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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.4 Vectors

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<h5eturnsthei <class/> a new codeclass<code<>

<div class="func">> a<code class="cveccode>varclass"Arg=" "" 10">r<ctc """&22; CVec(var"<> =>><d> classjava.lang.StringIndexOutOfBoundsException: Range [195, 194) out of bounds for length 240
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<<id nameX8191F74E797B4A3D<pjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62

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<h5>4.1-4 CVec</h5>:a< ="code

<div=func ="=%">"c class="func&82;CVec/code(java.lang.StringIndexOutOfBoundsException: Range [125, 120) out of bounds for length 266
<p>Returns: a new mutable <code classjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>This method takes a coefficient list

<p>For a p><a id="X820D829E87A82A80"820D829E87A82A80></>

<p><a id="java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<h5

<div class="func"><table class="func" width="1d class="functable: a< class"">cvecclass/><p>
<p>p>All argumentsmust integers arguments < classArgp/> and <varclass">< positive base w/> <var="">s/>, <var="">fr<var,< classArg>o/java.lang.StringIndexOutOfBoundsException: Range [0, 251) out of bounds for length 23

<p><var class="Arg">v</var> must be a <strong

<p><a id="

<h5>4<> id=X846D1EDA7B5B1B39>/p>

<div=">table= java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 240
<pReturnsa n <java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 60

<p>This method takes a coefficient list and a finite field <var class="Arg">f</var> as arguments. A new <code class="code">cvec</code> over <var var

<p>For a description of the possible values of the coefficient list <var class="Arg">coeffs</var> see the description of

<p>After having encountered java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<><idX7B9566C1867C5EA6=X7B9566C1867C5EA6">

<h5>4.1-7 CVecClass</h5

<div
<p>Returns: a <code class="

a ="<p><a id="X7F4B8B747E88C59B id"X87D5ABC1835C4A31 name=X87D5ABC1835C4A31"></a></p>

<p>Creates new <code class="code">cvecclass</code>1<h5

<p><a p>Returns:a code="code">cvecclass/code><pjava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53

<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<div classReturns < class"<> same< classcodecReturns: the zero cvec in the same cvecclass as /p>

<p>All<p><a i="X7BA2BD517C058720" name"X7BA2BD517C058720"">

<p>For an explanation of the term <code class="code">cvecclass</code> and its data structure see Section <a href

<p><a id="X871E42B97E3664EB" name="X871E42B97E3664EB"></a></p>

<h5>4.1-9 CVecClass</h5>

<div class="func"><table <div class="unc>Returns a copy ofthezero< class=code>cvec in thesame"cvecclass/> asArgv/>p> <p>The argument p<a ="X81C506327D635947 name=X81C506327D635947>/a>/p> <>4.11 </> <div class <: a <h51 ZeroVector> <p>The div=func class ="0%">< =">#;</>  ="java.lang.StringIndexOutOfBoundsException: Range [136, 137) out of bounds for length 0 <p><>< id=X84EBC4427913251F" <h5 < =""=10"<>/< =func"< class"width10< class#27CopySubVectorcode<  class"s, "st/> < class""rcposs><var/>dclass"(nbsp;&bsp;)/><>
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<p><a id="X7CFEB1507E279EF2" name="X7CFEB1507E279EF2"></

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<p>For<divclass="func"><tableclass"func" idth

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<>4.- AdditiveInverseSameMutability/>

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<p>For a <code class="code">cvec</code>< class

<p><a id="X7A34F9AA8330EBB9" name="X7A34F9AA8330EBB9"></a></p>

<h54- AdditiveInverseMutableh5>

<iv=
<p>Returns: the additive inverse of <varp>eturns class"true/ode codeclass"ode</codes< class"v/ar var class"rg">wareequal The vectors must over the same field must haveequal length java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <p><a id="X8191F74E797B4A3D" name <h5><code>4.2-6  ="code>or< =code> < <div=func>< class"/code> codeclass=code"></< lass"><varThe   be  same  must equal. The implemented very but e></em compatible lexicographic of offinite elements  method therefore only e  for search . Note the < class"LT< < scalarclass"">span\\cdot>arArg><> <p>For a <code class="code">cvec <>id" ="">a>/java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62 <h5>4.2-7 AddRowVector</h5> <div class="func"><table class="func" widthp>Returns <code class"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <div class="func"><table <p>Returns: nothingp> < class"code">true ifthe"code">cvec<code <p>var=""v/>and<var ="Arg">/varmust < class"ode <p>If either < <h5>4 < =Heading access<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <div class="func"><table class="func" width="100%"><tr><td class=" <div class="func"><table class="

gth 0
<

<p<iv=func =unc10"trtd =tdleft"< class>82;<code =""v,var""rs/td>method/>>/div

<p><a id

<h5>4.1-12 CVecClass<p< class"cvec/odesbehave some extend likelistswith respect element slicing. However, allow onlyactions that can be implemented efficiently and that not change their length. addition there is optimised function to copy contiguous sections of code<> < <> =>/var becode="ode"></code and class>/var be if. This changes vectorvar="Arg>GAP library is taken. < <p>: a <code var"< var ="cvec and="posv>must a integernotgreater the length Arg.a ="posvar> < classclass=">/ar returned> <p>The<5>4- class>Handling ofjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <h5<java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0 <div class="func>java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0 the < class></codein same<codeclass"cvecclass/>as">v

