551B83644B37" ],
485  [
486      "\033[2XLocalizedRcwaMapping\033[102X for an rcwa mapping of z and a prime"
487        , "2.2-6", [ 2, 2, 6 ], 415, 13,
488      "localizedrcwamapping for an rcwa mapping of z and a prime",
489      "X7F1A559387D0226E" ],
490  [
491      "\033[2XSemilocalizedRcwaMapping\033[102X for an rcwa mapping of z and a se\
492t of primes", "2.2-6", [ 2, 2, 6 ], 415, 13,
493      "semilocalizedrcwamapping for an rcwa mapping of z and a set of primes",
494      "X7F1A559387D0226E" ],
495  [ "\033[10XView\033[110X for an rcwa mapping", "2.2-6", [ 2, 2, 6 ], 415,
496      13, "view for an rcwa mapping", "X7F1A559387D0226E" ],
497  [ "\033[10XDisplay\033[110X for an rcwa mapping", "2.2-6", [ 2, 2, 6 ],
498      415, 13, "display for an rcwa mapping", "X7F1A559387D0226E" ],
499  [ "\033[10XPrint\033[110X for an rcwa mapping", "2.2-6", [ 2, 2, 6 ], 415,
500      13, "print for an rcwa mapping", "X7F1A559387D0226E" ],
501  [ "\033[10XString\033[110X for an rcwa mapping", "2.2-6", [ 2, 2, 6 ], 415,
502      13, "string for an rcwa mapping", "X7F1A559387D0226E" ],
503  [ "\033[10XLaTeXStringRcwaMapping\033[110X for an rcwa mapping", "2.2-6",
504      [ 2, 2, 6 ], 415, 13, "latexstringrcwamapping for an rcwa mapping",
505      "X7F1A559387D0226E" ],
506  [ "\033[10XLaTeXAndXDVI\033[110X for an rcwa mapping", "2.2-6",
507      [ 2, 2, 6 ], 415, 13, "latexandxdvi for an rcwa mapping",
508      "X7F1A559387D0226E" ],
509  [ "rcwa mapping arithmetic operations", "2.3", [ 2, 3, 0 ], 481, 14,
510      "rcwa mapping arithmetic operations", "X78E796B8824C4FC8" ],
511  [ "\033[10XOrder\033[110X of an rcwa permutation", "2.3", [ 2, 3, 0 ], 481,
512      14, "order of an rcwa permutation", "X78E796B8824C4FC8" ],
513  [ "\033[10XIsTame\033[110X for an rcwa mapping", "2.3", [ 2, 3, 0 ], 481,
514      14, "istame for an rcwa mapping", "X78E796B8824C4FC8" ],
515  [ "\033[10XIsInjective\033[110X for an rcwa mapping", "2.3", [ 2, 3, 0 ],
516      481, 14, "isinjective for an rcwa mapping", "X78E796B8824C4FC8" ],
517  [ "\033[10XIsSurjective\033[110X for an rcwa mapping", "2.3", [ 2, 3, 0 ],
518      481, 14, "issurjective for an rcwa mapping", "X78E796B8824C4FC8" ],
519  [ "\033[10XIsBijective\033[110X for an rcwa mapping", "2.3", [ 2, 3, 0 ],
520      481, 14, "isbijective for an rcwa mapping", "X78E796B8824C4FC8" ],
521  [ "\033[10XImage\033[110X of an rcwa mapping", "2.3", [ 2, 3, 0 ], 481, 14,
522      "image of an rcwa mapping", "X78E796B8824C4FC8" ],
523  [ "rcwa mapping images under", "2.3", [ 2, 3, 0 ], 481, 14,
524      "rcwa mapping images under", "X78E796B8824C4FC8" ],
525  [ "\033[10XPreImageElm\033[110X of a ring element under an rcwa mapping",
526      "2.3", [ 2, 3, 0 ], 481, 14,
527      "preimageelm of a ring element under an rcwa mapping",
528      "X78E796B8824C4FC8" ],
529  [ "\033[10XPreImagesElm\033[110X of a ring element under an rcwa mapping",
530      "2.3", [ 2, 3, 0 ], 481, 14,
531      "preimageselm of a ring element under an rcwa mapping",
532      "X78E796B8824C4FC8" ],
533  [
534      "\033[10XPreImage\033[110X of a set of ring elements under an rcwa mapping"
535        , "2.3", [ 2, 3, 0 ], 481, 14,
536      "preimage of a set of ring elements under an rcwa mapping",
537      "X78E796B8824C4FC8" ],
538  [ "\033[10XPreImage\033[110X of a residue class union under an rcwa mapping"
539        , "2.3", [ 2, 3, 0 ], 481, 14,
540      "preimage of a residue class union under an rcwa mapping",
541      "X78E796B8824C4FC8" ],
542  [ "\033[10XSupport\033[110X of an rcwa mapping", "2.3", [ 2, 3, 0 ], 481,
543      14, "support of an rcwa mapping", "X78E796B8824C4FC8" ],
544  [ "\033[10XMovedPoints\033[110X of an rcwa mapping", "2.3", [ 2, 3, 0 ],
545      481, 14, "movedpoints of an rcwa mapping", "X78E796B8824C4FC8" ],
546  [
547      "\033[10XRestrictedPerm\033[110X for an rcwa permutation and a residue clas\
548s union", "2.3", [ 2, 3, 0 ], 481, 14,
549      "restrictedperm for an rcwa permutation and a residue class union",
550      "X78E796B8824C4FC8" ],
551  [ "\033[10XDensityOfSupport\033[110X of an rcwa mapping", "2.3",
552      [ 2, 3, 0 ], 481, 14, "densityofsupport of an rcwa mapping",
553      "X78E796B8824C4FC8" ],
554  [ "\033[10XDensityOfSetOfFixedPoints\033[110X of an rcwa mapping", "2.3",
555      [ 2, 3, 0 ], 481, 14, "densityofsetoffixedpoints of an rcwa mapping",
556      "X78E796B8824C4FC8" ],
557  [ "\033[10XModulus\033[110X of an rcwa mapping", "2.3", [ 2, 3, 0 ], 481,
558      14, "modulus of an rcwa mapping", "X78E796B8824C4FC8" ],
559  [ "\033[10XMod\033[110X for an rcwa mapping", "2.3", [ 2, 3, 0 ], 481, 14,
560      "mod for an rcwa mapping", "X78E796B8824C4FC8" ],
561  [ "\033[10XCoefficients\033[110X of an rcwa mapping", "2.3", [ 2, 3, 0 ],
562      481, 14, "coefficients of an rcwa mapping", "X78E796B8824C4FC8" ],
563  [ "rcwa mapping coercion", "2.3", [ 2, 3, 0 ], 481, 14,
564      "rcwa mapping coercion", "X78E796B8824C4FC8" ],
565  [ "rcwa group coercion", "2.3", [ 2, 3, 0 ], 481, 14, "rcwa group coercion",
566      "X78E796B8824C4FC8" ],
567  [ "class-wise translating definition", "2.4", [ 2, 4, 0 ], 605, 16,
568      "class-wise translating definition", "X7C16D22C7BD40FDC" ],
569  [ "integral definition", "2.4", [ 2, 4, 0 ], 605, 16, "integral definition",
570      "X7C16D22C7BD40FDC" ],
571  [ "balanced definition", "2.4", [ 2, 4, 0 ], 605, 16, "balanced definition",
572      "X7C16D22C7BD40FDC" ],
573  [ "sign-preserving definition", "2.4", [ 2, 4, 0 ], 605, 16,
574      "sign-preserving definition", "X7C16D22C7BD40FDC" ],
575  [ "maximal shift definition", "2.4", [ 2, 4, 0 ], 605, 16,
576      "maximal shift definition", "X7C16D22C7BD40FDC" ],
577  [ "rcwa mapping prime set", "2.4", [ 2, 4, 0 ], 605, 16,
578      "rcwa mapping prime set", "X7C16D22C7BD40FDC" ],
579  [ "rcwa mapping maximal shift", "2.4", [ 2, 4, 0 ], 605, 16,
580      "rcwa mapping maximal shift", "X7C16D22C7BD40FDC" ],
581  [ "rcwa mapping class-wise translating", "2.4", [ 2, 4, 0 ], 605, 16,
582      "rcwa mapping class-wise translating", "X7C16D22C7BD40FDC" ],
583  [ "rcwa mapping integral", "2.4", [ 2, 4, 0 ], 605, 16,
584      "rcwa mapping integral", "X7C16D22C7BD40FDC" ],
585  [ "rcwa mapping balanced", "2.4", [ 2, 4, 0 ], 605, 16,
586      "rcwa mapping balanced", "X7C16D22C7BD40FDC" ],
587  [ "rcwa mapping class-wise order-preserving", "2.4", [ 2, 4, 0 ], 605, 16,
588      "rcwa mapping class-wise order-preserving", "X7C16D22C7BD40FDC" ],
589  [ "rcwa mapping sign-preserving", "2.4", [ 2, 4, 0 ], 605, 16,
590      "rcwa mapping sign-preserving", "X7C16D22C7BD40FDC" ],
591  [ "\033[10XMultiplier\033[110X of an rcwa mapping", "2.4", [ 2, 4, 0 ],
592      605, 16, "multiplier of an rcwa mapping", "X7C16D22C7BD40FDC" ],
593  [ "\033[10XMult\033[110X for an rcwa mapping", "2.4", [ 2, 4, 0 ], 605, 16,
594      "mult for an rcwa mapping", "X7C16D22C7BD40FDC" ],
595  [ "\033[10XDivisor\033[110X of an rcwa mapping", "2.4", [ 2, 4, 0 ], 605,
596      16, "divisor of an rcwa mapping", "X7C16D22C7BD40FDC" ],
597  [ "\033[10XDiv\033[110X for an rcwa mapping", "2.4", [ 2, 4, 0 ], 605, 16,
598      "div for an rcwa mapping", "X7C16D22C7BD40FDC" ],
599  [ "\033[10XPrimeSet\033[110X of an rcwa mapping", "2.4", [ 2, 4, 0 ], 605,
600      16, "primeset of an rcwa mapping", "X7C16D22C7BD40FDC" ],
601  [ "\033[10XMaximalShift\033[110X of an rcwa mapping of Z", "2.4",
602      [ 2, 4, 0 ], 605, 16, "maximalshift of an rcwa mapping of z",
603      "X7C16D22C7BD40FDC" ],
604  [ "\033[10XIsClassWiseTranslating\033[110X for an rcwa mapping", "2.4",
