<?xml version="1.0" encoding="UTF-8"?>
<?latexml class="article"?>
<?latexml package="latexml"?>
<?latexml RelaxNGSchema="LaTeXML"?>
<document xmlns="http://dlmf.nist.gov/LaTeXML">
<resource src="LaTeXML.css" type="text/css"/>
<resource src="ltx-article.css" type="text/css"/>
<section inlist="toc" xml:id="S1">
<tags>
<tag>1</tag>
<tag role="refnum">1</tag>
<tag role="typerefnum">§1</tag>
</tags>
<title><tag close=" ">1</tag>Basics</title>
<declare xml:id="S1.XMD1">
<text>integer</text>
</declare>
<declare xml:id="S1.XMD2">
<text>hatted</text>
</declare>
<declare xml:id="S1.XMD3">
<text>widehatted</text>
</declare>
<declare xml:id="S1.XMD4">
<text>ecks</text>
</declare>
<declare xml:id="S1.XMD5">
<text>ecksprime</text>
</declare>
<declare xml:id="S1.XMD6">
<text>ecksindexed</text>
</declare>
<declare xml:id="S1.XMD7">
<text>ecksone</text>
</declare>
<declare xml:id="S1.XMD8">
<text>eckshat</text>
</declare>
<declare xml:id="S1.XMD9">
<text>why</text>
</declare>
<para xml:id="S1.p1">
<equation xml:id="S1.Ex1">
<Math mode="display" tex="x,x^{\prime},x_{1},x_{n},x_{2n-1},\hat{x},\widehat{x},\mathbf{x}" text="list@(x, x ^ prime, x _ 1, x _ n, x _ (2 * n - 1), hat@(x), widehat@(x), x)" xml:id="S1.Ex1.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S1.Ex1.m1.4"/>
<XMRef idref="S1.Ex1.m1.5"/>
<XMRef idref="S1.Ex1.m1.6"/>
<XMRef idref="S1.Ex1.m1.7"/>
<XMRef idref="S1.Ex1.m1.8"/>
<XMRef idref="S1.Ex1.m1.9"/>
<XMRef idref="S1.Ex1.m1.10"/>
<XMRef idref="S1.Ex1.m1.11"/>
</XMApp>
<XMWrap>
<XMTok decl_id="S1.XMD4" font="italic" role="ID" xml:id="S1.Ex1.m1.4">x</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMApp decl_id="S1.XMD5" role="ID" xml:id="S1.Ex1.m1.5">
<XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">x</XMTok>
<XMTok fontsize="70%" name="prime" role="SUPOP">′</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp decl_id="S1.XMD7" role="ID" xml:id="S1.Ex1.m1.6">
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">x</XMTok>
<XMTok fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S1.Ex1.m1.7">
<XMApp>
<XMTok decl_id="S1.XMD6"/>
<XMRef idref="S1.Ex1.m1.1"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">x</XMTok>
<XMTok decl_id="S1.XMD1" font="italic" fontsize="70%" role="ID" xml:id="S1.Ex1.m1.1">n</XMTok>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S1.Ex1.m1.8">
<XMApp>
<XMTok decl_id="S1.XMD6"/>
<XMRef idref="S1.Ex1.m1.2"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">x</XMTok>
<XMApp xml:id="S1.Ex1.m1.2">
<XMTok fontsize="70%" meaning="minus" role="ADDOP">-</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
<XMTok decl_id="S1.XMD1" font="italic" fontsize="70%" role="ID">n</XMTok>
</XMApp>
<XMTok fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMApp decl_id="S1.XMD8" role="ID" xml:id="S1.Ex1.m1.9">
<XMTok name="hat" role="OVERACCENT" stretchy="false">^</XMTok>
<XMTok font="italic" role="UNKNOWN">x</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp role="ID" xml:id="S1.Ex1.m1.10">
<XMTok decl_id="S1.XMD3" name="widehat" role="OVERACCENT">^</XMTok>
<XMTok decl_id="S1.XMD4" font="italic" role="ID" xml:id="S1.Ex1.m1.3">x</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMTok font="bold" role="UNKNOWN" xml:id="S1.Ex1.m1.11">x</XMTok>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S1.Ex2">
<Math mode="display" tex="y,y^{\prime},y_{1},y_{n},y_{2n-1},\hat{y},\widehat{y}" text="list@(y, y ^ prime, y _ 1, y _ n, y _ (2 * n - 1), hat@(y), widehat@(y))" xml:id="S1.Ex2.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S1.Ex2.m1.3"/>
<XMRef idref="S1.Ex2.m1.6"/>
<XMRef idref="S1.Ex2.m1.7"/>
<XMRef idref="S1.Ex2.m1.8"/>
<XMRef idref="S1.Ex2.m1.9"/>
<XMRef idref="S1.Ex2.m1.4"/>
<XMRef idref="S1.Ex2.m1.5"/>
</XMApp>
<XMWrap>
<XMTok decl_id="S1.XMD9" font="italic" role="ID" xml:id="S1.Ex2.m1.3">y</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S1.Ex2.m1.6">
<XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
<XMTok decl_id="S1.XMD9" font="italic" role="ID">y</XMTok>
