<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 length 69
<metameta"enerator"java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 47
<ink= ="css"href=java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 0
<<version"0" ncodingU-">
<java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 0
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<bodyjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 42
<class=" http:www.w3./R///xhtml1-."
<div class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<id"" class
<>aid="name /www.//.d"
<iv="hapSects>a =chap2.tmlX87273420791F220E"2<span
<ivscript>
</>
<metahttpequiv"content-type" contentp java.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length 62
<span class=">br /<span class="ocss" <name" =java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 47
< class<" java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 59
</div></div>
<divscript=span"> />java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 163
<//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 length 150
<span class="ContSS"><br /><spanspan ( -6 /java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 50
<span<br<span/><java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 12
</div></div>
</iv
<>2 java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 64
<>a=<class""
<h4
<<iv class="chlinktop">spanspan="< ><>
<h5>2.1-1 span class="ContSS"><br /><span java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<div class="func"><table class="func" width=pan class"ontSS"><br /><java.lang.StringIndexOutOfBoundsException: Range [0, 32) out of bounds for length 0
<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- IsHomalgComplex</></>
<span class="GAPprompt">gap></span> <span class="GAPinput"< "ontSS"< /java.lang.StringIndexOutOfBoundsException: Range [40, 38) out of bounds for length 136 51 ) ( 5[1, ] ,G(5 1 )
( GF>div
<span">span ="< ">;span< ".X"64<java.lang.StringIndexOutOfBoundsException: Range [129, 128) out of bounds for length 177
[ <java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
&divclass""
[8))of groupof sizejava.lang.StringIndexOutOfBoundsException: Range [45, 5) out of bounds for length 138
< );</span>
[ CF(5), CF(5), CF(5), CF(5), ( CF(5)[ 2, 2 ] ,
; product center NF(,[131 ]] overAsField(NF40,
[ 1, 31 ]), CF(40) ) of a group of size 2> ]
<pre>/div
<java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 136
<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 length 7
</p>
<p>and</p>
< "" class"< /classnjava.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 177
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 bounds for length 128
<<panclass=ContSS"/>span span class="ContSS"><br /><span classjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 147
<span class=GAPprompt>gt<java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 12
[ ationalsRationals Rationals, Rationals
<crossed product with center Rationals over CF(3) java.lang.StringIndexOutOfBoundsException: Range [0, 57) out of bounds for length 6
&crossedproduct withjava.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 82
size 2>/ 2&>6 Hjava.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 49
group java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
lt; product java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 0
<span java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0
[ CF(3), CF(3), CF
&t;product center(3 2))of a of 2gt, (3^ 2 java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
<crossed product java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ 1, 7 ]), CF(24) ) of a group span="ContSS"< /span
( <span class"unc class="func" width="100%"><tr>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
&^ , ]
</
<pIn cases ofthejava.lang.StringIndexOutOfBoundsException: Range [73, 72) out of bounds for length 676
<div class="example"><pre>
<span class="GAPprompt">gap>
<a-withone over Rationals, with java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<pan">gt<span>java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 97
Wedderga:Warning!!
Some of the Wedderburn components <div><>:<ode="true/codecode class="ode>
Rationals,Rationals, &=>=f""="span="<java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 191 5) ofa of size;, ( p>Returns: <code class="code">true</code< c"/<java.lang.StringIndexOutOfBoundsException: Index 81 out of bounds for length 81
( ^ ,5]) java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 73
<crossed 1,11],NF(0, 1, ] ) of agroupof 4&t,
[ 3/2,/iv
[1 ],NF(0,[131))of groupjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
</pre></
<p><a id="X8710F98A85F0DD29" name="java.lang.StringIndexOutOfBoundsException: Range [0, 52) out of bounds for length 0
<>.- <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 0
<p
<<d<h5>6.2-1 java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 28
<p="centerjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
n,]
</p>
<< java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 429
<java.lang.StringIndexOutOfBoundsException: Range [0, 2) out of bounds for length 0
<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 length 81
</<div class="spkg"GAP<strong representation of complexes of java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 75
<<panclass="APprompt"gap&t;/spanspan class="&tA 4java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 44
<p>< "java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 125
<p>panclass=" class="GAPpromptg;span>< java.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 79
<p="center"
=F(xi_k[g_1\dots,mmid
\java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 69 A&;A 4 gt
/
<p>whereltjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<div class="example"><pre>
<span class>.2< ="eading>l left &;
[ [ 1,java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
] [2 (8, 17]
<span class="
[ ,CF5java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[, 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.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 71
<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 for length 250
(
</p>
<div class="p<id"span class="GAPprompt">gap></span> <span class="GAPinput">C := HomalgComplex( N );<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<class=G">gap>/> <span class="GAPinput>F:FreeGroup(""");:F.1;;b=.2;rel=[^8^4*b^,^1*ba;;/java.lang.StringIndexOutOfBoundsException: Index 139 out of bounds for length 139
<panclass>>><classGAPinput=/;QQ16=java.lang.StringIndexOutOfBoundsException: Range [91, 90) out of bounds for length 117
<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 for length 0
<spanThe java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 286
[ [ 1, Rationals
[2,
