This is pdfTeX, Version 3.141592-1.40.0-rc4 (Web2C 7.5.5) (format=pdflatex 2007.1.7)  18 JAN 2008 15:55
entering extended mode
**manual
(./manual.tex
LaTeX2e <2005/12/01>
Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, basque, bulgarian, coptic, welsh, czech, slovak, german, ngerman, d
anish, spanish, catalan, galician, esperanto, estonian, finnish, french, greek,
 monogreek, ancientgreek, croatian, hungarian, interlingua, ibycus, indonesian,
 icelandic, italian, latin, mongolian, dutch, norsk, polish, portuguese, pinyin
, romanian, russian, slovene, uppersorbian, serbian, swedish, turkish, ukenglis
h, ukrainian, loaded.
(/usr/local/gwTeX/texmf.texlive/tex/latex/base/report.cls
Document Class: report 2005/09/16 v1.4f Standard LaTeX document class
(/usr/local/gwTeX/texmf.texlive/tex/latex/base/size11.clo
File: size11.clo 2005/09/16 v1.4f Standard LaTeX file (size option)
)
\c@part=\count79
\c@chapter=\count80
\c@section=\count81
\c@subsection=\count82
\c@subsubsection=\count83
\c@paragraph=\count84
\c@subparagraph=\count85
\c@figure=\count86
\c@table=\count87
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
)
(/usr/local/gwTeX/texmf.texlive/tex/latex/ltxmisc/a4wide.sty
Package: a4wide 1994/08/30

(/usr/local/gwTeX/texmf.texlive/tex/latex/ntgclass/a4.sty
Package: a4 2004/04/15 v1.2g A4 based page layout
))
(/usr/local/gwTeX/texmf.texlive/tex/latex/amsfonts/amssymb.sty
Package: amssymb 2002/01/22 v2.2d

(/usr/local/gwTeX/texmf.texlive/tex/latex/amsfonts/amsfonts.sty
Package: amsfonts 2001/10/25 v2.2f
\@emptytoks=\toks14
\symAMSa=\mathgroup4
\symAMSb=\mathgroup5
LaTeX Font Info:    Overwriting math alphabet `\mathfrak' in version `bold'
(Font)                  U/euf/m/n --> U/euf/b/n on input line 132.
))
(/usr/local/gwTeX/texmf.texlive/tex/latex/base/inputenc.sty
Package: inputenc 2006/05/05 v1.1b Input encoding file
\inpenc@prehook=\toks15
\inpenc@posthook=\toks16

(/usr/local/gwTeX/texmf.texlive/tex/latex/base/latin1.def
File: latin1.def 2006/05/05 v1.1b Input encoding file
))
(/usr/local/gwTeX/texmf.texlive/tex/latex/base/makeidx.sty
Package: makeidx 2000/03/29 v1.0m Standard LaTeX package
)
\@indexfile=\write3
\openout3 = `manual.idx'.


Writing index file manual.idx
(/usr/local/gwTeX/texmf.texlive/tex/latex/graphics/color.sty
Package: color 2005/11/14 v1.0j Standard LaTeX Color (DPC)

(/usr/local/gwTeX/texmf.texlive/tex/latex/config/color.cfg
File: color.cfg 2001/08/31 v1.1 color configuration of teTeX/TeXLive
)
Package color Info: Driver file: pdftex.def on input line 130.

(/usr/local/gwTeX/texmf.texlive/tex/latex/pdftex-def/pdftex.def
File: pdftex.def 2006/08/14 v0.03t Graphics/color for pdfTeX
\Gread@gobject=\count88
))
(/usr/local/gwTeX/texmf.texlive/tex/latex/fancyvrb/fancyvrb.sty
Package: fancyvrb 1998/07/17

Style option: `fancyvrb' v2.6, with DG/SPQR fixes <1998/07/17> (tvz)
(/usr/local/gwTeX/texmf.texlive/tex/latex/graphics/keyval.sty
Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
\KV@toks@=\toks17
)
\FV@CodeLineNo=\count89
\FV@InFile=\read1
\FV@TabBox=\box26
\c@FancyVerbLine=\count90
\FV@StepNumber=\count91
\FV@OutFile=\write4