<p><var class="Arg"p>eturns thesum<span

<p><a id="X7BA2BD517C058720

<5>41-4 ShallowCopy/5>

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<p>Returns a mutable "X7D12C17C873DE3B4" name""</>pjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62

<p><var class="

<p><a id="X84EBC4427913251F" name

<h5>eturns < class""cvec>pjava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48

ss"func>table class=""width"0%>> =tdleft =func#27 Randomize
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<< ="X79862FF37B75BF48 of Arg"> asa "cvec/ode

<h4>4

<>Of, the arithmetic operations class">\(+)/span>,SimpleMath>(\/<span"SimpleMath>(*\4.2-5 AdditiveInverseMutable

<p><a id="X788A3D6482290F7D" name="X788A3D6482290F7D"></a></p>

<h5>4.2-1 <span class="Heading">Handling of scalars in arithmetic operations</span></h5>

<p>In all placesp>Returns:</p>

<p><strong class

<p>Integers< "s and Arg<varbe=code<codeover .The from<ar"">srcpos> <span="SimpleMath">\java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p><a id="X7C2F565480B1A4A1" name="X7C2F565480B1A4A1"></a></p>

<h5><code>4.2-2 \+</codeh53- CopySubVector<h5

<div class"func">tableclassfunc width="100%"><tr<td class"tdleft"><code class="func>ã *( ">s, ></ar</>td"dright>&;method )

‣ PositionNonZero( veturns: a positive integer <p>eturns:nothingp> <p <p> either class=">fr or to is >\(1\<s> and< ">Length(v). <p><a idp>: a non-negative</p> <h5 p>Returnsthe of the entry in thecode="code">cvec<code var="Arg">v<v> that not to zero the vector is tozero, <span ="SimpleMath">\(\)</> isreturned<pjava.lang.StringIndexOutOfBoundsException: Index 220 out of bounds for length 220 <p>Returns: the scalar product</p> <p>Both <var class="Arg">v</var> and <var class="Arg">w</var> must be <code class="code">cvec</code>s over the same field with equal length. The function returns the scalar product of the two vectors. Note that there is a very efficient method for prime fields with <span class="SimpleMath">\(p < 65536\)</span>. In the other cases thedivclassfunc>table="func <p><a id="X86115BE97842EC3B" name="X86115BE97842EC3B"></java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <h5>4.2-10 ZeroMutable</h5> <div class="func"> <>Returns a mutable of the zerocode class""cvec>in <code="code"cvecclass>asclass"Arg"></var/ <p><var45-Unpackh5 <p>< ="X7FB1A37D7F8603B9" name"func"< =func=0tr=tdleft ""#7;Unpack(<rclassArgvartd< =tdright&;method;)</d>r>table></> <h5>4.2-11 ZeroVector</h5> <div class="func"><tablejava.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0 <>: mutableof <decode<> the than="Arg">/>but varArgl<v><> <p><var class="Arg">v</var> java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <p><a id=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <h4>4.3 <span class="Heading">Element access <p><code <><a idX7A6A222E87452C27name"/> <h5>4.3-1 ELM_LIST</h5> <div class="func"><table class="func" width="100%<>This operation unpacks a < class"code">varclass"">v its integer representation. new plain list containing the corresponding numbers of the vector is returned.The integer of a field element is either one integer (containingthe <p>Returns: a finite <>This java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0 <>Note that java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 0 <p><a id="< <<>Returnsan</p> < classfunc<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <p>Returns: nothing</p> <p>This is <p>The <varclassArg<var treated exactly described Subsectionahrefchap4_mjX788A3D6482290F7Dspan="RefLink">4.2-<span/><pjava.lang.StringIndexOutOfBoundsException: Index 170 out of bounds for length 170 <p>Note that the list access syntax <q><var classp>eturns: nothingpjava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23 <p><a id="X7D12C17C873DE3B4" name <h5>4.3-3 ELMS_LIST</h5> <div class="func"><table java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <p>Returns: a <codeh5java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0 <p>This <p>This is <p>Note that the list slice access syntax <q><var class="Arg">v</var>{<var class="Arg <p>Note <p><a id="X78878E5E839265A6" name="X78878E5E839265A6"></a></p> <>4.p>a id"58AE878B0CBF"name3">// <div divclass"<44Accessbase<san4java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 66 <Returns</> <p><var class="Arg" <pjava.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0 <p><a id="X80EC354D78D7B5A6" name="X80EC354D78D7B5A6java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <h5>4.3-5 CopySubVector</h5> <div class <p>Returns nothing/> <p>Implements the operation<odeclass="func">CopySubVector</> (< ="../<>turns: c class=""true/>or "> <p>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 <h5>4.3-6 CVEC_Concatenationh5.-LTeturns < =""<>/ div="">table=func <>: new classcode<ode / <p>This <p><a id=X81F3C9697E5636B6 ="X81F3C9697E5636B6"></a></p> <h4>4.4 <span class="Heading">Comparison of Vectors java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 0 << ="" name <div ="func">table=funcwidth0">rtd tdleft"<code=func&82;Characteristic>(<varArg<ar>class>&;methodnbsp/></tr><table/div> < class"func"<ableclass"func" width"00">><td="tdleft">codeclass">&82;=/> rg/>)/>td">( method )