<XMTok fontsize="70%" name="prime" role="SUPOP">′</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S1.Ex2.m1.7">
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok decl_id="S1.XMD9" font="italic" role="ID">y</XMTok>
<XMTok fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S1.Ex2.m1.8">
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok decl_id="S1.XMD9" font="italic" role="ID">y</XMTok>
<XMTok decl_id="S1.XMD1" font="italic" fontsize="70%" role="ID">n</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S1.Ex2.m1.9">
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok decl_id="S1.XMD9" font="italic" role="ID">y</XMTok>
<XMApp>
<XMTok fontsize="70%" meaning="minus" role="ADDOP">-</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
<XMTok decl_id="S1.XMD1" font="italic" fontsize="70%" role="ID">n</XMTok>
</XMApp>
<XMTok fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp role="ID" xml:id="S1.Ex2.m1.4">
<XMTok decl_id="S1.XMD2" name="hat" role="OVERACCENT" stretchy="false">^</XMTok>
<XMTok decl_id="S1.XMD9" font="italic" role="ID" xml:id="S1.Ex2.m1.2">y</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp role="ID" xml:id="S1.Ex2.m1.5">
<XMTok decl_id="S1.XMD3" name="widehat" role="OVERACCENT">^</XMTok>
<XMTok decl_id="S1.XMD9" font="italic" role="ID" xml:id="S1.Ex2.m1.1">y</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S2">
<tags>
<tag>2</tag>
<tag role="refnum">2</tag>
<tag role="typerefnum">§2</tag>
</tags>
<title><tag close=" ">2</tag>WildCards</title>
<declare xml:id="S2.XMD1">
<text>queue-zero</text>
</declare>
<declare xml:id="S2.XMD2">
<text>queue-one</text>
</declare>
<declare xml:id="S2.XMD3">
<text>queue-two</text>
</declare>
<declare xml:id="S2.XMD4">
<text>eff-zero</text>
</declare>
<declare xml:id="S2.XMD5">
<text>eff-one</text>
</declare>
<declare xml:id="S2.XMD6">
<text>eff-two</text>
</declare>
<declare xml:id="S2.XMD7">
<text>constant</text>
</declare>
<declare xml:id="S2.XMD8">
<text>functionalized</text>
</declare>
<declare xml:id="S2.XMD9">
<text>gee-zero</text>
</declare>
<declare xml:id="S2.XMD10">
<text>gee-one</text>
</declare>
<para xml:id="S2.p1">
<equation xml:id="S2.Ex3">
<Math mode="display" tex="q,q_{a},q_{a,b},\mbox{ but accidentally }q_{a+b}" text="list@(q, q _ a, q _ (list@(a, b)), [ but accidentally ] * q _ (a + b))" xml:id="S2.Ex3.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S2.Ex3.m1.5"/>
<XMRef idref="S2.Ex3.m1.6"/>
<XMRef idref="S2.Ex3.m1.7"/>
<XMRef idref="S2.Ex3.m1.8"/>
</XMApp>
<XMWrap>
<XMTok decl_id="S2.XMD1" font="italic" role="ID" xml:id="S2.Ex3.m1.5">q</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S2.Ex3.m1.6">
<XMApp>
<XMTok decl_id="S2.XMD2"/>
<XMRef idref="S2.Ex3.m1.3"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">q</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S2.Ex3.m1.3">a</XMTok>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S2.Ex3.m1.7">
<XMApp>
<XMTok decl_id="S2.XMD3"/>
<XMRef idref="S2.Ex3.m1.1"/>
<XMRef idref="S2.Ex3.m1.2"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">q</XMTok>
<XMWrap>
<XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S2.Ex3.m1.1">a</XMTok>
<XMTok fontsize="70%" role="PUNCT">,</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S2.Ex3.m1.2">b</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S2.Ex3.m1.8">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMText> but accidentally </XMText>
<XMDual role="ID">
<XMApp>
<XMTok decl_id="S2.XMD2"/>
<XMRef idref="S2.Ex3.m1.4"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">q</XMTok>
<XMApp xml:id="S2.Ex3.m1.4">
<XMTok fontsize="70%" meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN">a</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN">b</XMTok>
</XMApp>
</XMApp>
</XMDual>
</XMApp>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S2.Ex4">