605      [ 2, 4, 0 ], 605, 16, "isclasswisetranslating for an rcwa mapping",
606      "X7C16D22C7BD40FDC" ],
607  [ "\033[10XIsIntegral\033[110X for an rcwa mapping", "2.4", [ 2, 4, 0 ],
608      605, 16, "isintegral for an rcwa mapping", "X7C16D22C7BD40FDC" ],
609  [ "\033[10XIsBalanced\033[110X for an rcwa mapping", "2.4", [ 2, 4, 0 ],
610      605, 16, "isbalanced for an rcwa mapping", "X7C16D22C7BD40FDC" ],
611  [ "\033[10XIsClassWiseOrderPreserving\033[110X for an rcwa mapping", "2.4",
612      [ 2, 4, 0 ], 605, 16, "isclasswiseorderpreserving for an rcwa mapping",
613      "X7C16D22C7BD40FDC" ],
614  [ "\033[10XIsSignPreserving\033[110X for an rcwa mapping", "2.4",
615      [ 2, 4, 0 ], 605, 16, "issignpreserving for an rcwa mapping",
616      "X7C16D22C7BD40FDC" ],
617  [ "\033[2XLargestSourcesOfAffineMappings\033[102X for an rcwa mapping",
618      "2.4-1", [ 2, 4, 1 ], 663, 17,
619      "largestsourcesofaffinemappings for an rcwa mapping",
620      "X7C21406085B69C30" ],
621  [ "\033[2XFixedPointsOfAffinePartialMappings\033[102X for an rcwa mapping",
622      "2.4-2", [ 2, 4, 2 ], 686, 18,
623      "fixedpointsofaffinepartialmappings for an rcwa mapping",
624      "X7D6D0F2783AD02F4" ],
625  [ "\033[2XMultpk\033[102X for an rcwa mapping, a prime and an exponent",
626      "2.4-3", [ 2, 4, 3 ], 707, 18,
627      "multpk for an rcwa mapping a prime and an exponent",
628      "X7A2E308C860B46E3" ],
629  [ "\033[10XClassWiseOrderPreservingOn\033[110X", "2.4-3", [ 2, 4, 3 ], 707,
630      18, "classwiseorderpreservingon", "X7A2E308C860B46E3" ],
631  [ "\033[10XClassWiseConstantOn\033[110X", "2.4-3", [ 2, 4, 3 ], 707, 18,
632      "classwiseconstanton", "X7A2E308C860B46E3" ],
633  [ "\033[10XClassWiseOrderReversingOn\033[110X", "2.4-3", [ 2, 4, 3 ], 707,
634      18, "classwiseorderreversingon", "X7A2E308C860B46E3" ],
635  [ "\033[10XShiftsUpOn\033[110X", "2.4-3", [ 2, 4, 3 ], 707, 18,
636      "shiftsupon", "X7A2E308C860B46E3" ],
637  [ "\033[10XShiftsDownOn\033[110X", "2.4-3", [ 2, 4, 3 ], 707, 18,
638      "shiftsdownon", "X7A2E308C860B46E3" ],
639  [ "\033[2XDeterminant\033[102X of an rcwa mapping of z", "2.4-4",
640      [ 2, 4, 4 ], 749, 19, "determinant of an rcwa mapping of z",
641      "X7B1E53127D9AE52F" ],
642  [ "\033[2XSign\033[102X of an rcwa permutation of z", "2.4-5", [ 2, 4, 5 ],
643      783, 19, "sign of an rcwa permutation of z", "X8365EEEB82C946FD" ],
644  [ "\033[2XCTCSCRSplit\033[102X for an rcwa permutation of z", "2.5-1",
645      [ 2, 5, 1 ], 823, 20, "ctcscrsplit for an rcwa permutation of z",
646      "X829BA0537F2372FF" ],
647  [ "\033[2XFactorizationIntoCSCRCT\033[102X for an rcwa permutation of z",
648      "2.5-2", [ 2, 5, 2 ], 852, 20,
649      "factorizationintocscrct for an rcwa permutation of z",
650      "X853885A182EC5104" ],
651  [ "\033[2XFactorization\033[102X for an rcwa permutation of z", "2.5-2",
652      [ 2, 5, 2 ], 852, 20, "factorization for an rcwa permutation of z",
653      "X853885A182EC5104" ],
654  [ "\033[2XPrimeSwitch\033[102X p", "2.5-3", [ 2, 5, 3 ], 903, 21,
655      "primeswitch p", "X861C74E97AE5DA3B" ],
656  [ "\033[2XPrimeSwitch\033[102X p, k", "2.5-3", [ 2, 5, 3 ], 903, 21,
657      "primeswitch p k", "X861C74E97AE5DA3B" ],
658  [ "\033[2XPrimeSwitch\033[102X p, r, m", "2.5-3", [ 2, 5, 3 ], 903, 21,
659      "primeswitch p r m", "X861C74E97AE5DA3B" ],
660  [ "\033[2XPrimeSwitch\033[102X p, cl", "2.5-3", [ 2, 5, 3 ], 903, 21,
661      "primeswitch p cl", "X861C74E97AE5DA3B" ],
662  [ "\033[10XIsPrimeSwitch\033[110X for an rcwa mapping", "2.5-3",
663      [ 2, 5, 3 ], 903, 21, "isprimeswitch for an rcwa mapping",
664      "X861C74E97AE5DA3B" ],
665  [ "\033[2XmKnot\033[102X for an odd integer", "2.5-4", [ 2, 5, 4 ], 985,
666      23, "mknot for an odd integer", "X789CB69C7D97B0C4" ],
667  [ "\033[2XRoot\033[102X k-th root of an rcwa mapping", "2.6-1",
668      [ 2, 6, 1 ], 1014, 23, "root k-th root of an rcwa mapping",
669      "X873692CE78433859" ],
670  [ "\033[2XRightInverse\033[102X of an injective rcwa mapping", "2.7-1",
671      [ 2, 7, 1 ], 1046, 24, "rightinverse of an injective rcwa mapping",
672      "X7AEFF16E86533633" ],
673  [ "\033[2XCommonRightInverse\033[102X of two injective rcwa mappings",
674      "2.7-2", [ 2, 7, 2 ], 1061, 24,
675      "commonrightinverse of two injective rcwa mappings",
676      "X87C5B9CA7E319233" ],
677  [ "\033[2XImageDensity\033[102X of an rcwa mapping", "2.7-3", [ 2, 7, 3 ],
678      1086, 24, "imagedensity of an rcwa mapping", "X808D9EDF7BA27467" ],
679  [ "\033[10XInjectiveAsMappingFrom\033[110X for an rcwa mapping", "2.7-3",
680      [ 2, 7, 3 ], 1086, 24, "injectiveasmappingfrom for an rcwa mapping",
681      "X808D9EDF7BA27467" ],
682  [ "\033[2XTrajectory\033[102X for rcwa mapping, starting point, length",
683      "2.8-1", [ 2, 8, 1 ], 1122, 25,
684      "trajectory for rcwa mapping starting point length",
685      "X7C72174D7CCB6348" ],
686  [
687      "\033[2XTrajectory\033[102X for rcwa mapping, starting point, length, modul\
688us", "2.8-1", [ 2, 8, 1 ], 1122, 25,
689      "trajectory for rcwa mapping starting point length modulus",
690      "X7C72174D7CCB6348" ],
691  [
692      "\033[2XTrajectory\033[102X for rcwa mapping, starting point, set of end po\
693ints", "2.8-1", [ 2, 8, 1 ], 1122, 25,
694      "trajectory for rcwa mapping starting point set of end points",
695      "X7C72174D7CCB6348" ],
696  [
697      "\033[2XTrajectory\033[102X for rcwa mapping, starting point, set of end po\
698ints, modulus", "2.8-1", [ 2, 8, 1 ], 1122, 25,
699      "trajectory for rcwa mapping starting point set of end points modulus",
700      "X7C72174D7CCB6348" ],
701  [
702      "\033[2XTrajectory\033[102X for rcwa mapping, starting point, length, coeff\
703.-spec.", "2.8-2", [ 2, 8, 2 ], 1156, 25,
704      "trajectory for rcwa mapping starting point length coeff.-spec.",
705      "X7FFD09837E934853" ],
706  [
707      "\033[2XTrajectory\033[102X for rcwa mapping, starting point, set of end po\
708ints, coeff.-spec.", "2.8-2", [ 2, 8, 2 ], 1156, 25,
709      "trajectory for rcwa mapping starting point set of end points coeff.-spe\
710c.", "X7FFD09837E934853" ],
711  [ "\033[2XIncreasingOn\033[102X for an rcwa mapping", "2.8-3", [ 2, 8, 3 ],
712      1185, 26, "increasingon for an rcwa mapping", "X7E0244A386744185" ],
713  [ "\033[2XDecreasingOn\033[102X for an rcwa mapping", "2.8-3", [ 2, 8, 3 ],
714      1185, 26, "decreasingon for an rcwa mapping", "X7E0244A386744185" ],
715  [ "\033[2XTransitionGraph\033[102X for an rcwa mapping and a modulus",
716      "2.8-4", [ 2, 8, 4 ], 1216, 26,
717      "transitiongraph for an rcwa mapping and a modulus",
718      "X780841E07CAE7543" ],
719  [ "rcwa mapping transition graph", "2.8-4", [ 2, 8, 4 ], 1216, 26,
720      "rcwa mapping transition graph", "X780841E07CAE7543" ],
721  [ "\033[2XOrbitsModulo\033[102X for an rcwa mapping and a modulus",
722      "2.8-5", [ 2, 8, 5 ], 1235, 27,
723      "orbitsmodulo for an rcwa mapping and a modulus", "X7F03CC4179424AA9" ],
724  [ "\033[2XFactorizationOnConnectedComponents\033[102X for an rcwa mapping an\
725d a modulus", "2.8-6", [ 2, 8, 6 ], 1249, 27,
726      "factorizationonconnectedcomponents for an rcwa mapping and a modulus",
727      "X7F11051E866C197F" ],
728  [ "\033[2XTransitionMatrix\033[102X for an rcwa mapping and a modulus",
729      "2.8-7", [ 2, 8, 7 ], 1268, 27,
730      "transitionmatrix for an rcwa mapping and a modulus",
731      "X7B6833D67D916EF9" ],
732  [ "\033[2XSources\033[102X of an rcwa mapping", "2.8-8", [ 2, 8, 8 ], 1295,
