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<div class="ChapSects"><a href="chap35_mj.html#X7B71D3EA7B30ADAB">35 <span class="Heading"> Arrays and Pseudo lists</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap35_mj.html#X7CFDEEC07F15CF82">35.1 <span class="Heading">  </span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X81B7CDF487BC322B">35.1-1 Array</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X7C8BACC87E7CB7A8">35.1-2 PermuteArray</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X82573BFC835FC676">35.1-3 ArrayDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X82CFCED3782CE80C">35.1-4 ArrayDimensions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X81EBEEDA7C5E2062">35.1-5 ArraySum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X7C1AC8B77E8859C7">35.1-6 ArrayValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X8169303B7C5F779F">35.1-7 ArrayValueFunctions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X7A64A28E84797139">35.1-8 ArrayAssign</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X79A3E1968330BB3E">35.1-9 ArrayAssignFunctions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X86F867787E75FF68">35.1-10 ArrayIterate</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X869B32CC80D03046">35.1-11 BinaryArrayToTextFile</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X7DE8BB8D86A2D34B">35.1-12 FrameArray</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X824B37627D6B979B">35.1-13 UnframeArray</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X795EC9D67E34DAB0">35.1-14 Add</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X79E31DB27C82D6E1">35.1-15 Append</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap35_mj.html#X8308C3198094AA55">35.1-16 ListToPseudoList</a></span>
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<h3>35 <span class="Heading"> Arrays and Pseudo lists</span></h3>

<p><a id="X7CFDEEC07F15CF82" name="X7CFDEEC07F15CF82"></a></p>

<h4>35.1 <span class="Heading">  </span></h4>

<p><a id="X81B7CDF487BC322B" name="X81B7CDF487BC322B"></a></p>

<h5>35.1-1 Array</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Array</code>( <var class="Arg">A</var>, <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> and a function <span class="SimpleMath">\(f\)</span>. It returns the the array obtained by applying <span class="SimpleMath">\(f\)</span> to each entry of <span class="SimpleMath">\(A\)</span> (and leaves <span class="SimpleMath">\(A\)</span> unchanged).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap2.html">1</a></span> , <span class="URL"><a href="../tutorial/chap10.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPeripheral.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCubical.html">4</a></span> </p>

<p><a id="X7C8BACC87E7CB7A8" name="X7C8BACC87E7CB7A8"></a></p>

<h5>35.1-2 PermuteArray</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PermuteArray</code>( <var class="Arg">A</var>, <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> of dimension <span class="SimpleMath">\(d\)</span> and a permutation <span class="SimpleMath">\(f\)</span> of degree at most <span class="SimpleMath">\(d\)</span>. It returns the array <span class="SimpleMath">\(B\)</span> defined by <span class="SimpleMath">\(B[i1][i2]...[id] = A[f(i1)][f(i2)]...A[f(id)]\)</span> (and leaves <span class="SimpleMath">\(A\)</span> unchanged).</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X82573BFC835FC676" name="X82573BFC835FC676"></a></p>

<h5>35.1-3 ArrayDimension</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayDimension</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> and returns its dimension.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X82CFCED3782CE80C" name="X82CFCED3782CE80C"></a></p>

<h5>35.1-4 ArrayDimensions</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayDimensions</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> and returns its dimensions.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X81EBEEDA7C5E2062" name="X81EBEEDA7C5E2062"></a></p>

<h5>35.1-5 ArraySum</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArraySum</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> and returns the sum of its entries.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7C1AC8B77E8859C7" name="X7C1AC8B77E8859C7"></a></p>

<h5>35.1-6 ArrayValue</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayValue</code>( <var class="Arg">A</var>, <var class="Arg">x</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> and a coordinate vector <span class="SimpleMath">\(x\)</span>. It returns the value of the entry in <span class="SimpleMath">\(A\)</span> with coordinate <span class="SimpleMath">\(x\)</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X8169303B7C5F779F" name="X8169303B7C5F779F"></a></p>

<h5>35.1-7 ArrayValueFunctions</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayValueFunctions</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a positive integer <span class="SimpleMath">\(d\)</span> and returns an efficient version of the function ArrayValue for arrays of dimension <span class="SimpleMath">\(d\)</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7A64A28E84797139" name="X7A64A28E84797139"></a></p>

<h5>35.1-8 ArrayAssign</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayAssign</code>( <var class="Arg">A</var>, <var class="Arg">x</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> and a coordinate vector <span class="SimpleMath">\(x\)</span> and an integer <span class="SimpleMath">\(n\)</span>. It sets the entry of <span class="SimpleMath">\(A\)</span> with coordinate <span class="SimpleMath">\(x\)</span> equal to <span class="SimpleMath">\(n\)</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X79A3E1968330BB3E" name="X79A3E1968330BB3E"></a></p>

