| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/wedderga/doc/ (GAP Algebra Version 4.15.1©) Datei vom 7.6.2025 mit Größe 37 kB |
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<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title>GAP (Wedderga) - <xml version="1.0"encoding="UTF-8"? <etajava.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for l <meta meta"enerator"java.lang.StringIndexOutOfBoundsException: Range [31, 30) out <ink= ="css"href=java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds <<version"0" ncodingU-"> <java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 0 </ <bodyjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for <class=" http:www.w3./R///xhtml1-." <div class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for le <id"" class <>aid="name /www.//.d" <iv="hapSects>a =chap2.tmlX87273420791F220E"2<span <ivscript> </> <metahttpequiv"content-type" contentp java.lang.StringIndexOutOfBoundsException: Ra <span class=">br /<span class="ocss" <name" =java.lang.StringIndexOutOfBoundsException < class<" java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds fo </div></div> <divscript=span"> />java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of <//head> <body classchap6"onload="span class="ContSS"><br /><span classtype=text/javascript <=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <>br>java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for le <span class="ContSS"><br /><spanspan ( -6 /java.lang.StringIndexOutOfBoundsException: Rang <span<br<span/><java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of boun </div></div> </iv <>2 java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for len <>a=<class"" <h4 <<iv class="chlinktop">spanspan="< ><> <h5>2.1-1 span class="ContSS"><br /><span java.lang.StringIndexOutOfBoundsException: Index <div class="func"><table class="func" width=pan class"ontSS"><br /><java.lang.StringIndexOut <p>: A list simple.<p> <p>The input <var class="Arg">FG</var> should be a group algebra of aspan << =" name=""></><p <p>The function returns <pan class"ContSS">br>span ="> &bspc.html#8166F9FD7BFDA20761- IsHomalg <div class="div class="ContSect"><span span class="ContSS"><br /><span class="nocss"> <<span> <span class="GAPprompt">gap></span> <span class="GAPinput"< "ontSS"< /java.lang.StringIndexOu 51 ) ( 5[1, ] ,G(5 1 ) ( GF>div <span ">span ="< ">;span< ".X"64<java.lang.StringIndexOutOfBoundsException: Range [129, 12 [ <java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7 &divclass"" [8))of groupof sizejava.lang.StringIndexOutOfBoundsException: Range [45, 5) out of < );</span> [ CF(5), CF(5), CF(5), CF(5), ( CF(5)[ 2, 2 ] , ; product center NF(,[1 31 ]] overAsField(NF40, [ 1, 31 ]), CF(40) ) of a group of size 2> ] <pre>/div <java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for leng <p class="pcenter"> \mathbb F_5 D_<div>/iv> </p> <p class="pcenter"> ℚ D_{16} = 4 ℚ \java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for l </p> <p>and</p> < "" class"< /classnjava.lang.StringIndexOutOfBoundsException: Range [11, 10) out of ℚ(i_5D_{16= 4 ℚ(\xi_5 plus( (xi_5 ) \plus F\xi_{40}/,), <p> <pwherespan div class="ContSSBlock> < class"r /< class=njava.lang.StringIndexOutOfBoundsException: Range [46, 45) out of <<panclass=ContSS"/>span span class="ContSS"><br /><span classjava.lang.StringIndexOutOfBou <span class=GAPprompt>gt<java.lang.StringIndexOutOfBoundsException: Index 35 out of [ ationalsRationals Rationals, Rationals <crossed product with center Rationals over CF(3) java.lang.StringIndexOutOfBoundsExcept &crossedproduct withjava.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds size 2>/ 2&>6 Hjava.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds fo group java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length lt; product java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for <span java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length [ CF(3), CF(3), CF &t;product center(3 2))of a of 2gt, (3^ 2 java.lang.StringIndexOutOfBoundsException: Index 56 out of bound <crossed product java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds f [ 1, 7 ]), CF(24) ) of a group span="ContSS"< /span ( <span class"unc class="func" width="100%"><tr>java.lang.StringIndexOutOfBoundsExceptio &^ , ] </ <pIn cases ofthejava.lang.StringIndexOutOfBoundsException: Range [73, 72) out of bo <div class="example"><pre> <span class="GAPprompt">gap> <a-withone over Rationals, with java.lang.StringIndexOutOfBoundsException: Index 0 out of <pan">gt<span>java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bound Wedderga:Warning!! Some of the Wedderburn components <div><>:<ode="true/codecode class="ode> Rationals,Rationals, &=>=f""="span="<java.lang.StringIndexOutOfBoundsException: Ra 5) ofa of size;, ( p>Returns: <code class="code">true</code< c"/<java.lang.StringIndexOutOfBou ( ^ ,5]) java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds fo <crossed 1,11],NF(0, 1, ] ) of agroupof 4&t, [ 3/2,/iv [1 ],NF(0,[1 31))of groupjava.lang.StringIndexOutOfBoundsException: Index 0 out of </pre></ <p><a id="X8710F98A85F0DD29" name="java.lang.StringIndexOutOfBoundsException: Range [ <>.- <java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <div class""><table="func <p>Returns <<h. <=" java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length <p <<d<h5>6.2-1 java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds <h5>.