01ALG:Kapitola6
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This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024/Arch Linux) (preloaded format=pdflatex 2024.6.2) 1 NOV 2024 01:03 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **01ALG_Kapitola6_5ea138af.tex (./01ALG_Kapitola6_5ea138af.tex LaTeX2e <2023-11-01> patch level 1 L3 programming layer <2024-02-20> (./header.tex (/usr/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2023/05/17 v1.4n Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo File: size12.clo 2023/05/17 v1.4n Standard LaTeX file (size option) ) \c@part=\count188 \c@section=\count189 \c@subsection=\count190 \c@subsubsection=\count191 \c@paragraph=\count192 \c@subparagraph=\count193 \c@figure=\count194 \c@table=\count195 \abovecaptionskip=\skip48 \belowcaptionskip=\skip49 \bibindent=\dimen140 ) (/usr/share/texmf-dist/tex/generic/babel/babel.sty Package: babel 2024/02/07 v24.2 The Babel package \babel@savecnt=\count196 \U@D=\dimen141 \l@unhyphenated=\language7 (/usr/share/texmf-dist/tex/generic/babel/txtbabel.def) \bbl@readstream=\read2 \bbl@dirlevel=\count197 (/usr/share/texmf-dist/tex/generic/babel-czech/czech.ldf Language: czech 2008/07/06 v3.1a Czech support from the babel system Package babel Info: Making " an active character on input line 172. \cs@wordlen=\count198 Package babel Info: Making - an active character on input line 226. )) (/usr/share/texmf-dist/tex/generic/babel/locale/cs/babel-czech.tex Package babel Info: Importing font and identification data for czech (babel) from babel-cs.ini. 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LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for IL2/cmr/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. (./alg_ring.tex Overfull \hbox (483.0pt too wide) detected at line 3 [] [] LaTeX Font Info: Trying to load font information for U+msa on input line 5. (/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2013/01/14 v3.01 AMS symbols A ) LaTeX Font Info: Trying to load font information for U+msb on input line 5. (/usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) Underfull \hbox (badness 10000) detected at line 5 $\OMS/cmsy/m/n/12 ^^O$ [] Underfull \hbox (badness 10000) detected at line 8 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 22 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 25 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 28 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 31 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 34 $\U/msa/m/n/12 I$ [] Overfull \hbox (1.39798pt too wide) in paragraph at lines 34--36 []\IL2/cmr/m/sc/12 1.1.6. De-fi-nice.[] \IL2/cmr/m/n/12 ?ek-neme, ?e okruh $\O ML/cmm/m/it/12 R$ \IL2/cmr/m/n/12 je $[]$[], resp. je $[]$[], resp. $[]$[], [] Underfull \hbox (badness 10000) detected at line 38 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 50 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 53 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 56 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 66 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 74 $\U/msa/m/n/12 I$ [] [1 {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] Underfull \hbox (badness 10000) detected at line 78 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 82 $\U/msa/m/n/12 I$ [] Package amsmath Warning: Foreign command \atop; (amsmath) \frac or \genfrac should be used instead (amsmath) on input line 82. Underfull \hbox (badness 10000) detected at line 85 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 89 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 92 $\U/msa/m/n/12 I$ [] Overfull \hbox (5.03085pt too wide) in paragraph at lines 96--98 []\IL2/cmr/m/n/12 Takov? $\OML/cmm/m/it/12 n \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 N []$\IL2/cmr/m/n/12 , ?e $\OML/cmm/m/it/12 a[] \OMS/cmsy/m/n/12 6\OT1/cmr/m/n/12 = 0$ \IL2/cmr/m/n/12 a $\OT1/cmr/m/n/12 (\OMS/cmsy/m/n/12 8\OML/cmm/m/it/12 i > n\OT1/cmr/m/n/12 )(\OML/cmm/m/it/12 a[] \OT1/cmr/m/n/12 = 0)$\IL2/cmr/m/n/12 , na-zveme $[]$[]. Pro $[]$[] [] Underfull \hbox (badness 10000) detected at line 105 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 108 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 113 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 116 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 119 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 124 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 127 $\OMS/cmsy/m/n/12 ^^N$ [] [2] Underfull \hbox (badness 10000) detected at line 134 