733      28, "sources of an rcwa mapping", "X81DBA2D58526BE7E" ],
734  [ "\033[2XSinks\033[102X of an rcwa mapping", "2.8-8", [ 2, 8, 8 ], 1295,
735      28, "sinks of an rcwa mapping", "X81DBA2D58526BE7E" ],
736  [ "\033[2XLoops\033[102X of an rcwa mapping", "2.8-9", [ 2, 8, 9 ], 1318,
737      28, "loops of an rcwa mapping", "X80221A4D81AF7453" ],
738  [ "\033[2XGluckTaylorInvariant\033[102X of a trajectory", "2.8-10",
739      [ 2, 8, 10 ], 1338, 28, "glucktaylorinvariant of a trajectory",
740      "X8773152E81A30123" ],
741  [ "\033[2XLikelyContractionCentre\033[102X of an rcwa mapping", "2.8-11",
742      [ 2, 8, 11 ], 1370, 29, "likelycontractioncentre of an rcwa mapping",
743      "X84F6A29280E2F925" ],
744  [ "\033[2XGuessedDivergence\033[102X of an rcwa mapping", "2.8-12",
745      [ 2, 8, 12 ], 1398, 29, "guesseddivergence of an rcwa mapping",
746      "X81E0D8E3817B3D16" ],
747  [ "rcwa mapping sparse representation", "2.9", [ 2, 9, 0 ], 1415, 30,
748      "rcwa mapping sparse representation", "X86F0E0D17E6A9663" ],
749  [
750      "\033[10XRcwaMapping\033[110X by list of coefficients, sparse representatio\
751n", "2.9", [ 2, 9, 0 ], 1415, 30,
752      "rcwamapping by list of coefficients sparse representation",
753      "X86F0E0D17E6A9663" ],
754  [ "\033[2XSparseRepresentation\033[102X of an rcwa mapping", "2.9-1",
755      [ 2, 9, 1 ], 1448, 30, "sparserepresentation of an rcwa mapping",
756      "X879451B17AD78B07" ],
757  [ "\033[2XSparseRep\033[102X of an rcwa mapping", "2.9-1", [ 2, 9, 1 ],
758      1448, 30, "sparserep of an rcwa mapping", "X879451B17AD78B07" ],
759  [ "\033[2XStandardRepresentation\033[102X of an rcwa mapping", "2.9-1",
760      [ 2, 9, 1 ], 1448, 30, "standardrepresentation of an rcwa mapping",
761      "X879451B17AD78B07" ],
762  [ "\033[2XStandardRep\033[102X of an rcwa mapping", "2.9-1", [ 2, 9, 1 ],
763      1448, 30, "standardrep of an rcwa mapping", "X879451B17AD78B07" ],
764  [ "\033[2XIsRcwaMapping\033[102X", "2.10-1", [ 2, 10, 1 ], 1502, 31,
765      "isrcwamapping", "X7927C13782729CE9" ],
766  [ "\033[2XIsRcwaMappingOfZ\033[102X", "2.10-1", [ 2, 10, 1 ], 1502, 31,
767      "isrcwamappingofz", "X7927C13782729CE9" ],
768  [ "\033[2XIsRcwaMappingOfZ_pi\033[102X", "2.10-1", [ 2, 10, 1 ], 1502, 31,
769      "isrcwamappingofz_pi", "X7927C13782729CE9" ],
770  [ "\033[2XIsRcwaMappingOfGFqx\033[102X", "2.10-1", [ 2, 10, 1 ], 1502, 31,
771      "isrcwamappingofgfqx", "X7927C13782729CE9" ],
772  [ "\033[10XIsRcwaMappingOfZOrZ_pi\033[110X", "2.10-1", [ 2, 10, 1 ], 1502,
773      31, "isrcwamappingofzorz_pi", "X7927C13782729CE9" ],
774  [ "\033[10XIsRcwaMappingStandardRep\033[110X", "2.10-1", [ 2, 10, 1 ],
775      1502, 31, "isrcwamappingstandardrep", "X7927C13782729CE9" ],
776  [ "\033[10XExtRepOfObj\033[110X", "2.10-1", [ 2, 10, 1 ], 1502, 31,
777      "extrepofobj", "X7927C13782729CE9" ],
778  [ "\033[10XObjByExtRep\033[110X", "2.10-1", [ 2, 10, 1 ], 1502, 31,
779      "objbyextrep", "X7927C13782729CE9" ],
780  [ "\033[2XRcwaMappingsFamily\033[102X of a ring", "2.10-2", [ 2, 10, 2 ],
781      1520, 31, "rcwamappingsfamily of a ring", "X825DD365822934AF" ],
782  [ "\033[10XGroup\033[110X", "3.1", [ 3, 1, 0 ], 7, 32, "group",
783      "X81242A6586A604A3" ],
784  [ "\033[10XGroupByGenerators\033[110X", "3.1", [ 3, 1, 0 ], 7, 32,
785      "groupbygenerators", "X81242A6586A604A3" ],
786  [ "\033[10XGroupWithGenerators\033[110X", "3.1", [ 3, 1, 0 ], 7, 32,
787      "groupwithgenerators", "X81242A6586A604A3" ],
788  [ "\033[2XIsomorphismRcwaGroup\033[102X for a group, over a given ring",
789      "3.1-1", [ 3, 1, 1 ], 28, 32,
790      "isomorphismrcwagroup for a group over a given ring",
791      "X7EB8A301790290C7" ],
792  [ "\033[2XIsomorphismRcwaGroup\033[102X for a group", "3.1-1", [ 3, 1, 1 ],
793      28, 32, "isomorphismrcwagroup for a group", "X7EB8A301790290C7" ],
794  [ "\033[2XDirectProduct\033[102X for rcwa groups over z", "3.1-2",
795      [ 3, 1, 2 ], 65, 33, "directproduct for rcwa groups over z",
796      "X79CAE48981C11FE8" ],
797  [
798      "\033[2XWreathProduct\033[102X for an rcwa group over z and a permutation g\
799roup", "3.1-3", [ 3, 1, 3 ], 86, 33,
800      "wreathproduct for an rcwa group over z and a permutation group",
801      "X80D13D2A7AD73C2C" ],
802  [
803      "\033[2XWreathProduct\033[102X for an rcwa group over z and the infinite cy\
804clic group", "3.1-3", [ 3, 1, 3 ], 86, 33,
805      "wreathproduct for an rcwa group over z and the infinite cyclic group",
806      "X80D13D2A7AD73C2C" ],
807  [ "\033[2XMergerExtension\033[102X for finite permutation groups", "3.1-4",
808      [ 3, 1, 4 ], 128, 34, "mergerextension for finite permutation groups",
809      "X8794913B878DD5C4" ],
810  [
811      "\033[2XGroupByResidueClasses\033[102X the group `permuting a given list of\
812 residue classes'", "3.1-5", [ 3, 1, 5 ], 180, 35,
813      "groupbyresidueclasses the group permuting a given list of residue class\
814es", "X8143AB647801F438" ],
815  [
816      "\033[2XRestriction\033[102X of an rcwa mapping, by an injective rcwa mappi\
817ng", "3.1-6", [ 3, 1, 6 ], 214, 35,
818      "restriction of an rcwa mapping by an injective rcwa mapping",
819      "X852EF2C079E4D7FF" ],
820  [
821      "\033[2XRestriction\033[102X of an rcwa group, by an injective rcwa mapping\
822", "3.1-6", [ 3, 1, 6 ], 214, 35,
823      "restriction of an rcwa group by an injective rcwa mapping",
824      "X852EF2C079E4D7FF" ],
825  [
826      "\033[2XInduction\033[102X of an rcwa mapping, by an injective rcwa mapping\
827", "3.1-7", [ 3, 1, 7 ], 242, 36,
828      "induction of an rcwa mapping by an injective rcwa mapping",
829      "X82171D7287CBED95" ],
830  [ "\033[2XInduction\033[102X of an rcwa group, by an injective rcwa mapping"
831        , "3.1-7", [ 3, 1, 7 ], 242, 36,
832      "induction of an rcwa group by an injective rcwa mapping",
833      "X82171D7287CBED95" ],
834  [ "\033[10XSmallGeneratingSet\033[110X", "3.1-7", [ 3, 1, 7 ], 242, 36,
835      "smallgeneratingset", "X82171D7287CBED95" ],
836  [ "\033[10XView\033[110X for an rcwa group", "3.1-7", [ 3, 1, 7 ], 242, 36,
837      "view for an rcwa group", "X82171D7287CBED95" ],
838  [ "\033[10XDisplay\033[110X for an rcwa group", "3.1-7", [ 3, 1, 7 ], 242,
839      36, "display for an rcwa group", "X82171D7287CBED95" ],
840  [ "\033[10XPrint\033[110X for an rcwa group", "3.1-7", [ 3, 1, 7 ], 242,
841      36, "print for an rcwa group", "X82171D7287CBED95" ],
842  [ "\033[10XString\033[110X for an rcwa group", "3.1-7", [ 3, 1, 7 ], 242,
843      36, "string for an rcwa group", "X82171D7287CBED95" ],
844  [ "rcwa group modulus", "3.1-7", [ 3, 1, 7 ], 242, 36, "rcwa group modulus",
845      "X82171D7287CBED95" ],
846  [ "rcwa group multiplier", "3.1-7", [ 3, 1, 7 ], 242, 36,
847      "rcwa group multiplier", "X82171D7287CBED95" ],
848  [ "rcwa group divisor", "3.1-7", [ 3, 1, 7 ], 242, 36, "rcwa group divisor",
849      "X82171D7287CBED95" ],
850  [ "rcwa group prime set", "3.1-7", [ 3, 1, 7 ], 242, 36,
851      "rcwa group prime set", "X82171D7287CBED95" ],
852  [ "rcwa group class-wise translating", "3.1-7", [ 3, 1, 7 ], 242, 36,
853      "rcwa group class-wise translating", "X82171D7287CBED95" ],
854  [ "rcwa group integral", "3.1-7", [ 3, 1, 7 ], 242, 36,
855      "rcwa group integral", "X82171D7287CBED95" ],
856  [ "rcwa group class-wise order-preserving", "3.1-7", [ 3, 1, 7 ], 242, 36,
857      "rcwa group class-wise order-preserving", "X82171D7287CBED95" ],
858  [ "rcwa group sign-preserving", "3.1-7", [ 3, 1, 7 ], 242, 36,