No file fancyvrb.cfg.
) (/usr/local/gwTeX/texmf.texlive/tex/latex/pslatex/pslatex.sty
Package: pslatex 1996/07/24 v1.2 pslatex emulation (DPC)
LaTeX Font Info:    Redeclaring symbol font `operators' on input line 65.
LaTeX Font Info:    Overwriting symbol font `operators' in version `normal'
(Font)                  OT1/cmr/m/n --> OT1/ptmcm/m/n on input line 65.
LaTeX Font Info:    Overwriting symbol font `operators' in version `bold'
(Font)                  OT1/cmr/bx/n --> OT1/ptmcm/m/n on input line 65.
LaTeX Font Info:    Redeclaring symbol font `letters' on input line 66.
LaTeX Font Info:    Overwriting symbol font `letters' in version `normal'
(Font)                  OML/cmm/m/it --> OML/ptmcm/m/it on input line 66.
LaTeX Font Info:    Overwriting symbol font `letters' in version `bold'
(Font)                  OML/cmm/b/it --> OML/ptmcm/m/it on input line 66.
LaTeX Font Info:    Redeclaring symbol font `symbols' on input line 67.
LaTeX Font Info:    Overwriting symbol font `symbols' in version `normal'
(Font)                  OMS/cmsy/m/n --> OMS/pzccm/m/n on input line 67.
LaTeX Font Info:    Overwriting symbol font `symbols' in version `bold'
(Font)                  OMS/cmsy/b/n --> OMS/pzccm/m/n on input line 67.
LaTeX Font Info:    Redeclaring symbol font `largesymbols' on input line 68.
LaTeX Font Info:    Overwriting symbol font `largesymbols' in version `normal'
(Font)                  OMX/cmex/m/n --> OMX/psycm/m/n on input line 68.
LaTeX Font Info:    Overwriting symbol font `largesymbols' in version `bold'
(Font)                  OMX/cmex/m/n --> OMX/psycm/m/n on input line 68.
\symbold=\mathgroup6
\symitalic=\mathgroup7
LaTeX Font Info:    Redeclaring math alphabet \mathbf on input line 74.
LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `normal'
(Font)                  OT1/cmr/bx/n --> OT1/ptm/bx/n on input line 74.
LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `bold'
(Font)                  OT1/cmr/bx/n --> OT1/ptm/bx/n on input line 74.
LaTeX Font Info:    Redeclaring math alphabet \mathit on input line 75.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `normal'
(Font)                  OT1/cmr/m/it --> OT1/ptm/m/it on input line 75.
LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `bold'
(Font)                  OT1/cmr/bx/it --> OT1/ptm/m/it on input line 75.
)
(/usr/local/gwTeX/texmf.texlive/tex/latex/hyperref/hyperref.sty
Package: hyperref 2006/12/21 v6.75j Hypertext links for LaTeX
\@linkdim=\dimen103
\Hy@linkcounter=\count92
\Hy@pagecounter=\count93

(/usr/local/gwTeX/texmf.texlive/tex/latex/hyperref/pd1enc.def
File: pd1enc.def 2006/12/21 v6.75j Hyperref: PDFDocEncoding definition (HO)
)
(/usr/local/gwTeX/texmf.texlive/tex/latex/config/hyperref.cfg
File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive
)
(/usr/local/gwTeX/texmf.texlive/tex/latex/oberdiek/kvoptions.sty
Package: kvoptions 2006/08/22 v2.4 Connects package keyval with LaTeX options (
HO)
)
Package hyperref Info: Option `bookmarks' set `false' on input line 2212.
Package hyperref Info: Option `colorlinks' set `true' on input line 2212.
Package hyperref Info: Option `breaklinks' set `true' on input line 2212.
Package hyperref Info: Hyper figures OFF on input line 2262.
Package hyperref Info: Link nesting OFF on input line 2267.
Package hyperref Info: Hyper index ON on input line 2270.
Package hyperref Info: Plain pages OFF on input line 2277.
Package hyperref Info: Backreferencing ON on input line 2280.