<Math mode="display" tex="f,f(a),f(q),f(a,b),\mbox{ but }f(a+b)" text="list@(f, f@(a), f@(q), f@(a, b), [ but ] * f * (a + b))" xml:id="S2.Ex4.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S2.Ex4.m1.8"/>
<XMRef idref="S2.Ex4.m1.9"/>
<XMRef idref="S2.Ex4.m1.10"/>
<XMRef idref="S2.Ex4.m1.11"/>
<XMRef idref="S2.Ex4.m1.12"/>
</XMApp>
<XMWrap>
<XMTok decl_id="S2.XMD4" font="italic" role="ID" xml:id="S2.Ex4.m1.8">f</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMDual xml:id="S2.Ex4.m1.9">
<XMApp>
<XMRef idref="S2.Ex4.m1.1"/>
<XMRef idref="S2.Ex4.m1.2"/>
</XMApp>
<XMApp>
<XMTok decl_id="S2.XMD5" font="italic" role="FUNCTION" xml:id="S2.Ex4.m1.1">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S2.Ex4.m1.2">a</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual xml:id="S2.Ex4.m1.10">
<XMApp>
<XMRef idref="S2.Ex4.m1.3"/>
<XMRef idref="S2.Ex4.m1.4"/>
</XMApp>
<XMApp>
<XMTok decl_id="S2.XMD5" font="italic" role="FUNCTION" xml:id="S2.Ex4.m1.3">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok decl_id="S2.XMD1" font="italic" role="ID" xml:id="S2.Ex4.m1.4">q</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual xml:id="S2.Ex4.m1.11">
<XMApp>
<XMRef idref="S2.Ex4.m1.5"/>
<XMRef idref="S2.Ex4.m1.6"/>
<XMRef idref="S2.Ex4.m1.7"/>
</XMApp>
<XMApp>
<XMTok decl_id="S2.XMD6" font="italic" role="FUNCTION" xml:id="S2.Ex4.m1.5">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S2.Ex4.m1.6">a</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S2.Ex4.m1.7">b</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S2.Ex4.m1.12">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMText> but </XMText>
<XMTok decl_id="S2.XMD4" font="italic" role="ID">f</XMTok>
<XMDual>
<XMRef idref="S2.Ex4.m1.12.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S2.Ex4.m1.12.1">
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
</XMApp>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S2.Ex5">
<Math mode="display" tex="g,g(a),g(a)(b)" text="list@(g, g * a, (g * a)@(b))" xml:id="S2.Ex5.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S2.Ex5.m1.9"/>
<XMRef idref="S2.Ex5.m1.10"/>
<XMRef idref="S2.Ex5.m1.11"/>
</XMApp>
<XMWrap>
<XMTok decl_id="S2.XMD9" font="italic" role="ID" xml:id="S2.Ex5.m1.9">g</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="FUNCTION" xml:id="S2.Ex5.m1.10">
<XMApp>
<XMTok decl_id="S2.XMD10"/>
<XMRef idref="S2.Ex5.m1.1"/>
<XMRef idref="S2.Ex5.m1.2"/>
<XMRef idref="S2.Ex5.m1.3"/>
</XMApp>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="UNKNOWN">g</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false" xml:id="S2.Ex5.m1.1">(</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S2.Ex5.m1.2">a</XMTok>
<XMTok role="CLOSE" stretchy="false" xml:id="S2.Ex5.m1.3">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual xml:id="S2.Ex5.m1.11">
<XMApp>
<XMRef idref="S2.Ex5.m1.7"/>
<XMRef idref="S2.Ex5.m1.8"/>
</XMApp>
<XMApp>
<XMDual role="FUNCTION" xml:id="S2.Ex5.m1.7">
<XMApp>
<XMTok decl_id="S2.XMD10"/>
<XMRef idref="S2.Ex5.m1.4"/>
<XMRef idref="S2.Ex5.m1.5"/>
<XMRef idref="S2.Ex5.m1.6"/>
</XMApp>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="UNKNOWN">g</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false" xml:id="S2.Ex5.m1.4">(</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S2.Ex5.m1.5">a</XMTok>
<XMTok role="CLOSE" stretchy="false" xml:id="S2.Ex5.m1.6">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S2.Ex5.m1.8">b</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S2.Ex6">
<Math mode="display" tex="z(a+b),\widehat{z}(a)" text="list@(z * (a + b), (widehat@(z))@(a))" xml:id="S2.Ex6.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S2.Ex6.m1.4"/>
<XMRef idref="S2.Ex6.m1.5"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S2.Ex6.m1.4">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok decl_id="S2.XMD7" font="italic" role="ID">z</XMTok>
<XMDual>
<XMRef idref="S2.Ex6.m1.4.1"/>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S2.Ex6.m1.4.1">
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMDual>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMDual xml:id="S2.Ex6.m1.5">
