<?xml version="1.0" encoding="UTF-8"?>span ="APprompt>ap&t<span><pan "APinput"s : ()<spanjava.lang.StringIndexOutOfBoundsException: Index 92 out of bounds for length 92
<h4>2.1 <span class="Heading">The method for <code class="code">Factors</code></span></h4>
<p>The <strong class="pkg">FactInt</strong> package provides a better method for the operation <code class="code">Factors</code> for integer arguments, which supersedes the one included in the <strong class="pkg">GAP</strong> Library:</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; Factors</code>( <var class="Arg">n</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a sorted list of the prime factors of <var class="Arg">n</var>.</p>
<p>The returned factors pass the built-in probabilistic primality test of <strong class="pkg">GAP</strong> (<code class="code">IsProbablyPrimeInt</code>, Baillie-PSW Primality Test; see the <strong class="pkg">GAP</strong> Reference Manual). If the method fails to compute the prime factorization of <var class="Arg">n</var>, an error is signalled. The same holds for all other factorization routines provided by this package. It follows a rough description how the factorization method works:</p>
<p>First of all, the method checks whether <span class="SimpleMath">\(n = b^k \pm 1\)</span> for some <span class="SimpleMath">\(b\)</span>, <span class="SimpleMath">\(k\)</span> and looks for factors corresponding to polynomial factors of <span class="SimpleMath">\(x^k \pm 1\)</span>. Provided that <span class="SimpleMath">\(b\)</span> and <span class="SimpleMath">\(k\)</span> are not too large, the factors that do not correspond to polynomial factors are taken from Richard P. Brent's java.lang.StringIndexOutOfBoundsException: Index 496 out of bounds for length 29
<p>Then the method uses trial division and a number of cheap<div class="><pre>
<p>If there is still an unfactored part remaining afterinput>mat:IdentityMat(6,GF());/java.lang.StringIndexOutOfBoundsException: Range [97, 98) out of bounds for length 97
<p>The following options are interpreted:</p>
<dl>
<dt><strong class="Mark"><var class="Arg">TDHints</var></strong></dt>
<dd><p>A list of span class="GAPpromptgap>/span>< =GAPinput">form := BilinearFormByMatrix(mat,GF(5));</span>
</dd>
<dt><strong class="Mark"><var class="Arg">RhoSteps</var></strong></dt>&t;bilinear form gt;
<dd><p>The number of steps for Pollard's Rho.</pspan=GAPprompt>&t<span s class=GAPinput>s = PolarSpaceform);<s>
</dd>
<dt><strong class="Mark"><var class="Arg">java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 35
<dd><,GF(5) ^x_2^2x3^+2x_5+_^= gt;
</dd>
<dt><strong class="Mark"><var class="Arg">Pminus1Limit1</var> / <var class<span ="APprompt">gapgt<>spanclass="APinput"IsEllipticQuadricps);/pan>
<dd><p>The first- / second stage limitjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
</dd>
<dt><strong class="Mark"><var class="Arg">Pplus1Residues</var></java.lang.StringIndexOutOfBoundsException: Range [64, 70) out of bounds for length 50
<dd><p>The number of residues to be tried by Williamsspan class"APprompt>apgt;/> span "APinput"form:=BilinearFormByMatrix(,7)<span>
</dd>
<dt><strong class= t java.lang.StringIndexOutOfBoundsException: Range [18, 13) out of bounds for length 23
dp secondjava.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 226
</dd>
<dt><strong class="Mark"><var class="Arg">ECMCurves</var></strong></dt>
<dd><p>The number of elliptic curves to be java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 35
</dd>
<dt><strong class="Mark"><var class="Arg">ECMDelta</var></<pre</java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
<dd><p>The increment per curve for the first stage <p><a id="X87ADB8B5790776C7" name="X87ADB8B5790776C7"><
</dd>
<dt><strong class="Mark
<dd><p>If true, ECM chooses its curves deterministically, i.e. repeatable (see <7.38IsParabolicQuadric</h5java.lang.StringIndexOutOfBoundsException: Range [33, 34) out of bounds for length 33
</dd>
<dt><strongfunc"<able "" =100%>tr><class="dleft"><code =f"&8227 IsParabolicQuadric/odevar class=">s<var )/td>td "tdright">( property )</td></tr></table></div>
<dd><p>Specifies which of the factor base methods should be used to do the "hard work". Currently pReturns: true or <p>
</dd>
</dl>
<p>For the use of the <strong class="pkg">GAP</p>returns if only if v ""><var> is a parabolic quadric./>
<div class="func"><table class="func" width="100%"><tr><td class="[0*() 0*(3, 0*(33,0Z(3) (3)0]]
<p>Returns: a list of two lists, where the first list contains the determined prime factors of <var class="Arg">n</var&;/pan> sjava.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 109
<p>java.lang.StringIndexOutOfBoundsException: Range [70, 4) out of bounds for length 70
<p><code class="code">Factors(<var class="Arg">n</var>)</code> is equivalent to <code class="code">FactInt(<var class="Arg">n</var>:<var class="Arg">cheap</var>:=false, <var class="Arg">FactIntPartial</var>:=false)[1]</code>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; InfoFactInt</code></td><td class="tdright">( info class )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class<span class=GAPprompt>g<s> <pan class=""v: [,1,]Z()0<span>
<p>This Info class allows to monitor what happens during the factoring process.</p>
<p>If <code class="code">InfoLevel(InfoFactInt) [ Z()^0, 0Z(2) Z2^,0Z2 java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
<p>Enter <code class="code">FactIntInfo(<var class="Arg">level</var>)</code> to set the <code class="code">InfoLevel</code> of <code class="code">InfoFactInt</code> to the java.lang.StringIndexOutOfBoundsException: Index 179 out of bounds for length 106
<pError lt;> notgenerate an element of <geom> called from
<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><acalled fromeval at line12 f *stdinjava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
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