Implicit mode ON; LaTeX internals redefined
Package hyperref Info: Bookmarks OFF on input line 2418.
(/usr/local/gwTeX/texmf.texlive/tex/latex/hyperref/backref.sty
Package: backref 2006/10/06 v1.27 Bibliographical back referencing
)
(/usr/local/gwTeX/texmf.texlive/tex/latex/ltxmisc/url.sty
\Urlmuskip=\muskip10
Package: url 2005/06/27  ver 3.2  Verb mode for urls, etc.
)
LaTeX Info: Redefining \url on input line 2567.
\Fld@menulength=\count94
\Field@Width=\dimen104
\Fld@charsize=\dimen105
\Choice@toks=\toks18
\Field@toks=\toks19
Package hyperref Info: Hyper figures OFF on input line 3045.
Package hyperref Info: Link nesting OFF on input line 3050.
Package hyperref Info: Hyper index ON on input line 3053.
Package hyperref Info: backreferencing ON on input line 3058.
Package hyperref Info: Link coloring ON on input line 3063.
\Hy@abspage=\count95
\c@Item=\count96
\c@Hfootnote=\count97
)
*hyperref using driver hpdftex*
(/usr/local/gwTeX/texmf.texlive/tex/latex/hyperref/hpdftex.def
File: hpdftex.def 2006/12/21 v6.75j Hyperref driver for pdfTeX
\Fld@listcount=\count98
)
\pagenrlog=\write5
\openout5 = `manual.pnr'.

 (./manual.aux)
\openout1 = `manual.aux'.

LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for OMS/pzccm/m/n on input line 43.
LaTeX Font Info:    Try loading font information for OMS+pzccm on input line 43
.

(/usr/local/gwTeX/texmf.texlive/tex/latex/psnfss/omspzccm.fd
File: omspzccm.fd 2000/01/03 Fontinst v1.801 font definitions for OMS/pzccm.
)
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.
LaTeX Font Info:    Checking defaults for PD1/pdf/m/n on input line 43.
LaTeX Font Info:    ... okay on input line 43.

(/usr/local/gwTeX/texmf.texlive/tex/context/base/supp-pdf.tex
[Loading MPS to PDF converter (version 2006.09.02).]
\scratchcounter=\count99
\scratchdimen=\dimen106
\scratchbox=\box27
\nofMPsegments=\count100
\nofMParguments=\count101
\MPscratchCnt=\count102
\MPscratchDim=\dimen107
\MPnumerator=\count103
\everyMPtoPDFconversion=\toks20
)
Package hyperref Info: Link coloring ON on input line 43.
 (/usr/local/gwTeX/texmf.texlive/tex/latex/hyperref/nameref.sty
Package: nameref 2006/12/21 v2.27 Cross-referencing by name of section

(/usr/local/gwTeX/texmf.texlive/tex/latex/oberdiek/refcount.sty
Package: refcount 2006/02/20 v3.0 Data extraction from references (HO)
)
\c@section@level=\count104
)
LaTeX Info: Redefining \ref on input line 43.
LaTeX Info: Redefining \pageref on input line 43.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <24.88> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 47.
LaTeX Font Info:    Font shape `OT1/phv/bx/n' in size <24.88> not available
(Font)              Font shape `OT1/phv/b/n' tried instead on input line 47.
LaTeX Font Info:    Font shape `OT1/phv/b/n' will be
(Font)              scaled to size 22.39185pt on input line 47.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <14.4> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 50.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <12> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 54.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <10> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 61.

Underfull \hbox (badness 10000) in paragraph at lines 59--76

 []

[1

{/usr/local/gwTeX/texmf.local/fonts/map/pdftex/updmap/pdftex.map}]
LaTeX Font Info:    Font shape `OT1/phv/m/n' will be
(Font)              scaled to size 8.99994pt on input line 82.
LaTeX Font Info:    Try loading font information for OT1+ptmcm on input line 84
.

(/usr/local/gwTeX/texmf.texlive/tex/latex/psnfss/ot1ptmcm.fd
File: ot1ptmcm.fd 2000/01/03 Fontinst v1.801 font definitions for OT1/ptmcm.
)
LaTeX Font Info:    Try loading font information for OML+ptmcm on input line 84
.

(/usr/local/gwTeX/texmf.texlive/tex/latex/psnfss/omlptmcm.fd
File: omlptmcm.fd 2000/01/03 Fontinst v1.801 font definitions for OML/ptmcm.
)
LaTeX Font Info:    Try loading font information for OMX+psycm on input line 84
.

(/usr/local/gwTeX/texmf.texlive/tex/latex/psnfss/omxpsycm.fd
File: omxpsycm.fd 2000/01/03 Fontinst v1.801 font definitions for OMX/psycm.
)
LaTeX Font Info:    Try loading font information for U+msa on input line 84.

(/usr/local/gwTeX/texmf.texlive/tex/latex/amsfonts/umsa.fd
File: umsa.fd 2002/01/19 v2.2g AMS font definitions
)
LaTeX Font Info:    Try loading font information for U+msb on input line 84.