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 138 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 141 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 148 $\OMS/cmsy/m/n/12 ^^O$ [] Underfull \hbox (badness 10000) detected at line 151 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 157 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 160 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 170 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 178 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 181 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 187 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 195 $\OMS/cmsy/m/n/12 ^^N$ [] [3] Underfull \hbox (badness 10000) detected at line 204 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 219 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 228 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 232 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 237 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 241 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 245 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 249 $\OMS/cmsy/m/n/12 ^^O$ [] Underfull \hbox (badness 10000) detected at line 252 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 257 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 262 $\U/msa/m/n/12 I$ [] [4] Underfull \hbox (badness 10000) detected at line 266 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 270 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 273 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 277 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 280 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 284 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 292 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 296 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 317 $\U/msa/m/n/12 I$ [] [5] Underfull \hbox (badness 10000) detected at line 325 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 330 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 334 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 340 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 347 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 354 $\OMS/cmsy/m/n/12 ^^O$ [] Underfull \hbox (badness 10000) detected at line 357 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 362 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 370 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 383 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 386 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 389 $\OMS/cmsy/m/n/12 ^^N$ [] [6] Underfull \hbox (badness 10000) detected at line 413 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 418 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 424 $\U/msa/m/n/12 I$ [] Overfull \hbox (16.44553pt too wide) in paragraph at lines 424--426 []\IL2/cmr/m/sc/12 1.4.7. Lemma.[] \IL2/cmr/m/n/12 Ne-ch? $\OML/cmm/m/it/12 R$ \IL2/cmr/m/n/12 je aso-ci-a-tivn? a ko-mu-ta-tivn? okruh, $\OML/cmm/m/it/12 a \OMS/cmsy/m/n/12 2 \OML/cmm/m/it/12 R$ \IL2/cmr/m/n/12 a ozna-?me $\OML/cmm/m/i t/12 J[] \OT1/cmr/m/n/12 := []$\IL2/cmr/m/n/12 . [] Underfull \hbox (badness 10000) detected at line 434 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 443 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 447 $\U/msa/m/n/12 I$ [] Overfull \hbox (1.08386pt too wide) in paragraph at lines 447--453 []\IL2/cmr/m/sc/12 1.4.9. P??-klad.[] \IL2/cmr/m/n/12 Uk?eme, ?e $\OML/cmm/m/ it/12 Z \OT1/cmr/m/n/12 = (\U/msb/m/n/12 Z\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 +\ OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 ^^A\OT1/cmr/m/n/12 )$ \IL2/cmr/m/n/12 je okr uh hlav-n?ch ide-?l?. Ide-?ly $\OML/cmm/m/it/12 I[] \OT1/cmr/m/n/12 = []$ [] Underfull \hbox (badness 10000) detected at line 454 $\OMS/cmsy/m/n/12 ^^O$ [] Underfull \hbox (badness 10000) detected at line 457 $\U/msa/m/n/12 I$ [] [7] Underfull \hbox (badness 10000) detected at line 465 $\U/msa/m/n/12 I$ [] Overfull \hbox (28.96054pt too wide) in paragraph at lines 465--470 []\IL2/cmr/m/sc/12 1.5.2. De-fi-nice.[] \IL2/cmr/m/n/12 Po-dobn?, jako na gru- p?ch, de-fi-nu-jeme na okru-z?ch $[]$[], $[]$[], [] Underfull \hbox (badness 10000) detected at line 472 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 476 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 479 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 483 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 486 $\U/msa/m/n/12 I$ [] Overfull \hbox (2.66284pt too wide) in paragraph at lines 486--488 []\IL2/cmr/m/sc/12 1.5.7. De-fi-nice.