<pan class="APprompt"gap&t<span><span java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 26
[ 3, Rationals ] ]
<spanclass"GAPprompt"<arnot java.lang.StringIndexOutOfBoundsException: Range [88, 49) out of bounds for length 269
<p>In the previous example div
<p>Theclass<div class="func"><tab"java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 251
<p classjava.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 1
>The first syntax creates a cocomplex (i.e. java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 44
/>
<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.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 44
<p java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 0 A =GAPprompt&;/span> <spanclass"GAPprompt"gapgt;</panAPpromptg< "APinput"N: );java.lang.StringIndexOutOfBoundsException: Index 111 out of bounds for length 111
</p>
<lt;java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 44 Bℚ\|xi31[ g=x^2 x^1,g2=]
<p>
<p> <span="SimpleMath">span class=span="gt<> "java.lang.StringIndexOutOfBoundsException: Range [58, 57) out of bounds for length 79
<p>The class=">&;/> < java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 0
<div class="span class"p&< spanclass<classGAPprompt">ap&tspan><span class="GAPinput> : HomalgComplexNl;A non-ero gradedjava.lang.StringIndexOutOfBoundsException: Range [21, 3) out of bounds for length 41
<span ="APprompt">gap></span> <span class="GAPinput">phi;</span>
[, Rationals ]java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 7 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 0
[ [ 1, CF=xample 2 (3 , [ CF()java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ 2, CF(3) ], [ 4, CF(3) ] ]
</pre></div>
<> some casesspanclass="GAPprompt> &;
<divpre<div>
<spanlA
<algebrawithone over Rationals,0. ]g;
<span classjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
!!
pan ""gt<><class"java.lang.StringIndexOutOfBoundsException: Range [62, 60) out of bounds for length 97
[ [ 1, Rationals degrees [0. 1 ]gt;
<=java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 62
[
,[ 1 )10 ,35]
<p class="pcenter
B_1 = java.lang.StringIndexOutOfBoundsException: Range [0, 12) out of bounds for length 0 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 length 0
x{605
xi_60}^ =\i_60}{31,v
<p
< precisejava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 1
<< idXjava.lang.StringIndexOutOfBoundsException: Range [33, 27) out of bounds for length 62
<h4>22p<id"74927337891 "java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 0
<p><a id="java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 0
<java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 0
=""<java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 261
<>eturns: simplealgebra.</>
<java.lang.StringIndexOutOfBoundsException: Range [0, 2) out of bounds for length 0
<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 bounds for length 81
(, ,4)[,3 ]java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
<pan class=GAPpromptjava.lang.StringIndexOutOfBoundsException: Range [22, 5) out of bounds for length 94
< java.lang.StringIndexOutOfBoundsException: Range [13, 11) out of bounds for length 79
<span class="GAPprompt">gap></span> <span class="GAPinput">G:=SmallGroupclass=G">gt;</span> < class="GAPinput">]", 3, 4, zz );</span>
<pc group of java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 0
<class""java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 111
<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 bounds for length 87 1 ],() ) java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
&tcproductwithcenter NF8[, 3] over AsField (, 13] (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 for length 30
<>
76 =>a<p
<
< class=func pjava.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 190
<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.StringIndexOutOfBoundsException: Range [54, 50) out of bounds for length 82
& 1287 java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 10
< >:G;>
<algebrap>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<">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 length 25
</pre>
<p><<p>Se <"/ < class"">phi )<
<h5>2-h5java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<div h5>.11>v
< classdiv classf"< ""width100%">tr>td class="dleft"><code class="func">‣ IsExactTriangle</code>( <var class="Arg">C</var> )</td><td class=p>java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 81
<p<idXh463""java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<div>4< "java.lang.StringIndexOutOfBoundsException: Range [30, 28) out of bounds for length 63
<>
<p>Injava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
hep><=java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 217
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 [29, 27) out of bounds for length 62
<
<63-<h5
<>The of strong"><> =><>of modules<java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<pan class=GAPpromptjava.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 0
<p>eturns:<codejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<pCheck<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
&;
<span class="java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 0
( GF
<
F7)[2, )
</pre></java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 0
<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 of bounds for length 1
<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 length 776
<p>In the
<Theending java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<div"java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 83
<span class="GAPprompt">gap></span
< "java.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 125
<span<pan class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 input>lA2 overaninternal&tjava.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
<span class="GAPpromptspan class="APprompt">gap></java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 25
<<panclass="GAPprompt">gap></span> <span
&;crossed java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 14
<span class map java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 58
(6,G"&;/><java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 83 span"GAPprompt">java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 21
[27 ]
<<spanjava.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 79
[ 2, 7 ]
</pre << 2java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
<div"hlinkprevnextbot"&-----java.lang.StringIndexOutOfBoundsException: Range [13, 13) out of bounds for length 0
<java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 418
<hr />
<p class="foot">generated by <a href="https--------v-----
</body>
</span=""gt;/ java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 84
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