859      "rcwa group sign-preserving", "X82171D7287CBED95" ],
860  [ "\033[10XModulus\033[110X of an rcwa group", "3.1-7", [ 3, 1, 7 ], 242,
861      36, "modulus of an rcwa group", "X82171D7287CBED95" ],
862  [ "\033[10XMod\033[110X for an rcwa group", "3.1-7", [ 3, 1, 7 ], 242, 36,
863      "mod for an rcwa group", "X82171D7287CBED95" ],
864  [ "\033[10XModulusOfRcwaMonoid\033[110X for an rcwa group", "3.1-7",
865      [ 3, 1, 7 ], 242, 36, "modulusofrcwamonoid for an rcwa group",
866      "X82171D7287CBED95" ],
867  [ "\033[10XMultiplier\033[110X of an rcwa group", "3.1-7", [ 3, 1, 7 ],
868      242, 36, "multiplier of an rcwa group", "X82171D7287CBED95" ],
869  [ "\033[10XMult\033[110X for an rcwa group", "3.1-7", [ 3, 1, 7 ], 242, 36,
870      "mult for an rcwa group", "X82171D7287CBED95" ],
871  [ "\033[10XDivisor\033[110X of an rcwa group", "3.1-7", [ 3, 1, 7 ], 242,
872      36, "divisor of an rcwa group", "X82171D7287CBED95" ],
873  [ "\033[10XDiv\033[110X for an rcwa group", "3.1-7", [ 3, 1, 7 ], 242, 36,
874      "div for an rcwa group", "X82171D7287CBED95" ],
875  [ "\033[10XPrimeSet\033[110X of an rcwa group", "3.1-7", [ 3, 1, 7 ], 242,
876      36, "primeset of an rcwa group", "X82171D7287CBED95" ],
877  [ "\033[10XIsClassWiseTranslating\033[110X for an rcwa group", "3.1-7",
878      [ 3, 1, 7 ], 242, 36, "isclasswisetranslating for an rcwa group",
879      "X82171D7287CBED95" ],
880  [ "\033[10XIsIntegral\033[110X for an rcwa group", "3.1-7", [ 3, 1, 7 ],
881      242, 36, "isintegral for an rcwa group", "X82171D7287CBED95" ],
882  [ "\033[10XIsClassWiseOrderPreserving\033[110X for an rcwa group", "3.1-7",
883      [ 3, 1, 7 ], 242, 36, "isclasswiseorderpreserving for an rcwa group",
884      "X82171D7287CBED95" ],
885  [ "\033[10XIsSignPreserving\033[110X for an rcwa group", "3.1-7",
886      [ 3, 1, 7 ], 242, 36, "issignpreserving for an rcwa group",
887      "X82171D7287CBED95" ],
888  [ "\033[2XRCWA\033[102X the group formed by all rcwa permutations of a ring"
889        , "3.1-8", [ 3, 1, 8 ], 299, 37,
890      "rcwa the group formed by all rcwa permutations of a ring",
891      "X79450C1C8756FEB3" ],
892  [ "\033[10XNrConjugacyClassesOfRCWAZOfOrder\033[110X", "3.1-8",
893      [ 3, 1, 8 ], 299, 37, "nrconjugacyclassesofrcwazoforder",
894      "X79450C1C8756FEB3" ],
895  [
896      "\033[2XCT\033[102X the group generated by all class transpositions of a ri\
897ng", "3.1-9", [ 3, 1, 9 ], 329, 37,
898      "ct the group generated by all class transpositions of a ring",
899      "X7BD42D8481300E25" ],
900  [ "\033[2XCT\033[102X subgroup of ct(z)", "3.1-9", [ 3, 1, 9 ], 329, 37,
901      "ct subgroup of ct z", "X7BD42D8481300E25" ],
902  [ "\033[10XMirrored\033[110X", "3.1-9", [ 3, 1, 9 ], 329, 37, "mirrored",
903      "X7BD42D8481300E25" ],
904  [ "\033[10XAllElementsOfCTZWithGivenModulus\033[110X", "3.1-9",
905      [ 3, 1, 9 ], 329, 37, "allelementsofctzwithgivenmodulus",
906      "X7BD42D8481300E25" ],
907  [ "\033[10XNrElementsOfCTZWithGivenModulus\033[110X", "3.1-9", [ 3, 1, 9 ],
908      329, 37, "nrelementsofctzwithgivenmodulus", "X7BD42D8481300E25" ],
909  [ "\033[10XNrConjugacyClassesOfCTZOfOrder\033[110X", "3.1-9", [ 3, 1, 9 ],
910      329, 37, "nrconjugacyclassesofctzoforder", "X7BD42D8481300E25" ],
911  [ "\033[2XStructureDescription\033[102X for an rcwa group", "3.2-1",
912      [ 3, 2, 1 ], 405, 38, "structuredescription for an rcwa group",
913      "X864A7E3E87F366A8" ],
914  [ "\033[10XSize\033[110X for an rcwa group", "3.2-1", [ 3, 2, 1 ], 405, 38,
915      "size for an rcwa group", "X864A7E3E87F366A8" ],
916  [ "\033[10XIsomorphismPermGroup\033[110X for a finite rcwa group", "3.2-1",
917      [ 3, 2, 1 ], 405, 38, "isomorphismpermgroup for a finite rcwa group",
918      "X864A7E3E87F366A8" ],
919  [ "rcwa group membership test", "3.2-1", [ 3, 2, 1 ], 405, 38,
920      "rcwa group membership test", "X864A7E3E87F366A8" ],
921  [ "\033[10XOrbitLengthBound\033[110X", "3.2-1", [ 3, 2, 1 ], 405, 38,
922      "orbitlengthbound", "X864A7E3E87F366A8" ],
923  [ "rcwa group conjugacy problem", "3.2-1", [ 3, 2, 1 ], 405, 38,
924      "rcwa group conjugacy problem", "X864A7E3E87F366A8" ],
925  [ "\033[10XIsConjugate\033[110X for elements of RCWA(R)", "3.2-1",
926      [ 3, 2, 1 ], 405, 38, "isconjugate for elements of rcwa r",
927      "X864A7E3E87F366A8" ],
928  [ "\033[10XIsConjugate\033[110X for elements of CT(R)", "3.2-1",
929      [ 3, 2, 1 ], 405, 38, "isconjugate for elements of ct r",
930      "X864A7E3E87F366A8" ],
931  [ "\033[10XIsTame\033[110X for an rcwa group", "3.2-1", [ 3, 2, 1 ], 405,
932      38, "istame for an rcwa group", "X864A7E3E87F366A8" ],
933  [ "\033[10XIsSolvable\033[110X for an rcwa group", "3.2-1", [ 3, 2, 1 ],
934      405, 38, "issolvable for an rcwa group", "X864A7E3E87F366A8" ],
935  [ "\033[10XIsPerfect\033[110X for an rcwa group", "3.2-1", [ 3, 2, 1 ],
936      405, 38, "isperfect for an rcwa group", "X864A7E3E87F366A8" ],
937  [ "\033[10XDerivedSubgroup\033[110X of an rcwa group", "3.2-1",
938      [ 3, 2, 1 ], 405, 38, "derivedsubgroup of an rcwa group",
939      "X864A7E3E87F366A8" ],
940  [ "\033[10XIndex\033[110X for rcwa groups", "3.2-1", [ 3, 2, 1 ], 405, 38,
941      "index for rcwa groups", "X864A7E3E87F366A8" ],
942  [ "\033[10XIsomorphismMatrixGroup\033[110X for an rcwa group", "3.2-1",
943      [ 3, 2, 1 ], 405, 38, "isomorphismmatrixgroup for an rcwa group",
944      "X864A7E3E87F366A8" ],
945  [ "\033[10XExponent\033[110X of an rcwa group", "3.2-1", [ 3, 2, 1 ], 405,
946      38, "exponent of an rcwa group", "X864A7E3E87F366A8" ],
947  [
948      "\033[2XEpimorphismFromFpGroup\033[102X for an rcwa group and a search radi\
949us", "3.2-2", [ 3, 2, 2 ], 599, 42,
950      "epimorphismfromfpgroup for an rcwa group and a search radius",
951      "X83527DA37C5CB2C7" ],
952  [
953      "\033[2XEpimorphismFromFpGroup\033[102X for rcwa group, search radius and b\
954ound on number of affine parts", "3.2-2", [ 3, 2, 2 ], 599, 42,
955      "epimorphismfromfpgroup for rcwa group search radius and bound on number\
956 of affine parts", "X83527DA37C5CB2C7" ],
957  [
958      "\033[2XPreImagesRepresentative\033[102X for an epi. from a free group to a\
959n rcwa group", "3.2-3", [ 3, 2, 3 ], 632, 42,
960      "preimagesrepresentative for an epi. from a free group to an rcwa group"
961        , "X8463E34286344F06" ],
962  [
963      "\033[10XPreImagesRepresentatives\033[110X for an epi. from a free group to\
964 an rcwa group", "3.2-3", [ 3, 2, 3 ], 632, 42,
965      "preimagesrepresentatives for an epi. from a free group to an rcwa group\
966", "X8463E34286344F06" ],
967  [ "\033[10XSupport\033[110X of an rcwa group", "3.3", [ 3, 3, 0 ], 675, 43,
968      "support of an rcwa group", "X8151BE577FFDCE87" ],
969  [ "\033[10XMovedPoints\033[110X of an rcwa group", "3.3", [ 3, 3, 0 ], 675,
970      43, "movedpoints of an rcwa group", "X8151BE577FFDCE87" ],
971  [ "\033[10XIsTransitive\033[110X for an rcwa group, on its underlying ring",
972      "3.3", [ 3, 3, 0 ], 675, 43,
973      "istransitive for an rcwa group on its underlying ring",
974      "X8151BE577FFDCE87" ],
975  [
976      "\033[10XIsTransitiveOnNonnegativeIntegersInSupport\033[110X for an rcwa gr\
977oup over Z", "3.3", [ 3, 3, 0 ], 675, 43,
978      "istransitiveonnonnegativeintegersinsupport for an rcwa group over z",
979      "X8151BE577FFDCE87" ],
980  [
981      "\033[10XTryIsTransitiveOnNonnegativeIntegersInSupport\033[110X for an rcwa\
982 group over Z and a search limit", "3.3", [ 3, 3, 0 ], 675, 43,
983      "tryistransitiveonnonnegativeintegersinsupport for an rcwa group over z \
