This is TeX, Version 3.141592 (MiKTeX 2.3) (preloaded format=latex 2000.11.28) 29 APR 2004 10:12 **qzeil.tex (qzeil.tex LaTeX2e <2001/06/01> Babel <v3.7j> and hyphenation patterns for english, french, german, ngerman, du mylang, nohyphenation, loaded. (F:\CTeX\texmf\tex\latex\base\article.cls Document Class: article 2001/04/21 v1.4e Standard LaTeX document class (F:\CTeX\texmf\tex\latex\base\size10.clo File: size10.clo 2001/04/21 v1.4e Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (F:\CTeX\texmf\tex\latex\tools\bm.sty Package: bm 1999/07/05 v1.0g Bold Symbol Support (DPC/FMi) \symboldoperators=\mathgroup4 \symboldletters=\mathgroup5 \symboldsymbols=\mathgroup6 LaTeX Font Info: Redeclaring math alphabet \mathbf on input line 137. 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(F:\CTeX\texmf\tex\latex\graphics\dvips.def File: dvips.def 1999/02/16 v3.0i Driver-dependant file (DPC,SPQR) )) \Gin@req@height=\dimen112 \Gin@req@width=\dimen113 ) \c@theo=\count99 (qzeil.aux) LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 36. LaTeX Font Info: ... okay on input line 36. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 36. LaTeX Font Info: ... okay on input line 36. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 36. LaTeX Font Info: ... okay on input line 36. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 36. LaTeX Font Info: ... okay on input line 36. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 36. LaTeX Font Info: ... okay on input line 36. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 36. LaTeX Font Info: ... okay on input line 36. LaTeX Font Info: Try loading font information for U+msa on input line 39. (F:\CTeX\texmf\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 39. (F:\CTeX\texmf\tex\latex\amsfonts\umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) [1 ] Package amsmath Warning: Foreign command \over; (amsmath) \frac or \genfrac should be used instead (amsmath) on input line 116. [2] Underfull \hbox (badness 10000) in paragraph at lines 230--237 [] [3] Overfull \hbox (17.89635pt too wide) in paragraph at lines 238--241 [][]\OT1/cmr/m/n/10 We now come to the $\OML/cmm/m/it/10 q$\OT1/cmr/m/n/10 -mul tiplicative rep-re-sen-ta-tion of a gen-eral $\OML/cmm/m/it/10 q$\OT1/cmr/m/n/1 0 -hypergeometric [] [4] [5] LaTeX Font Info: Try loading font information for OMS+cmr on input line 390. (F:\CTeX\texmf\tex\latex\base\omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 390. [6] [7] [8] [9] [10] Overfull \hbox (16.52603pt too wide) in paragraph at lines 757--762 \OT1/cmr/m/n/10 need the con-cept of sim-i-lar $\OML/cmm/m/it/10 q$\OT1/cmr/m/n /10 -hypergeometric terms. Two bi-vari-ate $\OML/cmm/m/it/10 q$\OT1/cmr/m/n/10 -hypergeometric [] Overfull \hbox (17.00183pt too wide) in paragraph at lines 766--769 [][]\OT1/cmr/m/it/10 Suppose there ex-ist $\OML/cmm/m/it/10 qZ$\OT1/cmr/m/it/10 -pairs for two sim-i-lar bi-vari-ate $\OML/cmm/m/it/10 q$\OT1/cmr/m/it/10 -hyp ergeometric [] [11] Overfull \hbox (3.4566pt too wide) in paragraph at lines 812--818 []\OT1/cmr/m/n/10 and $\OML/cmm/m/it/10 F[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 k\ OT1/cmr/m/n/10 )$ has a $\OML/cmm/m/it/10 q$\OT1/cmr/m/n/10 -MR $(\OML/cmm/m/it /10 f[]=f[]; v[]=v[]; \OT1/cmr/m/n/10 0)$ with $\OML/cmm/m/it/10 v[]$ \OT1/cmr/ m/n/10 be-ing $[][]$-free. Since $\OML/cmm/m/it/10 f[]=f[]; v[]=v[] \OMS/cmsy/m /n/10 2 [] [12] Overfull \hbox (17.94997pt too wide) in paragraph at lines 848--850 [][]\OT1/cmtt/m/n/10 Apply the algorithm in [7] to find a rational function $\O ML/cmm/m/it/10 R \OMS/cmsy/m/n/10 2 \U/msb/m/n/10 F\OT1/cmr/m/n/10 (\OML/cmm/m/ it/10 x; y\OT1/cmr/m/n/10 )$ [] Overfull \hbox (1.63614pt too wide) in paragraph at lines 852--853 [][]\OT1/cmtt/m/n/10 For $\OML/cmm/m/it/10 D \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 r=s; U \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 u=v$ \OT1/cmtt/m/n/10 and $\OML/cmm/ m/it/10 n[] \OT1/cmr/m/n/10 = 0$\OT1/cmtt/m/n/10 , apply the algorithm `$\OML/c mm/m/it/10 q$\OT1/cmtt/m/n/10 -decomp' [] Overfull \hbox (3.9036pt too wide) in paragraph at lines 853--856 [][]\OT1/cmtt/m/n/10 Use the algorithm in [13] to determine whether $\OML/cmm/m /it/10 v[]$ \OT1/cmtt/m/n/10 is $\OML/cmm/m/it/10 q$\OT1/cmtt/m/n/10 -proper. [] Overfull \hbox (6.0773pt too wide) in paragraph at lines 853--856 \OT1/cmtt/m/n/10 If the answer is yes, then $\OML/cmm/m/it/10 T$ \OT1/cmtt/m/n/ 10 has a $\OML/cmm/m/it/10 qZ$\OT1/cmtt/m/n/10 -pair; otherwise, $\OML/cmm/m/it /10 T$ \OT1/cmtt/m/n/10 does [] [13] Missing character: There is no � in font cmr9! Missing character: There is no � in font cmr9! Missing character: There is no � in font cmr9! Missing character: There is no � in font cmr9! Underfull \hbox (badness 7869) in paragraph at lines 955--957 [][]\OT1/cmr/m/n/10 Q.H. Hou, $\OML/cmm/m/it/10 k$\OT1/cmr/m/n/10 -Free re-cur- rences of dou-ble hy-per-ge-o-met-ric terms, [] [14] [15] (qzeil.aux) ) Here is how much of TeX's memory you used: 1724 strings out of 96049 17491 string characters out of 1196993 71810 words of memory out of 1067805 4586 multiletter control sequences out of 35000 16032 words of font info for 60 fonts, out of 500000 for 1000 14 hyphenation exceptions out of 607 27i,12n,22p,222b,290s stack positions out of 1500i,500n,5000p,200000b,32768s Output written on qzeil.dvi (15 pages, 72192 bytes).