(/usr/local/gwTeX/texmf.texlive/tex/latex/amsfonts/umsb.fd
File: umsb.fd 2002/01/19 v2.2g AMS font definitions
)
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <7.4> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 84.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <6> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 84.

Underfull \hbox (badness 10000) in paragraph at lines 86--88

 []

LaTeX Font Info:    Font shape `OMS/ptm/m/n' in size <10> not available
(Font)              Font shape `OMS/pzccm/m/n' tried instead on input line 90.

Underfull \hbox (badness 4752) in paragraph at lines 101--103
[]\OT1/ptm/m/n/10 A. Kono-valov, P. Soules. \OT1/ptm/m/it/10 Cir-cle --- Ad-joi
nt groups of fi-nite rings, Ver-sion 1.3.1; \OT1/ptm/m/n/10 2008
 []


Underfull \hbox (badness 10000) in paragraph at lines 101--103

 []


Underfull \hbox (badness 10000) in paragraph at lines 109--110

 []

LaTeX Font Info:    Font shape `OT1/phv/m/sl' will be
(Font)              scaled to size 7.19995pt on input line 110.
[2] (./manual.toc
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <10.95> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 1.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <8> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 2.
LaTeX Font Info:    Font shape `OT1/phv/bx/n' in size <10.95> not available
(Font)              Font shape `OT1/phv/b/n' tried instead on input line 8.
LaTeX Font Info:    Font shape `OT1/phv/b/n' will be
(Font)              scaled to size 9.85492pt on input line 8.
)
\tf@toc=\write6
\openout6 = `manual.toc'.

 [3

]
Chapter 1.
LaTeX Font Info:    Font shape `OT1/ptm/bx/n' in size <20.74> not available
(Font)              Font shape `OT1/ptm/b/n' tried instead on input line 118.
LaTeX Font Info:    Font shape `OT1/phv/m/n' will be
(Font)              scaled to size 9.85492pt on input line 157.
[4

]
Underfull \hbox (badness 1292) in paragraph at lines 175--177
[]\OT1/ptm/m/n/10.95 To use the \OT1/phv/m/n/10.95 Cir-cle \OT1/ptm/m/n/10.95 o
n-line help it is nec-es-sary to in-stall the \OT1/phv/m/n/10.95 GAP\OT1/ptm/m/
n/10.95 4 pack-age \OT1/phv/m/n/10.95 GAP-Doc \OT1/ptm/m/n/10.95 by
 []


Underfull \hbox (badness 2689) in paragraph at lines 175--177
\OT1/ptm/m/n/10.95 Frank L\OT1/pcr/m/n/10.95 \\OT1/ptm/m/n/10.95 "ubeck and Max
 Ne-unh\OT1/pcr/m/n/10.95 \\OT1/ptm/m/n/10.95 "offer, which is avail-able from 
the \OT1/phv/m/n/10.95 GAP \OT1/ptm/m/n/10.95 site or from
 []

[5]
Chapter 2.
[6

]
Underfull \hbox (badness 10000) in paragraph at lines 262--263
[]\OT1/ptm/m/n/10.95 We start with declar-ing the cat-e-gory \OT1/pcr/m/n/10.95
 IsCircleObject \OT1/ptm/m/n/10.95 as a sub-cat-e-gory of
 []


Underfull \hbox (badness 1783) in paragraph at lines 262--263
\OT1/pcr/m/n/10.95 IsMultiplicativeElementWithInverse\OT1/ptm/m/n/10.95 . Thus,
 each cir-cle ob-ject will "know" that it is
 []

[7] [8]
LaTeX Font Info:    Try loading font information for OML+pcr on input line 344.

 (/usr/local/gwTeX/texmf.texlive/tex/latex/psnfss/omlpcr.fd
File: omlpcr.fd 
)
LaTeX Font Info:    Font shape `OML/pcr/m/n' in size <10.95> not available
(Font)              Font shape `OML/cmm/m/it' tried instead on input line 344.
 [9]
[10] [11]
Underfull \hbox (badness 1184) in paragraph at lines 514--515
\OT1/ptm/m/n/10.95 The \OT1/phv/m/n/10.95 GAP \OT1/ptm/m/n/10.95 code used in t
his Chap-ter, is con-tained in the files \OT1/pcr/m/n/10.95 circle/lib/circle.g
d \OT1/ptm/m/n/10.95 and
 []

[12]
Chapter 3.