984and a search limit", "X8151BE577FFDCE87" ],
985  [
986      "\033[10XTransitivityCertificate\033[110X for an rcwa group over Z and a se\
987arch limit", "3.3", [ 3, 3, 0 ], 675, 43,
988      "transitivitycertificate for an rcwa group over z and a search limit",
989      "X8151BE577FFDCE87" ],
990  [
991      "\033[10XTryToComputeTransitivityCertificate\033[110X for an rcwa group ove\
992r Z and a search limit", "3.3", [ 3, 3, 0 ], 675, 43,
993      "trytocomputetransitivitycertificate for an rcwa group over z and a sear\
994ch limit", "X8151BE577FFDCE87" ],
995  [
996      "\033[10XSimplifiedCertificate\033[110X for a transitivity certificate of a\
997n rcwa groups over Z", "3.3", [ 3, 3, 0 ], 675, 43,
998      "simplifiedcertificate for a transitivity certificate of an rcwa groups \
999over z", "X8151BE577FFDCE87" ],
1000  [ "\033[2XOrbit\033[102X for an rcwa group and a point", "3.3-1",
1001      [ 3, 3, 1 ], 797, 45, "orbit for an rcwa group and a point",
1002      "X7C046BE97EE53692" ],
1003  [ "\033[2XOrbit\033[102X for an rcwa group and a set", "3.3-1",
1004      [ 3, 3, 1 ], 797, 45, "orbit for an rcwa group and a set",
1005      "X7C046BE97EE53692" ],
1006  [
1007      "\033[2XGrowthFunctionOfOrbit\033[102X for an rcwa group, a point and bound\
1008s on radius and sphere size", "3.3-2", [ 3, 3, 2 ], 840, 46,
1009      "growthfunctionoforbit for an rcwa group a point and bounds on radius an\
1010d sphere size", "X7B7A3AF97D195E33" ],
1011  [
1012      "\033[2XGrowthFunctionOfOrbit\033[102X for an rcwa group orbit and bounds o\
1013n radius and sphere size", "3.3-2", [ 3, 3, 2 ], 840, 46,
1014      "growthfunctionoforbit for an rcwa group orbit and bounds on radius and \
1015sphere size", "X7B7A3AF97D195E33" ],
1016  [ "\033[10XDistanceToNextSmallerPointInOrbit\033[110X", "3.3-2",
1017      [ 3, 3, 2 ], 840, 46, "distancetonextsmallerpointinorbit",
1018      "X7B7A3AF97D195E33" ],
1019  [
1020      "\033[2XDrawOrbitPicture\033[102X g, p0, bound, h, w, colored, palette, fil\
1021ename", "3.3-3", [ 3, 3, 3 ], 891, 47,
1022      "draworbitpicture g p0 bound h w colored palette filename",
1023      "X7D9DFAC97F9F0891" ],
1024  [
1025      "\033[2XShortOrbits\033[102X for rcwa group, set of points and bound on len\
1026gth", "3.3-4", [ 3, 3, 4 ], 925, 47,
1027      "shortorbits for rcwa group set of points and bound on length",
1028      "X78F145197F63A25D" ],
1029  [
1030      "\033[2XShortOrbits\033[102X for rcwa group, set of points and bounds on le\
1031ngth and points", "3.3-4", [ 3, 3, 4 ], 925, 47,
1032      "shortorbits for rcwa group set of points and bounds on length and point\
1033s", "X78F145197F63A25D" ],
1034  [
1035      "\033[2XShortCycles\033[102X for rcwa permutation, set of points and bound \
1036on length", "3.3-4", [ 3, 3, 4 ], 925, 47,
1037      "shortcycles for rcwa permutation set of points and bound on length",
1038      "X78F145197F63A25D" ],
1039  [
1040      "\033[2XShortCycles\033[102X for rcwa permutation, set of points and bounds\
1041 on length and points", "3.3-4", [ 3, 3, 4 ], 925, 47,
1042      "shortcycles for rcwa permutation set of points and bounds on length and\
1043 points", "X78F145197F63A25D" ],
1044  [ "\033[2XShortCycles\033[102X for rcwa permutation and bound on length",
1045      "3.3-4", [ 3, 3, 4 ], 925, 47,
1046      "shortcycles for rcwa permutation and bound on length",
1047      "X78F145197F63A25D" ],
1048  [ "\033[10XCyclesOnFiniteOrbit\033[110X", "3.3-4", [ 3, 3, 4 ], 925, 47,
1049      "cyclesonfiniteorbit", "X78F145197F63A25D" ],
1050  [
1051      "\033[2XShortResidueClassOrbits\033[102X for rcwa group and bounds on modul\
1052us and length", "3.3-5", [ 3, 3, 5 ], 980, 48,
1053      "shortresidueclassorbits for rcwa group and bounds on modulus and length\
1054", "X80D18D0778A96C16" ],
1055  [
1056      "\033[2XShortResidueClassCycles\033[102X for rcwa permutation and bounds on\
1057 modulus and length", "3.3-5", [ 3, 3, 5 ], 980, 48,
1058      "shortresidueclasscycles for rcwa permutation and bounds on modulus and \
1059length", "X80D18D0778A96C16" ],
1060  [ "\033[2XComputeCycleLength\033[102X for an rcwa permutation and a point",
1061      "3.3-6", [ 3, 3, 6 ], 1025, 49,
1062      "computecyclelength for an rcwa permutation and a point",
1063      "X80C080287A355EFF" ],
1064  [
1065      "\033[2XCycleRepresentativesAndLengths\033[102X for rcwa permutation and se\
1066t of seed points", "3.3-7", [ 3, 3, 7 ], 1071, 50,
1067      "cyclerepresentativesandlengths for rcwa permutation and set of seed poi\
1068nts", "X7F76B04E86C77B94" ],
1069  [
1070      "\033[2XFixedResidueClasses\033[102X for rcwa mapping and bound on modulus"
1071        , "3.3-8", [ 3, 3, 8 ], 1121, 50,
1072      "fixedresidueclasses for rcwa mapping and bound on modulus",
1073      "X8777A62286597D53" ],
1074  [ "\033[2XFixedResidueClasses\033[102X for rcwa group and bound on modulus",
1075      "3.3-8", [ 3, 3, 8 ], 1121, 50,
1076      "fixedresidueclasses for rcwa group and bound on modulus",
1077      "X8777A62286597D53" ],
1078  [ "\033[2XBall\033[102X for group, element and radius", "3.3-9",
1079      [ 3, 3, 9 ], 1144, 51, "ball for group element and radius",
1080      "X8735855587CC029F" ],
1081  [ "\033[2XBall\033[102X for group, point, radius and action", "3.3-9",
1082      [ 3, 3, 9 ], 1144, 51, "ball for group point radius and action",
1083      "X8735855587CC029F" ],
1084  [ "\033[2XBall\033[102X for group, point and radius", "3.3-9", [ 3, 3, 9 ],
1085      1144, 51, "ball for group point and radius", "X8735855587CC029F" ],
1086  [ "\033[10XRestrictedBall\033[110X G, g, r, modulusbound", "3.3-9",
1087      [ 3, 3, 9 ], 1144, 51, "restrictedball g g r modulusbound",
1088      "X8735855587CC029F" ],
1089  [ "\033[2XRepresentativeAction\033[102X g, source, destination, action",
1090      "3.3-10", [ 3, 3, 10 ], 1190, 52,
1091      "representativeaction g source destination action", "X87A3462C82FD376E"
1092     ],
1093  [
1094      "\033[10XRepresentativeActionPreImage\033[110X G, source, destination, acti\
1095on, F", "3.3-10", [ 3, 3, 10 ], 1190, 52,
1096      "representativeactionpreimage g source destination action f",
1097      "X87A3462C82FD376E" ],
1098  [
1099      "\033[2XProjectionsToInvariantUnionsOfResidueClasses\033[102X for rcwa grou\
1100p and modulus", "3.3-11", [ 3, 3, 11 ], 1266, 53,
1101      "projectionstoinvariantunionsofresidueclasses for rcwa group and modulus\
1102", "X8587246A7F890849" ],
1103  [ "\033[10XOrbitsModulo\033[110X for an rcwa group and a modulus",
1104      "3.3-11", [ 3, 3, 11 ], 1266, 53,
1105      "orbitsmodulo for an rcwa group and a modulus", "X8587246A7F890849" ],
1106  [ "\033[2XRepresentativeAction\033[102X for rcwa(r) and 2 partitions of r in\
1107to residue classes", "3.3-12", [ 3, 3, 12 ], 1292, 53,
1108      "representativeaction for rcwa r and 2 partitions of r into residue clas\
1109ses", "X866843D08213067E" ],
1110  [
1111      "\033[2XCollatzLikeMappingByOrbitTree\033[102X for rcwa group, root point a\
1112nd range of radii", "3.3-13", [ 3, 3, 13 ], 1333, 54,
1113      "collatzlikemappingbyorbittree for rcwa group root point and range of ra\
1114dii", "X82DBAF35788FA239" ],
1115  [ "\033[2XRespectedPartition\033[102X of a tame rcwa group", "3.4-1",
1116      [ 3, 4, 1 ], 1396, 55, "respectedpartition of a tame rcwa group",
1117      "X7F523A6B87825AB8" ],
1118  [ "\033[2XRespectedPartition\033[102X of a tame rcwa permutation", "3.4-1",
1119      [ 3, 4, 1 ], 1396, 55, "respectedpartition of a tame rcwa permutation",