[] $[]$[] \IL2/cmr/m/n/12 ho-mo-mor-fismu $\OML/cmm/m/it/12 h \OT1/cmr/m/n/12 : \OML/cmm/m/it/12 R[] \OMS/cmsy/m/n/12 ! \OML/cmm/m/it/12 R[]$ \IL2/cmr/m/n/12 ro-zu-m?me mno?inu $[] \OML/cmm/m/it/12 h \OT1/cmr/m/n/12 := \OML/cmm/m/it/12 h[]\OT1/cmr/m/n/12 (\OMS/cmsy/m/n/12 f\OT1 /cmr/m/n/12 0\OMS/cmsy/m/n/12 g\OT1/cmr/m/n/12 ) = [] Underfull \hbox (badness 10000) detected at line 490 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 497 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 500 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 504 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 507 $\OMS/cmsy/m/n/12 ^^O$ [] Underfull \hbox (badness 10000) detected at line 510 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 514 $\OMS/cmsy/m/n/12 ^^N$ [] [8] Underfull \hbox (badness 10000) detected at line 526 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 532 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 546 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 549 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 553 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 565 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 568 $\OMS/cmsy/m/n/12 ^^N$ [] [9] Underfull \hbox (badness 10000) detected at line 605 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 608 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 622 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 625 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 629 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 637 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 640 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 656 $\U/msa/m/n/12 I$ [] [10] Underfull \hbox (badness 10000) detected at line 658 $\OMS/cmsy/m/n/12 ^^O$ [] Underfull \hbox (badness 10000) detected at line 661 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 666 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 669 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 676 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 680 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 690 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 694 $\OMS/cmsy/m/n/12 ^^N$ [] Underfull \hbox (badness 10000) detected at line 698 $\OMS/cmsy/m/n/12 ^^O$ [] Underfull \hbox (badness 10000) detected at line 701 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 705 $\U/msa/m/n/12 I$ [] Underfull \hbox (badness 10000) detected at line 709 $\OMS/cmsy/m/n/12 ^^N$ [] [11] Underfull \hbox (badness 10000) detected at line 745 $\U/msa/m/n/12 I$ [] ) [12] (./01ALG_Kapitola6_5ea138af.aux) *********** LaTeX2e <2023-11-01> patch level 1 L3 programming layer <2024-02-20> *********** ) Here is how much of TeX's memory you used: 3592 strings out of 476042 51050 string characters out of 5792599 1949187 words of memory out of 5000000 25689 multiletter control sequences out of 15000+600000 571235 words of font info for 74 fonts, out of 8000000 for 9000 24 hyphenation exceptions out of 8191 61i,12n,68p,259b,218s stack positions out of 10000i,1000n,20000p,200000b,200000s </usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></usr/share/ texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texmf-dist/fon ts/type1/public/amsfonts/cm/cmmi12.pfb></usr/share/texmf-dist/fonts/type1/publi c/amsfonts/cm/cmmi6.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/c mmi8.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/ share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/share/texmf-dis t/fonts/type1/public/amsfonts/cm/cmr6.pfb></usr/share/texmf-dist/fonts/type1/pu blic/amsfonts/cm/cmr8.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm /cmsy10.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy6.pfb></u sr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb></usr/share/texmf- dist/fonts/type1/public/cs/csbx10.pfb></usr/share/texmf-dist/fonts/type1/public /cs/csbx12.pfb></usr/share/texmf-dist/fonts/type1/public/cs/cscsc10.pfb></usr/s hare/texmf-dist/fonts/type1/public/cs/csr12.pfb></usr/share/texmf-dist/fonts/ty pe1/public/cs/csr8.pfb></usr/share/texmf-dist/fonts/type1/public/cs/csti12.pfb> </usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb></usr/sha re/texmf-dist/fonts/type1/public/amsfonts/symbols/msam7.pfb></usr/share/texmf-d ist/fonts/type1/public/amsfonts/symbols/msbm10.pfb> Output written on 01ALG_Kapitola6_5ea138af.pdf (12 pages, 245411 bytes). 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