This is pdfTeX, Version 3.141592-1.40.0-rc4 (Web2C 7.5.5) (format=pdflatex 2007.1.7) 7 FEB 2007 17:39 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. 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Type H <return> for immediate help. ... l.154 }\\[1cm] Your command was ignored. Type I <command> <return> to replace it with another command, or <return> to continue without it. LaTeX Font Info: Font shape `OT1/phv/m/sl' will be (Font) scaled to size 7.19995pt on input line 155. [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 7. LaTeX Font Info: Font shape `OT1/phv/b/n' will be (Font) scaled to size 9.85492pt on input line 7. [3 ] [4]) \tf@toc=\write6 \openout6 = `manual.toc'. [5] 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 163. LaTeX Font Info: Font shape `OT1/phv/m/n' will be (Font) scaled to size 9.85492pt on input line 170. [6 ] Underfull \hbox (badness 2903) in paragraph at lines 222--223 []\OT1/ptm/m/n/10.95 To use the \OT1/phv/m/n/10.95 LA-GUNA \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- [] [7] Chapter 2. [8 ] [9] [10] [11] [12] [13] Chapter 3. [14 ] LaTeX Warning: Command \textless invalid in math mode on input line 548. LaTeX Font Info: Try loading font information for OML+ptm on input line 548. (/usr/local/gwTeX/texmf.texlive/tex/latex/psnfss/omlptm.fd File: omlptm.fd ) LaTeX Font Info: Font shape `OML/ptm/m/n' in size <10.95> not available (Font) Font shape `OML/cmm/m/it' tried instead on input line 548. LaTeX Warning: Command \textless invalid in math mode on input line 548. [15] Underfull \hbox (badness 10000) in paragraph at lines 610--614 \OT1/ptm/m/n/10.95 Thus $\OT1/ptmcm/m/n/10.95 1 + \OML/ptmcm/m/it/10.95 w[] \OT 1/ptmcm/m/n/10.95 = (\OML/ptmcm/m/it/10.95 y[]\OT1/ptmcm/m/n/10.95 )[] [] (\OML /ptmcm/m/it/10.95 y[]\OT1/ptmcm/m/n/10.95 )[](1 + \OML/ptmcm/m/it/10.95 w[]\OT1 /ptmcm/m/n/10.95 )$ \OT1/ptm/m/n/10.95 for some $\OML/ptmcm/m/it/10.95 w[] \OMS /pzccm/m/n/10.95 2 \OML/ptmcm/m/it/10.95 A[]$\OT1/ptm/m/n/10.95 , and so $\OT1/ ptmcm/m/n/10.95 1 + \OML/ptmcm/m/it/10.95 w \OT1/ptmcm/m/n/10.95 = [] LaTeX Warning: Command \textless invalid in math mode on input line 620. LaTeX Warning: Command \textless invalid in math mode on input line 620. [16] [17] Chapter 4. Underfull \hbox (badness 10000) in paragraph at lines 648--651 [] Underfull \hbox (badness 10000) in paragraph at lines 669--672 [] Underfull \hbox (badness 10000) in paragraph at lines 690--693 [] [18 ] [19] [20] Underfull \hbox (badness 10000) in paragraph at lines 870--873 [] [21] Underfull \hbox (badness 10000) in paragraph at lines 977--980 [] [22] Underfull \hbox (badness 10000) in paragraph at lines 997--1000 [] Underfull \hbox (badness 10000) in paragraph at lines 1021--1027 [] [23] [24] Underfull \hbox (badness 1033) in paragraph at lines 1140--1142 []\OT1/ptm/m/n/10.95 Please note that for cal-cu-la-tion of the aug-men-ta-tion of an el-e-ment of a group ring the [] Underfull \hbox (badness 1286) in paragraph at lines 1140--1142 \OT1/ptm/m/n/10.95 user is strongly rec-om-mended to use \OT1/pcr/m/n/10.95 Aug mentation \OT1/ptm/m/n/10.95 ([][]4.2.5[][]) which works much faster than [] LaTeX Font Info: Font shape `OMS/ptm/m/n' in size <10.95> not available (Font) Font shape `OMS/pzccm/m/n' tried instead on input line 1179 . [25] [26] Underfull \hbox (badness 10000) in paragraph at lines 1288--1291 [] Underfull \hbox (badness 10000) in paragraph at lines 1309--1312 [] [27] [28] Underfull \hbox (badness 10000) in paragraph at lines 1426--1428 []\OT1/ptm/m/n/10.95 The ar-gu-ment [] is a $\OML/ptmcm/m/it/10.95 p$\OT1/ptm/m /n/10.95 -modular group al-ge-bra over the field of $\OML/ptmcm/m/it/10.95 p$ \ OT1/ptm/m/n/10.95 el-e-ments. [] [29] [30] [31] Underfull \hbox (badness 10000) in paragraph at lines 1612--1615 [] Underfull \hbox (badness 10000) in paragraph at lines 1632--1635 [] Underfull \hbox (badness 10000) in paragraph at lines 1652--1655 [] [32] Underfull \hbox (badness 2762) in paragraph at lines 1680--1681 []\OT1/ptm/m/n/10.95 If [] is the (nor-mal-ized) unit group of a $\OML/ptmcm/m/ it/10.95 p$\OT1/ptm/m/n/10.95 -modular group al-ge-bra $\OML/ptmcm/m/it/10.95 K G$ \OT1/ptm/m/n/10.95 ob-tained us- [] Underfull \hbox (badness 10000) in paragraph at lines 1680--1681 \OT1/ptm/m/n/10.95 ing one of the func-tions \OT1/pcr/m/n/10.95 Units(KG)\OT1/p tm/m/n/10.95 , \OT1/pcr/m/n/10.95 PcUnits(KG)\OT1/ptm/m/n/10.95 , \OT1/pcr/m/n/ 10.95 NormalizedUnitGroup(KG) \OT1/ptm/m/n/10.95 or [] [33] [34] Underfull \hbox (badness 10000) in paragraph at lines 1834--1837 [] [35] Underfull \hbox (badness 10000) in paragraph at lines 1857--1860 [] [36] Underfull \hbox (badness 10000) in paragraph at lines 1947--1950 [] Underfull \hbox (badness 10000) in paragraph at lines 1975--1978 [] [37] [38] [39] Underfull \hbox (badness 10000) in paragraph at lines 2143--2146 [] Underfull \hbox (badness 10000) in paragraph at lines 2171--2174 [] Underfull \hbox (badness 10000) in paragraph at lines 2199--2202 [] [40] Underfull \hbox (badness 10000) in paragraph at lines 2227--2230 [] Underfull \hbox (badness 10000) in paragraph at lines 2253--2256 [] [41] Underfull \hbox (badness 10000) in paragraph at lines 2313--2316 [] [42] Underfull \hbox (badness 10000) in paragraph at lines 2342--2345 [] Underfull \hbox (badness 10000) in paragraph at lines 2370--2373 [] Underfull \hbox (badness 10000) in paragraph at lines 2390--2393 [] [43] Underfull \hbox (badness 10000) in paragraph at lines 2416--2419 [] Underfull \hbox (badness 10000) in paragraph at lines 2445--2448 [] Underfull \hbox (badness 10000) in paragraph at lines 2465--2468 [] [44] [45] Underfull \hbox (badness 10000) in paragraph at lines 2568--2571 [] Underfull \hbox (badness 10000) in paragraph at lines 2598--2601 [] [46] Underfull \hbox (badness 10000) in paragraph at lines 2613--2616 [] (./manual.bbl (./manual.brf) \tf@brf=\write7 \openout7 = `manual.brf'. 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