1120      "X7F523A6B87825AB8" ],
1121  [ "\033[10XRespectsPartition\033[110X for an rcwa group", "3.4-1",
1122      [ 3, 4, 1 ], 1396, 55, "respectspartition for an rcwa group",
1123      "X7F523A6B87825AB8" ],
1124  [ "\033[10XRespectsPartition\033[110X for an rcwa permutation", "3.4-1",
1125      [ 3, 4, 1 ], 1396, 55, "respectspartition for an rcwa permutation",
1126      "X7F523A6B87825AB8" ],
1127  [ "\033[10XPermutationOpNC\033[110X g, P, OnPoints", "3.4-1", [ 3, 4, 1 ],
1128      1396, 55, "permutationopnc g p onpoints", "X7F523A6B87825AB8" ],
1129  [ "\033[2XActionOnRespectedPartition\033[102X for a tame rcwa group",
1130      "3.4-2", [ 3, 4, 2 ], 1430, 56,
1131      "actiononrespectedpartition for a tame rcwa group", "X831ADC1584DE6113"
1132     ],
1133  [ "\033[2XKernelOfActionOnRespectedPartition\033[102X for a tame rcwa group"
1134        , "3.4-2", [ 3, 4, 2 ], 1430, 56,
1135      "kernelofactiononrespectedpartition for a tame rcwa group",
1136      "X831ADC1584DE6113" ],
1137  [
1138      "\033[2XRankOfKernelOfActionOnRespectedPartition\033[102X for a tame rcwa g\
1139roup", "3.4-2", [ 3, 4, 2 ], 1430, 56,
1140      "rankofkernelofactiononrespectedpartition for a tame rcwa group",
1141      "X831ADC1584DE6113" ],
1142  [ "\033[10XIntegralConjugate\033[110X of a tame rcwa group", "3.4-2",
1143      [ 3, 4, 2 ], 1430, 56, "integralconjugate of a tame rcwa group",
1144      "X831ADC1584DE6113" ],
1145  [ "\033[10XIntegralConjugate\033[110X of a tame rcwa permutation", "3.4-2",
1146      [ 3, 4, 2 ], 1430, 56, "integralconjugate of a tame rcwa permutation",
1147      "X831ADC1584DE6113" ],
1148  [ "\033[10XIntegralizingConjugator\033[110X of a tame rcwa group", "3.4-2",
1149      [ 3, 4, 2 ], 1430, 56, "integralizingconjugator of a tame rcwa group",
1150      "X831ADC1584DE6113" ],
1151  [ "\033[10XIntegralizingConjugator\033[110X of a tame rcwa permutation",
1152      "3.4-2", [ 3, 4, 2 ], 1430, 56,
1153      "integralizingconjugator of a tame rcwa permutation",
1154      "X831ADC1584DE6113" ],
1155  [ "\033[10XRandom\033[110X RCWA(R)", "3.5", [ 3, 5, 0 ], 1492, 57,
1156      "random rcwa r", "X81941A247942FB99" ],
1157  [ "\033[10XRandom\033[110X CT(R)", "3.5", [ 3, 5, 0 ], 1492, 57,
1158      "random ct r", "X81941A247942FB99" ],
1159  [ "\033[2XIsRcwaGroup\033[102X", "3.6-1", [ 3, 6, 1 ], 1543, 58,
1160      "isrcwagroup", "X84AFBB997B694A3D" ],
1161  [ "\033[2XIsRcwaGroupOverZ\033[102X", "3.6-1", [ 3, 6, 1 ], 1543, 58,
1162      "isrcwagroupoverz", "X84AFBB997B694A3D" ],
1163  [ "\033[2XIsRcwaGroupOverZ_pi\033[102X", "3.6-1", [ 3, 6, 1 ], 1543, 58,
1164      "isrcwagroupoverz_pi", "X84AFBB997B694A3D" ],
1165  [ "\033[2XIsRcwaGroupOverGFqx\033[102X", "3.6-1", [ 3, 6, 1 ], 1543, 58,
1166      "isrcwagroupovergfqx", "X84AFBB997B694A3D" ],
1167  [ "\033[10XIsRcwaGroupOverZOrZ_pi\033[110X", "3.6-1", [ 3, 6, 1 ], 1543,
1168      58, "isrcwagroupoverzorz_pi", "X84AFBB997B694A3D" ],
1169  [ "\033[10XIsNaturalRCWA\033[110X", "3.6-1", [ 3, 6, 1 ], 1543, 58,
1170      "isnaturalrcwa", "X84AFBB997B694A3D" ],
1171  [ "\033[10XIsNaturalCT\033[110X", "3.6-1", [ 3, 6, 1 ], 1543, 58,
1172      "isnaturalct", "X84AFBB997B694A3D" ],
1173  [ "rcwa monoid definition", "4.", [ 4, 0, 0 ], 1, 59,
1174      "rcwa monoid definition", "X81C90F7C7BA25BDF" ],
1175  [ "\033[10XMonoid\033[110X", "4.1", [ 4, 1, 0 ], 8, 59, "monoid",
1176      "X83D42E26849D5580" ],
1177  [ "\033[10XMonoidByGenerators\033[110X", "4.1", [ 4, 1, 0 ], 8, 59,
1178      "monoidbygenerators", "X83D42E26849D5580" ],
1179  [ "\033[10XView\033[110X for an rcwa monoid", "4.1", [ 4, 1, 0 ], 8, 59,
1180      "view for an rcwa monoid", "X83D42E26849D5580" ],
1181  [ "\033[10XDisplay\033[110X for an rcwa monoid", "4.1", [ 4, 1, 0 ], 8, 59,
1182      "display for an rcwa monoid", "X83D42E26849D5580" ],
1183  [ "\033[10XPrint\033[110X for an rcwa monoid", "4.1", [ 4, 1, 0 ], 8, 59,
1184      "print for an rcwa monoid", "X83D42E26849D5580" ],
1185  [ "\033[10XString\033[110X for an rcwa monoid", "4.1", [ 4, 1, 0 ], 8, 59,
1186      "string for an rcwa monoid", "X83D42E26849D5580" ],
1187  [ "\033[2XRcwa\033[102X the monoid formed by all rcwa mappings of a ring",
1188      "4.1-1", [ 4, 1, 1 ], 42, 60,
1189      "rcwa the monoid formed by all rcwa mappings of a ring",
1190      "X7B95FCA279E0D6CC" ],
1191  [
1192      "\033[10XRestriction\033[110X for an rcwa monoid, by an injective rcwa mapp\
1193ing", "4.1-1", [ 4, 1, 1 ], 42, 60,
1194      "restriction for an rcwa monoid by an injective rcwa mapping",
1195      "X7B95FCA279E0D6CC" ],
1196  [
1197      "\033[10XInduction\033[110X for an rcwa monoid, by an injective rcwa mappin\
1198g", "4.1-1", [ 4, 1, 1 ], 42, 60,
1199      "induction for an rcwa monoid by an injective rcwa mapping",
1200      "X7B95FCA279E0D6CC" ],
1201  [ "\033[10XSize\033[110X for an rcwa monoid", "4.2", [ 4, 2, 0 ], 78, 60,
1202      "size for an rcwa monoid", "X8759954F7EB1A658" ],
1203  [ "\033[10Xrcwa monoids\033[110X membership test", "4.2", [ 4, 2, 0 ], 78,
1204      60, "rcwa monoids membership test", "X8759954F7EB1A658" ],
1205  [ "\033[10XIsSubset\033[110X for two rcwa monoids", "4.2", [ 4, 2, 0 ], 78,
1206      60, "issubset for two rcwa monoids", "X8759954F7EB1A658" ],
1207  [ "\033[10XSupport\033[110X of an rcwa monoid", "4.2", [ 4, 2, 0 ], 78, 60,
1208      "support of an rcwa monoid", "X8759954F7EB1A658" ],
1209  [ "\033[10XModulus\033[110X of an rcwa monoid", "4.2", [ 4, 2, 0 ], 78, 60,
1210      "modulus of an rcwa monoid", "X8759954F7EB1A658" ],
1211  [ "\033[10XIsTame\033[110X for an rcwa monoid", "4.2", [ 4, 2, 0 ], 78, 60,
1212      "istame for an rcwa monoid", "X8759954F7EB1A658" ],
1213  [ "\033[10XPrimeSet\033[110X of an rcwa monoid", "4.2", [ 4, 2, 0 ], 78,
1214      60, "primeset of an rcwa monoid", "X8759954F7EB1A658" ],
1215  [ "\033[10XIsIntegral\033[110X for an rcwa monoid", "4.2", [ 4, 2, 0 ], 78,
1216      60, "isintegral for an rcwa monoid", "X8759954F7EB1A658" ],
1217  [ "\033[10XIsClassWiseOrderPreserving\033[110X for an rcwa monoid", "4.2",
1218      [ 4, 2, 0 ], 78, 60, "isclasswiseorderpreserving for an rcwa monoid",
1219      "X8759954F7EB1A658" ],
1220  [ "\033[10XIsSignPreserving\033[110X for an rcwa monoid", "4.2",
1221      [ 4, 2, 0 ], 78, 60, "issignpreserving for an rcwa monoid",
1222      "X8759954F7EB1A658" ],
1223  [ "rcwa monoid modulus", "4.2", [ 4, 2, 0 ], 78, 60, "rcwa monoid modulus",
1224      "X8759954F7EB1A658" ],
1225  [ "rcwa monoid tame", "4.2", [ 4, 2, 0 ], 78, 60, "rcwa monoid tame",
1226      "X8759954F7EB1A658" ],
1227  [ "rcwa monoid wild", "4.2", [ 4, 2, 0 ], 78, 60, "rcwa monoid wild",
1228      "X8759954F7EB1A658" ],
1229  [ "rcwa monoid prime set", "4.2", [ 4, 2, 0 ], 78, 60,
1230      "rcwa monoid prime set", "X8759954F7EB1A658" ],
1231  [ "rcwa monoid integral", "4.2", [ 4, 2, 0 ], 78, 60,
1232      "rcwa monoid integral", "X8759954F7EB1A658" ],
1233  [ "rcwa monoid class-wise order-preserving", "4.2", [ 4, 2, 0 ], 78, 60,
1234      "rcwa monoid class-wise order-preserving", "X8759954F7EB1A658" ],
1235  [ "rcwa monoid sign-preserving", "4.2", [ 4, 2, 0 ], 78, 60,
1236      "rcwa monoid sign-preserving", "X8759954F7EB1A658" ],
1237  [
1238      "\033[2XShortOrbits\033[102X for rcwa monoid, set of points and bound on le\
1239ngth", "4.2-1", [ 4, 2, 1 ], 136, 61,
1240      "shortorbits for rcwa monoid set of points and bound on length",
1241      "X87DB896687475084" ],
1242  [ "\033[2XBall\033[102X for monoid, element and radius", "4.2-2",
1243      [ 4, 2, 2 ], 165, 62, "ball for monoid element and radius",