Underfull \hbox (badness 10000) in paragraph at lines 548--551

 []


Underfull \hbox (badness 10000) in paragraph at lines 567--570

 []

[13

]
Underfull \hbox (badness 10000) in paragraph at lines 588--594

 []


Underfull \hbox (badness 10000) in paragraph at lines 617--623

 []


Underfull \hbox (badness 2503) in paragraph at lines 625--628
\OT1/ptm/m/n/10.95 for a more gen-eral case. Then we de-fined \OT1/pcr/m/n/10.9
5 IsDefaultCircleObject \OT1/ptm/m/n/10.95 as a syn-onym of
 []


Underfull \hbox (badness 10000) in paragraph at lines 643--646

 []

[14]
Underfull \hbox (badness 10000) in paragraph at lines 671--674

 []


Underfull \hbox (badness 10000) in paragraph at lines 696--699

 []

[15]
Underfull \hbox (badness 10000) in paragraph at lines 735--738

 []


Underfull \hbox (badness 10000) in paragraph at lines 777--780

 []

[16]
Underfull \hbox (badness 10000) in paragraph at lines 828--831

 []


Underfull \hbox (badness 10000) in paragraph at lines 853--856

 []

[17]
Underfull \hbox (badness 3746) in paragraph at lines 864--865
[]\OT1/ptm/m/n/10.95 The warn-ing is dis-played by \OT1/pcr/m/n/10.95 IsGenerat
orsOfMagmaWithInverses \OT1/ptm/m/n/10.95 method de-fined in
 []

[18] [19] [20]
Underfull \hbox (badness 10000) in paragraph at lines 1072--1075

 []

[21]
Underfull \hbox (badness 10000) in paragraph at lines 1100--1103

 []


Underfull \hbox (badness 10000) in paragraph at lines 1116--1119

 []

[22]
Chapter 4.

Underfull \hbox (badness 1320) in paragraph at lines 1171--1173
\OT1/ptm/m/n/10.95 Then we com-pute the ad-joint group of \OT1/pcr/m/n/10.95 R\
OT1/ptm/m/n/10.95 . Dur-ing the com-pu-ta-tion a warn-ing will be dis-
 []

[23

] [24] (./manual.bbl (./manual.brf)
\tf@brf=\write7
\openout7 = `manual.brf'.

 [25]) (./manual.ind [26

] [27


])
(./manual.aux) ) 
Here is how much of TeX's memory you used:
 3937 strings out of 94087
 55759 string characters out of 1163859
 2102425 words of memory out of 4553638
 7032 multiletter control sequences out of 10000+50000
 56497 words of font info for 109 fonts, out of 2000000 for 2000
 645 hyphenation exceptions out of 5000
 27i,7n,27p,776b,629s stack positions out of 5000i,500n,6000p,200000b,50000s
{/usr/local/gwTeX/texmf.texlive/fonts/enc/dvips/base/8r.enc}</u
sr/local/gwTeX/texmf.texlive/fonts/type1/bluesky/cm/cmmi10.pfb></usr/local/gwTe
X/texmf.texlive/fonts/type1/bluesky/cm/cmr10.pfb></usr/local/gwTeX/texmf.texliv
e/fonts/type1/bluesky/cm/cmsy10.pfb></usr/local/gwTeX/texmf.texlive/fonts/type1
/bluesky/ams/msam10.pfb></usr/local/gwTeX/texmf.texlive/fonts/type1/urw/courier
/ucrr8a.pfb></usr/local/gwTeX/texmf.texlive/fonts/type1/urw/courier/ucrro8a.pfb
></usr/local/gwTeX/texmf.texlive/fonts/type1/urw/helvetic/uhvb8a.pfb></usr/loca
l/gwTeX/texmf.texlive/fonts/type1/urw/helvetic/uhvr8a.pfb></usr/local/gwTeX/tex
mf.texlive/fonts/type1/urw/helvetic/uhvro8a.pfb></usr/local/gwTeX/texmf.texlive
/fonts/type1/urw/times/utmb8a.pfb></usr/local/gwTeX/texmf.texlive/fonts/type1/u
rw/times/utmr8a.pfb></usr/local/gwTeX/texmf.texlive/fonts/type1/urw/times/utmri
8a.pfb>
Output written on manual.pdf (27 pages, 194677 bytes).
PDF statistics:
 336 PDF objects out of 1000 (max. 8388607)
 97 named destinations out of 1000 (max. 131072)
 17 words of extra memory for PDF output out of 10000 (max. 10000000)