<h5>35.1-9 ArrayAssignFunctions</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayAssignFunctions</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a positive integer <span class="SimpleMath">\(d\)</span> and returns an efficient version of the function ArrayAssign for arrays of dimension <span class="SimpleMath">\(d\)</span>.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X86F867787E75FF68" name="X86F867787E75FF68"></a></p>

<h5>35.1-10 ArrayIterate</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ArrayIterate</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a positive integer <span class="SimpleMath">\(d\)</span> and returns a function ArrayIt(Dimensions,f). This function inputs a list Dimensions of <span class="SimpleMath">\(d\)</span> positive integers and also a function <span class="SimpleMath">\(f(x)\)</span>. It applies the function <span class="SimpleMath">\(f(x)\)</span> to each integer list <span class="SimpleMath">\(x\)</span> of length <span class="SimpleMath">\(d\)</span> with entries <span class="SimpleMath">\(x[i]\)</span> in the range [1..Dimension[i]].</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X869B32CC80D03046" name="X869B32CC80D03046"></a></p>

<h5>35.1-11 BinaryArrayToTextFile</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ BinaryArrayToTextFile</code>( <var class="Arg">file</var>, <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a string containing the address of a file, and an array <span class="SimpleMath">\(A\)</span> of 0s and 1s. The array represents a pure cubical complex. A representation of this complex is written to the file in a format that can be read by the CAPD (Computer Assisted Proofs in Dynamics) software developed by Marian Mrozek and others.</p>

<p>The second input <span class="SimpleMath">\(A\)</span> can also be a pure cubical complex.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X7DE8BB8D86A2D34B" name="X7DE8BB8D86A2D34B"></a></p>

<h5>35.1-12 FrameArray</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FrameArray</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> and returns the array obtained by appending a 0 to the beginning and end of each "row" of the array.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutPeripheral.html">1</a></span> </p>

<p><a id="X824B37627D6B979B" name="X824B37627D6B979B"></a></p>

<h5>35.1-13 UnframeArray</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UnframeArray</code>( <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an array <span class="SimpleMath">\(A\)</span> and returns the array obtained by removing the first and last entry in each "row" of the array.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X795EC9D67E34DAB0" name="X795EC9D67E34DAB0"></a></p>

<h5>35.1-14 Add</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Add</code>( <var class="Arg">L</var>, <var class="Arg">x</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <span class="SimpleMath">\(L\)</span> be a pseudo list of length <span class="SimpleMath">\(n\)</span>, and <span class="SimpleMath">\(x\)</span> an object compatible with the entries in <span class="SimpleMath">\(L\)</span>. If <span class="SimpleMath">\(x\)</span> is not in <span class="SimpleMath">\(L\)</span> then this operation converts <span class="SimpleMath">\(L\)</span> into a pseudo list of length n+1 by adding <span class="SimpleMath">\(x\)</span> as the final entry. If <span class="SimpleMath">\(x\)</span> is in <span class="SimpleMath">\(L\)</span> the operation has no effect on <span class="SimpleMath">\(L\)</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap4.html">1</a></span> , <span class="URL"><a href="../tutorial/chap5.html">2</a></span> , <span class="URL"><a href="../tutorial/chap10.html">3</a></span> , <span class="URL"><a href="../tutorial/chap12.html">4</a></span> , <span class="URL"><a href="../tutorial/chap13.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutBogomolov.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles2.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutQuandles.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutquasi.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutRandomComplexes.html">10</a></span> </p>

<p><a id="X79E31DB27C82D6E1" name="X79E31DB27C82D6E1"></a></p>

<h5>35.1-15 Append</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Append</code>( <var class="Arg">L</var>, <var class="Arg">K</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Let <span class="SimpleMath">\(L\)</span> be a pseudo list and <span class="SimpleMath">\(K\)</span> a list whose objects are compatible with those in <span class="SimpleMath">\(L\)</span>. This operation applies Add(L,x) for each x in <span class="SimpleMath">\(K\)</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap12.html">1</a></span> , <span class="URL"><a href="../tutorial/chap13.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutBogomolov.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutParallel.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTensorSquare.html">5</a></span> </p>

<p><a id="X8308C3198094AA55" name="X8308C3198094AA55"></a></p>

<h5>35.1-16 ListToPseudoList</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ListToPseudoList</code>( <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a list <span class="SimpleMath">\(L\)</span> and returns the pseudo list representation of <span class="SimpleMath">\(L\)</span>.</p>

<p><strong class="button">Examples:</strong></p>


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