1244      "X787848137DF1C245" ],
1245  [ "\033[2XBall\033[102X for monoid, point, radius and action", "4.2-2",
1246      [ 4, 2, 2 ], 165, 62, "ball for monoid point radius and action",
1247      "X787848137DF1C245" ],
1248  [ "rcwa mapping of Z x Z, definition", "5.1", [ 5, 1, 0 ], 22, 63,
1249      "rcwa mapping of z x z definition", "X781907CA785CC7AC" ],
1250  [ "rcwa mapping modulus", "5.1", [ 5, 1, 0 ], 22, 63,
1251      "rcwa mapping modulus", "X781907CA785CC7AC" ],
1252  [ "rcwa mapping class-wise translating", "5.1", [ 5, 1, 0 ], 22, 63,
1253      "rcwa mapping class-wise translating", "X781907CA785CC7AC" ],
1254  [ "class-wise translating definition", "5.1", [ 5, 1, 0 ], 22, 63,
1255      "class-wise translating definition", "X781907CA785CC7AC" ],
1256  [ "prime set definition", "5.1", [ 5, 1, 0 ], 22, 63,
1257      "prime set definition", "X781907CA785CC7AC" ],
1258  [ "\033[2XRcwaMapping\033[102X by ring = z x z, modulus and coefficients",
1259      "5.2-1", [ 5, 2, 1 ], 52, 64,
1260      "rcwamapping by ring = z x z modulus and coefficients",
1261      "X790649618012C606" ],
1262  [
1263      "\033[2XRcwaMapping\033[102X by two partitions of z x z into residue classe\
1264s", "5.2-1", [ 5, 2, 1 ], 52, 64,
1265      "rcwamapping by two partitions of z x z into residue classes",
1266      "X790649618012C606" ],
1267  [ "\033[2XRcwaMapping\033[102X of z x z, by residue class cycles", "5.2-1",
1268      [ 5, 2, 1 ], 52, 64, "rcwamapping of z x z by residue class cycles",
1269      "X790649618012C606" ],
1270  [ "\033[2XRcwaMapping\033[102X of z x z, by projections to coordinates",
1271      "5.2-1", [ 5, 2, 1 ], 52, 64,
1272      "rcwamapping of z x z by projections to coordinates",
1273      "X790649618012C606" ],
1274  [ "\033[2XClassTransposition\033[102X r1, l1, r2, l2 (for z x z)", "5.2-2",
1275      [ 5, 2, 2 ], 201, 66, "classtransposition r1 l1 r2 l2 for z x z",
1276      "X7B450EE17B465E02" ],
1277  [ "\033[2XClassTransposition\033[102X cl1, cl2 (for z x z)", "5.2-2",
1278      [ 5, 2, 2 ], 201, 66, "classtransposition cl1 cl2 for z x z",
1279      "X7B450EE17B465E02" ],
1280  [ "\033[10XTransposedClasses\033[110X of a class transposition of Z x Z",
1281      "5.2-2", [ 5, 2, 2 ], 201, 66,
1282      "transposedclasses of a class transposition of z x z",
1283      "X7B450EE17B465E02" ],
1284  [
1285      "\033[10XSplittedClassTransposition\033[110X for a class transposition of Z\
1286 x Z", "5.2-2", [ 5, 2, 2 ], 201, 66,
1287      "splittedclasstransposition for a class transposition of z x z",
1288      "X7B450EE17B465E02" ],
1289  [ "\033[2XClassRotation\033[102X r, l, u; for z x z", "5.2-3", [ 5, 2, 3 ],
1290      267, 67, "classrotation r l u for z x z", "X828438127DDAEBB4" ],
1291  [ "\033[2XClassRotation\033[102X cl, u; for z x z", "5.2-3", [ 5, 2, 3 ],
1292      267, 67, "classrotation cl u for z x z", "X828438127DDAEBB4" ],
1293  [ "\033[10XRotationFactor\033[110X of a class rotation of Z x Z", "5.2-3",
1294      [ 5, 2, 3 ], 267, 67, "rotationfactor of a class rotation of z x z",
1295      "X828438127DDAEBB4" ],
1296  [ "\033[2XClassShift\033[102X r, l, k; for z x z", "5.2-4", [ 5, 2, 4 ],
1297      304, 68, "classshift r l k for z x z", "X7A14A8F48247E651" ],
1298  [ "\033[2XClassShift\033[102X cl, k; for z x z", "5.2-4", [ 5, 2, 4 ], 304,
1299      68, "classshift cl k for z x z", "X7A14A8F48247E651" ],
1300  [ "\033[10XIsClassTransposition\033[110X for an rcwa mapping of Z x Z",
1301      "5.2-4", [ 5, 2, 4 ], 304, 68,
1302      "isclasstransposition for an rcwa mapping of z x z",
1303      "X7A14A8F48247E651" ],
1304  [ "\033[10XIsClassRotation\033[110X for an rcwa mapping of Z x Z", "5.2-4",
1305      [ 5, 2, 4 ], 304, 68, "isclassrotation for an rcwa mapping of z x z",
1306      "X7A14A8F48247E651" ],
1307  [ "\033[10XIsClassShift\033[110X for an rcwa mapping of Z x Z", "5.2-4",
1308      [ 5, 2, 4 ], 304, 68, "isclassshift for an rcwa mapping of z x z",
1309      "X7A14A8F48247E651" ],
1310  [ "\033[10XView\033[110X for an rcwa mapping of Z x Z", "5.3", [ 5, 3, 0 ],
1311      342, 69, "view for an rcwa mapping of z x z", "X8531E39785FFF8A7" ],
1312  [ "\033[10XDisplay\033[110X for an rcwa mapping of Z x Z", "5.3",
1313      [ 5, 3, 0 ], 342, 69, "display for an rcwa mapping of z x z",
1314      "X8531E39785FFF8A7" ],
1315  [ "\033[10XPrint\033[110X for an rcwa mapping of Z x Z", "5.3",
1316      [ 5, 3, 0 ], 342, 69, "print for an rcwa mapping of z x z",
1317      "X8531E39785FFF8A7" ],
1318  [ "\033[10XString\033[110X for an rcwa mapping of Z x Z", "5.3",
1319      [ 5, 3, 0 ], 342, 69, "string for an rcwa mapping of z x z",
1320      "X8531E39785FFF8A7" ],
1321  [ "\033[10XLaTeXStringRcwaMapping\033[110X for an rcwa mapping of Z x Z",
1322      "5.3", [ 5, 3, 0 ], 342, 69,
1323      "latexstringrcwamapping for an rcwa mapping of z x z",
1324      "X8531E39785FFF8A7" ],
1325  [ "\033[10XLaTeXAndXDVI\033[110X for an rcwa mapping of Z x Z", "5.3",
1326      [ 5, 3, 0 ], 342, 69, "latexandxdvi for an rcwa mapping of z x z",
1327      "X8531E39785FFF8A7" ],
1328  [ "\033[10XModulus\033[110X of an rcwa mapping of Z x Z", "5.3",
1329      [ 5, 3, 0 ], 342, 69, "modulus of an rcwa mapping of z x z",
1330      "X8531E39785FFF8A7" ],
1331  [ "\033[10XCoefficients\033[110X of an rcwa mapping of Z x Z", "5.3",
1332      [ 5, 3, 0 ], 342, 69, "coefficients of an rcwa mapping of z x z",
1333      "X8531E39785FFF8A7" ],
1334  [ "\033[10XSupport\033[110X of an rcwa mapping of Z x Z", "5.3",
1335      [ 5, 3, 0 ], 342, 69, "support of an rcwa mapping of z x z",
1336      "X8531E39785FFF8A7" ],
1337  [ "\033[10XMovedPoints\033[110X of an rcwa mapping of Z x Z", "5.3",
1338      [ 5, 3, 0 ], 342, 69, "movedpoints of an rcwa mapping of z x z",
1339      "X8531E39785FFF8A7" ],
1340  [ "\033[10XOrder\033[110X of an rcwa mapping of Z x Z", "5.3", [ 5, 3, 0 ],
1341      342, 69, "order of an rcwa mapping of z x z", "X8531E39785FFF8A7" ],
1342  [ "\033[10XMultiplier\033[110X of an rcwa mapping of Z x Z", "5.3",
1343      [ 5, 3, 0 ], 342, 69, "multiplier of an rcwa mapping of z x z",
1344      "X8531E39785FFF8A7" ],
1345  [ "\033[10XDivisor\033[110X of an rcwa mapping of Z x Z", "5.3",
1346      [ 5, 3, 0 ], 342, 69, "divisor of an rcwa mapping of z x z",
1347      "X8531E39785FFF8A7" ],
1348  [ "\033[10XPrimeSet\033[110X of an rcwa mapping of Z x Z", "5.3",
1349      [ 5, 3, 0 ], 342, 69, "primeset of an rcwa mapping of z x z",
1350      "X8531E39785FFF8A7" ],
1351  [ "\033[10XOne\033[110X for an rcwa mapping of Z x Z", "5.3", [ 5, 3, 0 ],
1352      342, 69, "one for an rcwa mapping of z x z", "X8531E39785FFF8A7" ],
1353  [ "\033[10XZero\033[110X for an rcwa mapping of Z x Z", "5.3", [ 5, 3, 0 ],
1354      342, 69, "zero for an rcwa mapping of z x z", "X8531E39785FFF8A7" ],
1355  [ "\033[10XIsInjective\033[110X for an rcwa mapping of Z x Z", "5.3",
1356      [ 5, 3, 0 ], 342, 69, "isinjective for an rcwa mapping of z x z",
1357      "X8531E39785FFF8A7" ],
1358  [ "\033[10XIsSurjective\033[110X for an rcwa mapping of Z x Z", "5.3",
1359      [ 5, 3, 0 ], 342, 69, "issurjective for an rcwa mapping of z x z",
1360      "X8531E39785FFF8A7" ],
1361  [ "\033[10XIsBijective\033[110X for an rcwa mapping of Z x Z", "5.3",
1362      [ 5, 3, 0 ], 342, 69, "isbijective for an rcwa mapping of z x z",
1363      "X8531E39785FFF8A7" ],
1364  [ "\033[10XIsTame\033[110X for an rcwa mapping of Z x Z", "5.3",
1365      [ 5, 3, 0 ], 342, 69, "istame for an rcwa mapping of z x z",
1366      "X8531E39785FFF8A7" ],
1367  [ "\033[10XIsIntegral\033[110X for an rcwa mapping of Z x Z", "5.3",