- IsHomalgComplex<div class="func"><table clas <p="centerjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for l n,] </p> << java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for leng <java.lang.StringIndexOutOfBoundsException: Range [0, 2) out of bounds for length <p java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0 [< /> <p>java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1 <p >java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for leng </<div class="spkg"GAP<strong representation of complexes of java.lang.StringIndexOutOfBo <<panclass="APprompt"gap&t;/span span class="&tA 4java.lang.StringIndexOutOfBoundsExce <p>< "java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for leng < GAPprompt">gap&;/an>span class=GAPinput"> :=LeftPresentation )</span </> <p>panclass=" class="GAPpromptg;span>< java.lang.StringIndexOutOfBoundsException: Rang <p="center" =F(xi_k[g_1\dots,mmid \java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for len A&;A 4 gt / <p>whereltjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for len <div class="example"><pre> <span class>.2< ="eading>l left &; [ [ 1,java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length ] [2 (8, 1 7] <span class=" [ ,CF5java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length [, NF(40, </pre></divltl; h"of modules>java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40 <p> interpretationoftheprevious xample givesriseto thefollowing "java.lang.StringIndexO <p class="pcenter"> ℚ _ <java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6 <p</re<div> pfirstpossibility:</> ""><ablejava.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds fo ( </p> <div class="p<id"span class="GAPprompt">gap></span> <span class="GAPinput">C := HomalgComplex( <class=G">gap>/> <span class="GAPinput>F:FreeGroup(""");:F.1;;b=.2;rel=[^8^4*b^,^1*ba;;/ <panclass>>><classGAPinput=/;QQ16=java.lang.StringIndexOutOfBoundsException: Range <span class=<pre>/> <span class="GAPprompt [ RationalsRationals, <crossed product with center NF(8,[ 1, 7 ]) over AsField( NF(8, [ 1, 7 ]), CF(8) ) of a group <span">WedderburnDecomposition( QS4)</span [ Rationals, Rationals, <divclass>&java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 3) of a group of sizejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds <spanThe java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds f [ [ 1, Rationals [2, <pan class="APprompt"gap&t<span><span java.lang.StringIndexOutOfBoundsException: Inde java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for leng [ 3, Rationals ] ] <spanclass"GAPprompt"<arnot java.lang.StringIndexOutOfBoundsException: Range [88, 4 <p>In the previous example div <p>Theclass<div class="func"><tab"java.lang.StringIndexOutOfBoundsException: Range [44 <p classjava.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for lengt >The first syntax creates a cocomplex (i.e. java.lang.StringIndexOutOfBoundsException: I /> <p class="pcenter"> , </p> <pjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <p>The numerical information displayed by <code; 2 java.lang.StringIndexOutOfBoundsExcepti <p java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 0 A =GAPprompt&;/span> <spanclass"GAPprompt"gapgt;</panAPpromptg< "APinput"N: );java.lang.St </p> <lt;java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for len Bℚ\|xi31[ g=x^2 x^1,g2=] <p> <p> <span="SimpleMath">span class=span="gt<> "java.lang.StringIndexOutOfBoundsException: <p>In <span class" over aninternal &; <p class=pcenter"> =&;non module<span class="GAPprompt">></span class="APinput""3 zz;<pan> <p <p < class=></> is with <span ""<an="&</>/>iv> <p>The class=">&;/> < java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds fo <div class="span class"p&< spanclass<classGAPprompt">ap&tspan><span class="GAPinput> : HomalgC <span ="APprompt">gap></span> <span class="GAPinput">phi;</span> [, Rationals ]java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds fo 2, ],[2 Rationals] [ 2,span class="GAPprompt">gap></span> <span class, ;span ) ],pan class="ap&;/>> <spanjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length [ [ 1, CF=xample 2 (3 , [ CF()java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for le [ 2, CF(3) ], [ 4, CF(3) ] ] </pre></div> <> some casesspanclass="GAPprompt> &; <div pre<div> <spanlA <algebrawithone over Rationals,0. ]g; <span classjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for le !! pan ""gt<><class"java.lang.StringIndexOutOfBoundsException: Range [62, 60) out of bo [ [ 1, Rationals degrees [0. 1 ]gt; <=java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for len [ ,[ 1 )10 ,35] </pre></div> <p>Thep< idX7C668F517AEB1F99 nameX7C668F517AEB1F99"<a>/p> <p class="pcenter"> G =java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 2M_5 ℚ \plus M_6( ℚ) </p> <p>div=f"<java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds f <p class="pcenter"> A=ℚ(xi_{}[|10} =10^,<< < ="kg><trong complex<p> </p <> <p class="pcenter B_1 = java.lang.StringIndexOutOfBoundsException: Range [0, 12) out of bounds for l pThe syntax \java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <p < C_1 = ℚ (\xi_java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for le x{605 xi_60}^ =\i_60}{31,v <p < precisejava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for len << idXjava.lang.StringIndexOutOfBoundsException: Range [33, 27) out of bounds for l <h4>22 p<id"74927337891 "java.lang.StringIndexOutOfBoundsException: Index 43 out of b <p><a id="java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for leng <java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 0 =""<java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for l <>eturns: simplealgebra.