<p>Returns: <code class="code">true<

<p>Returns <odeclass="code">true/ode< =code< or ="code>





<p><a id="X790D69A88340E510" name="X790D69A88340E510"></a></p>



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<div><="" nameX7F42E5AD87EC9D5Aa>p>

<p>Returns: <code<>4.-PositionNonZeroh5



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<h5>4.4-3 IsZero</h5>



<div classp>aidX8370979D7F451279name

<p>Returns: <code <>Returnsthe.-5PositionLastNonZeroh5



<p>Returns>aid"nameX823EFBDB7ED49554"<<>



<p><a id="p>

code>vec var"Arg">/



<h5



<divclassclass"> class" width%>>class">>#7Lengthcode>var=""v/>)/d< class/><iv

<p>Returns: a positive integer



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<p>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0



<h5>4.4-5 PositionLastNonZero</h5>



<diviv="< class="func

p>:   integer



<p>Returns



<p>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0



<h5>4.4-6 Length</h5>



<div 

<p>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0



<p>Returns the



<"java.lang.StringIndexOutOfBoundsException: Range [0, 1) out of bounds for length 0



<h4>4.5 <span class="Heading">



<p><a id="X7BD632E57E1EB300" name="X7BD632E57E1EB300"></a></p>



<h5>4.5-1 Unpack</h5>



<div class"unc"< ="unc" width="10%><>tdclass"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>Returns: a list of finite 



<p>his<="ã  varclass=rg">v/>varclassArgsz/> />< "tdright">&;method;/>>/></div



<p><a id="X850FB74483F87453" namepReturns:



<h5>4



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<p>This< class="foot:/wwwmathrwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>



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<h5>4.5-3 </html>



<div class="func"><table class="func" width="p>name">

<p>Returns: an integer</p>



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<p><a id="X7E055C467B1B54D8" name="X7E055C467B1B54D8"></a></p>



<h5>4.5-4 CVecNumber</h5>



<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CVecNumber</code>( <var class="Arg">nr</vardiv class"func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CVecNumber</code>( <var class="Arg">nr</var, <arclass="Arg">p<>, < class"Arg">d</var>, <var class="Arg">l</var> )</td><tdclass"">(&;operationnbsptd></><div

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CVecNumber</code>( <var class="Arg">nr</var>, <var class="Arg">p</var

<p>Returns==X854192428704857E<pjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62



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tdclass="tdleftclass">#27 ( varclass"Argv/>)> ""(&)/d</<able



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<h4>4.6java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0



<p><a id="X854192428704857E" name="X854192428704857E"></a></p>



<h5>4.6-1 BaseDomain</h5>



<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><

<">



<p>For a <code class="code



<p><a id="X842335E47DC49702" name="X842335E47DC49702"></a></p>



<h5>



<divclass""><tableclass""="0%>=tdleft>codeclass=func>82;BaseField( varclass"">v 



<p>For a <code class="code">cvec</



<p><a id



<h5>4.6-3 Characteristic</h5>



<div class="func"><<h554.6-3Characteristich5

<p>Returns: the characteristic ofdivclasstr>td="">code class=func>#827 Characteristic</code>( <var="Arg">v<var </td>< class"tdright"(nbsp ></<table>



<p>Returns the characteristic of the base field of <var class="Arg">v



<p><a id="X81E3BBBB80096DC2" name="code class"&82; < class="Arg> <td< =""(; /d>/>/able>

<p>Returns: the degree of the base field of <varpReturns degree the field < class<var its fieldp>



<pReturns degreethe of =Argvar primesee =func<>(java.lang.StringIndexOutOfBoundsException: Range [134, 133) out of bounds for length 218



<p><a id="X823EFBDB7ED49554" name="X823EFBDB7ED49554"></a></p>



<h4>4.7 h4 span=HeadingHashing <class<><>h4



<> " name="X7F0228A18327F87D"



<h5



<div class="func"><table class="func" width="100%"><tr><td<p>:  integer value

<p>Returns an  value



<> java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 568



<p><a id="X82C8DE4C78B80B1E" name="X82C8DE4C78B80B1E"></a></p>



<h5>4.7-2 ChooseHashFunction</h5>



<div=functable=func=00>tr=tdleft class&2;ChooseHashFunction> var=Arg/> < classArg<var/d><td="tdright">( method )<td>/r<table<div

<p>Returns: a record describing class"< ="func=0">codeclassfunc82;ChooseHashFunction(< class><varvar""hashlen <>< =tdright>nbsp)/<>/able



<p: r  ahash<p>





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