1368      [ 5, 3, 0 ], 342, 69, "isintegral for an rcwa mapping of z x z",
1369      "X8531E39785FFF8A7" ],
1370  [ "\033[10XIsBalanced\033[110X for an rcwa mapping of Z x Z", "5.3",
1371      [ 5, 3, 0 ], 342, 69, "isbalanced for an rcwa mapping of z x z",
1372      "X8531E39785FFF8A7" ],
1373  [ "\033[10XIsClassWiseOrderPreserving\033[110X for an rcwa mapping of Z x Z"
1374        , "5.3", [ 5, 3, 0 ], 342, 69,
1375      "isclasswiseorderpreserving for an rcwa mapping of z x z",
1376      "X8531E39785FFF8A7" ],
1377  [ "\033[10XIsOne\033[110X for an rcwa mapping of Z x Z", "5.3",
1378      [ 5, 3, 0 ], 342, 69, "isone for an rcwa mapping of z x z",
1379      "X8531E39785FFF8A7" ],
1380  [ "\033[10XIsZero\033[110X for an rcwa mapping of Z x Z", "5.3",
1381      [ 5, 3, 0 ], 342, 69, "iszero for an rcwa mapping of z x z",
1382      "X8531E39785FFF8A7" ],
1383  [ "\033[10XTrajectory\033[110X for rcwa mappings of Z x Z", "5.3",
1384      [ 5, 3, 0 ], 342, 69, "trajectory for rcwa mappings of z x z",
1385      "X8531E39785FFF8A7" ],
1386  [
1387      "\033[10XShortCycles\033[110X for rcwa perm. of Z x Z, set of points and ma\
1388x. length", "5.3", [ 5, 3, 0 ], 342, 69,
1389      "shortcycles for rcwa perm. of z x z set of points and max. length",
1390      "X8531E39785FFF8A7" ],
1391  [ "\033[10XMultpk\033[110X for rcwa mapping of Z x Z, prime and exponent",
1392      "5.3", [ 5, 3, 0 ], 342, 69,
1393      "multpk for rcwa mapping of z x z prime and exponent",
1394      "X8531E39785FFF8A7" ],
1395  [ "\033[10XClassWiseOrderPreservingOn\033[110X for rcwa mappings of Z x Z",
1396      "5.3", [ 5, 3, 0 ], 342, 69,
1397      "classwiseorderpreservingon for rcwa mappings of z x z",
1398      "X8531E39785FFF8A7" ],
1399  [ "\033[10XClassWiseOrderReversingOn\033[110X for rcwa mappings of Z x Z",
1400      "5.3", [ 5, 3, 0 ], 342, 69,
1401      "classwiseorderreversingon for rcwa mappings of z x z",
1402      "X8531E39785FFF8A7" ],
1403  [ "\033[10XClassWiseConstantOn\033[110X for rcwa mappings of Z x Z", "5.3",
1404      [ 5, 3, 0 ], 342, 69, "classwiseconstanton for rcwa mappings of z x z",
1405      "X8531E39785FFF8A7" ],
1406  [ "\033[2XProjectionsToCoordinates\033[102X for an rcwa mapping of z x z",
1407      "5.3-1", [ 5, 3, 1 ], 376, 69,
1408      "projectionstocoordinates for an rcwa mapping of z x z",
1409      "X8408B7837C9EED36" ],
1410  [
1411      "\033[10XRcwa\033[110X the monoid formed by all rcwa permutations of Z x Z"
1412        , "5.4", [ 5, 4, 0 ], 407, 70,
1413      "rcwa the monoid formed by all rcwa permutations of z x z",
1414      "X83A1752F7BE9CE85" ],
1415  [ "\033[10XRCWA\033[110X the group formed by all rcwa permutations of Z x Z"
1416        , "5.4", [ 5, 4, 0 ], 407, 70,
1417      "rcwa the group formed by all rcwa permutations of z x z",
1418      "X83A1752F7BE9CE85" ],
1419  [
1420      "\033[10XCT\033[110X the group generated by all class transpositions of Z x\
1421 Z", "5.4", [ 5, 4, 0 ], 407, 70,
1422      "ct the group generated by all class transpositions of z x z",
1423      "X83A1752F7BE9CE85" ],
1424  [ "\033[10XSize\033[110X for an rcwa group over Z x Z", "5.4", [ 5, 4, 0 ],
1425      407, 70, "size for an rcwa group over z x z", "X83A1752F7BE9CE85" ],
1426  [ "\033[10XIsIntegral\033[110X for an rcwa group over Z x Z", "5.4",
1427      [ 5, 4, 0 ], 407, 70, "isintegral for an rcwa group over z x z",
1428      "X83A1752F7BE9CE85" ],
1429  [ "\033[10XIsClassWiseTranslating\033[110X for an rcwa group over Z x Z",
1430      "5.4", [ 5, 4, 0 ], 407, 70,
1431      "isclasswisetranslating for an rcwa group over z x z",
1432      "X83A1752F7BE9CE85" ],
1433  [ "\033[10XIsTame\033[110X for an rcwa group over Z x Z", "5.4",
1434      [ 5, 4, 0 ], 407, 70, "istame for an rcwa group over z x z",
1435      "X83A1752F7BE9CE85" ],
1436  [ "\033[10XModulus\033[110X of an rcwa group over Z x Z", "5.4",
1437      [ 5, 4, 0 ], 407, 70, "modulus of an rcwa group over z x z",
1438      "X83A1752F7BE9CE85" ],
1439  [ "\033[10XMultiplier\033[110X of an rcwa group over Z x Z", "5.4",
1440      [ 5, 4, 0 ], 407, 70, "multiplier of an rcwa group over z x z",
1441      "X83A1752F7BE9CE85" ],
1442  [ "\033[10XDivisor\033[110X of an rcwa group over Z x Z", "5.4",
1443      [ 5, 4, 0 ], 407, 70, "divisor of an rcwa group over z x z",
1444      "X83A1752F7BE9CE85" ],
1445  [ "\033[2XIsomorphismRcwaGroup\033[102X for sl(2,z) and a residue class",
1446      "5.4-1", [ 5, 4, 1 ], 424, 70,
1447      "isomorphismrcwagroup for sl 2 z and a residue class",
1448      "X79A8F9AD7E839862" ],
1449  [ "\033[2XIsomorphismRcwaGroup\033[102X for gl(2,z) and a residue class",
1450      "5.4-1", [ 5, 4, 1 ], 424, 70,
1451      "isomorphismrcwagroup for gl 2 z and a residue class",
1452      "X79A8F9AD7E839862" ],
1453  [ "\033[10XDrawOrbitPicture\033[110X for rcwa groups over Z x Z", "5.4-1",
1454      [ 5, 4, 1 ], 424, 70, "draworbitpicture for rcwa groups over z x z",
1455      "X79A8F9AD7E839862" ],
1456  [ "\033[2XDrawGrid\033[102X u, yrange, xrange, filename", "5.4-2",
1457      [ 5, 4, 2 ], 469, 71, "drawgrid u yrange xrange filename",
1458      "X812135EB87527F01" ],
1459  [ "\033[2XDrawGrid\033[102X p, yrange, xrange, filename", "5.4-2",
1460      [ 5, 4, 2 ], 469, 71, "drawgrid p yrange xrange filename",
1461      "X812135EB87527F01" ],
1462  [ "\033[2XLoadRCWAExamples\033[102X", "6.1-1", [ 6, 1, 1 ], 11, 72,
1463      "loadrcwaexamples", "X8714254784AFD64B" ],
1464  [
1465      "\033[2XLoadDatabaseOfGroupsGeneratedBy3ClassTranspositions\033[102X small \
1466database", "6.2-1", [ 6, 2, 1 ], 48, 73,
1467      "loaddatabaseofgroupsgeneratedby3classtranspositions small database",
1468      "X793E2C5C7FC935B8" ],
1469  [
1470      "\033[2XLoadDatabaseOfGroupsGeneratedBy3ClassTranspositions\033[102X both d\
1471atabases", "6.2-2", [ 6, 2, 2 ], 271, 76,
1472      "loaddatabaseofgroupsgeneratedby3classtranspositions both databases",
1473      "X7A77F7D57B08E4A5" ],
1474  [ "\033[2XLoadDatabaseOfGroupsGeneratedBy4ClassTranspositions\033[102X",
1475      "6.2-3", [ 6, 2, 3 ], 325, 77,
1476      "loaddatabaseofgroupsgeneratedby4classtranspositions",
1477      "X792C90B48692D0D7" ],
1478  [ "\033[2XLoadDatabaseOfProductsOf2ClassTranspositions\033[102X", "6.3-1",
1479      [ 6, 3, 1 ], 407, 79, "loaddatabaseofproductsof2classtranspositions",
1480      "X843E94467A1BB86C" ],
1481  [ "\033[2XLoadDatabaseOfNonbalancedProductsOfClassTranspositions\033[102X",
1482      "6.3-2", [ 6, 3, 2 ], 448, 79,
1483      "loaddatabaseofnonbalancedproductsofclasstranspositions",
1484      "X85B492697ACC4A54" ],
1485  [ "\033[10XLoadRCWAExamples\033[110X", "7.", [ 7, 0, 0 ], 1, 81,
1486      "loadrcwaexamples", "X7A489A5D79DA9E5C" ],
1487  [ "\033[10XAssignGlobals\033[110X", "7.", [ 7, 0, 0 ], 1, 81,
1488      "assignglobals", "X7A489A5D79DA9E5C" ],
1489  [ "\033[2XRCWABuildManual\033[102X", "9.3-1", [ 9, 3, 1 ], 29, 150,
1490      "rcwabuildmanual", "X7AA556D17F61A44C" ],
1491  [ "\033[2XRCWATestInstall\033[102X", "9.4-1", [ 9, 4, 1 ], 42, 151,
1492      "rcwatestinstall", "X8314E1597BF1555B" ],
1493  [ "\033[2XRCWATestAll\033[102X", "9.4-2", [ 9, 4, 2 ], 52, 151,
1494      "rcwatestall", "X877DDD787E4ABDC2" ],
1495  [ "\033[2XRCWATestExamples\033[102X", "9.4-3", [ 9, 4, 3 ], 75, 151,
1496      "rcwatestexamples", "X799793987AA3F34C" ],
1497  [ "\033[2XInfoRCWA\033[102X", "9.5-1", [ 9, 5, 1 ], 86, 151, "inforcwa",
1498      "X7BAF5F4986288983" ],
1499  [ "\033[10XRCWAInfo\033[110X", "9.5-1", [ 9, 5, 1 ], 86, 151, "rcwainfo",
1500      "X7BAF5F4986288983" ] ]
1501);
1502