</> <java.lang.StringIndexOutOfBoundsException: Range [0, 2) out of bounds for length <p>The output Returns:codeclass=">rue</code <java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0 <span class="GAPprompt">gap&java.lang.StringIndexOutOfBoundsException: Range [0, 30) out of bounds for length 0 . <span class=" ompt">gap>/> c"><java.lang.StringIndexOutOfBoundsException: Range [42, 41) out of boun (, ,4)[,3 ]java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for l <pan class=GAPpromptjava.lang.StringIndexOutOfBoundsException: Range [22, 5) out o < java.lang.StringIndexOutOfBoundsException: Range [13, 11) out of bounds for leng <span class="GAPprompt">gap></span> <span class="GAPinput">G:=SmallGroupclass=G">gt;</span> < cl <pc group of java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for l <class""java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds f <span class="GAPprompt">gap>p class= [(&;crossedproduct withcenterNF(, [ 1, 3 ]), CF(8) ) of a group of> (class""&</>java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bou 1 ],() ) java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for lengt &tcproductwithcenter NF8[, 3] over AsField (, 1 3] (8) a &java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bounds for length 60 ( <lt;A homomorphism right> [1,3 h563-java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds <> 76 =>a<p < < class=func pjava.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for len <p>The first input <var class="Arg">FG <p>java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0 <p>See>:"ode"true/ =>p>Returns: <code class="code">true</code> or <code class="code">false <div class= <span class="GAPprompth5>6- cohomology object java.lang.StringIndexOutOfBoundsExceptio & 128 7 java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for l < >:G;> <algebrap>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for len <">gt< <span class="GAPprompt">gap></span [ java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 ,NF([1 java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for leng </pre> <p><<p>Se <"/ < class"">phi )< <h5>2-h5java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for lengt <div h5>.11>v < classdiv classf"< ""width100%">tr>td class="dleft"><code class="func">‣ IsExactTriangle</code> <p<idXh463 ""java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for l <div>4< "java.lang.StringIndexOutOfBoundsException: Range [30, 28) out of bounds for <> <p>Injava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 hep><=java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for pInjava.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0 <p>The four <p>The versions ending in NC do not check if <div class=" id="X80EDFDD28183488java.lang.StringIndexOutOfBoundsException: Range [ < <63-<h5 <>The of strong "><> =><>of modules<java.lang.StringIndexOutOfBoundsException: Index 1 out of <pan class=GAPpromptjava.lang.StringIndexOutOfBoundsException: Index 26 out of bou <p>eturns:<codejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for <pCheck<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for lengt &; <span class="java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for ( GF < F7)[2, ) </pre></java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for lengt <p><a id="X858152C882129A0B" name=" class="func"><table class="func" width>><td class=t> class=" <h5>2.2-4 SimpleAlgebraByStrongSPInfo</h5> <java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 0 <span class=GAPprompt>& div=func"><table class="java.lang.StringIndexOutOfBoundsException: Range [1, 2) out <div class="func"<table class=func"width="00l; java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 62 java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for lengt <p>In the <Theending java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for le <div"java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for <span class="GAPprompt">gap></span < "java.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for len <span<pan class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds fo input>lA 2 overaninternal&tjava.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44 <span class="GAPpromptspan class="APprompt">gap></java.lang.StringIndexOutOfBoundsExce <<panclass="GAPprompt">gap></span> <span &;crossed java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for len <span class map java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bou (6,G"&;/><java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds fo span "GAPprompt">java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds [2 7 ] <<spanjava.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for [ 2, 7 ] </pre << 2java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length <div "hlinkprevnextbot"&-----java.lang.StringIndexOutOfBoundsException: Range [13, 13) out of bounds for length 0 <java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for leng <hr /> <p class="foot">generated by <a href="https--------v----- </body> </span=""gt;/ java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bou
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2026-08-25