<XMApp>
<XMRef idref="S2.Ex6.m1.2"/>
<XMRef idref="S2.Ex6.m1.3"/>
</XMApp>
<XMApp>
<XMApp role="FUNCTION" xml:id="S2.Ex6.m1.2">
<XMTok decl_id="S2.XMD8" name="widehat" role="OVERACCENT">^</XMTok>
<XMTok decl_id="S2.XMD7" font="italic" role="ID" xml:id="S2.Ex6.m1.1">z</XMTok>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S2.Ex6.m1.3">a</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S3">
<tags>
<tag>3</tag>
<tag role="refnum">3</tag>
<tag role="typerefnum">§3</tag>
</tags>
<title><tag close=" ">3</tag>Practical</title>
<declare xml:id="S3.XMD1">
<text>variable</text>
</declare>
<declare xml:id="S3.XMD2">
<text>integer</text>
</declare>
<declare xml:id="S3.XMD3">
<text>function</text>
</declare>
<declare xml:id="S3.XMD4">
<text>coefficient</text>
</declare>
<para xml:id="S3.p1">
<equation xml:id="S3.Ex7">
<Math mode="display" tex="f(x)=\sum_{i=0}^{\infty}f_{i}x^{i}" text="f@(x) = ((sum _ (i = 0)) ^ infinity)@(f _ i * x ^ i)" xml:id="S3.Ex7.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMDual>
<XMApp>
<XMRef idref="S3.Ex7.m1.2"/>
<XMRef idref="S3.Ex7.m1.3"/>
</XMApp>
<XMApp>
<XMTok decl_id="S3.XMD3" font="italic" role="FUNCTION" xml:id="S3.Ex7.m1.2">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok decl_id="S3.XMD1" font="italic" role="ID" xml:id="S3.Ex7.m1.3">x</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMApp>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="mid1"/>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="mid1"/>
<XMTok mathstyle="display" meaning="sum" role="SUMOP" scriptpos="mid">∑</XMTok>
<XMApp>
<XMTok fontsize="70%" meaning="equals" role="RELOP">=</XMTok>
<XMTok decl_id="S3.XMD2" font="italic" fontsize="70%" role="ID">i</XMTok>
<XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
</XMApp>
</XMApp>
<XMTok fontsize="70%" meaning="infinity" name="infty" role="ID">∞</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMDual role="ID">
<XMApp>
<XMTok decl_id="S3.XMD4"/>
<XMRef idref="S3.Ex7.m1.1"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">f</XMTok>
<XMTok decl_id="S3.XMD2" font="italic" fontsize="70%" role="ID" xml:id="S3.Ex7.m1.1">i</XMTok>
</XMApp>
</XMDual>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
<XMTok decl_id="S3.XMD1" font="italic" role="ID">x</XMTok>
<XMTok decl_id="S3.XMD2" font="italic" fontsize="70%" role="ID">i</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S4">
<tags>
<tag>4</tag>
<tag role="refnum">4</tag>
<tag role="typerefnum">§4</tag>
</tags>
<title><tag close=" ">4</tag>Impractical</title>
<declare xml:id="S4.XMD1">
<text>bafter</text>
</declare>
<declare xml:id="S4.XMD2">
<text>cafter</text>
</declare>
<para xml:id="S4.p1">
<equation xml:id="S4.Ex8">
<Math mode="display" tex="a,b,c,ab,bc,abc" text="list@(a, b, c, a * b, b * c, a * b * c)" xml:id="S4.Ex8.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S4.Ex8.m1.1"/>
<XMRef idref="S4.Ex8.m1.2"/>
<XMRef idref="S4.Ex8.m1.3"/>
<XMRef idref="S4.Ex8.m1.4"/>
<XMRef idref="S4.Ex8.m1.5"/>
<XMRef idref="S4.Ex8.m1.6"/>
</XMApp>
<XMWrap>
<XMTok font="italic" role="UNKNOWN" xml:id="S4.Ex8.m1.1">a</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S4.Ex8.m1.2">b</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S4.Ex8.m1.3">c</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S4.Ex8.m1.4">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok decl_id="S4.XMD1" font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S4.Ex8.m1.5">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
<XMTok font="italic" role="UNKNOWN">c</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S4.Ex8.m1.6">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok decl_id="S4.XMD1" font="italic" role="UNKNOWN">b</XMTok>
<XMTok decl_id="S4.XMD2" font="italic" role="UNKNOWN">c</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<declare xml:id="S4.XMD3">
<text>transformation</text>
</declare>
<declare xml:id="S4.XMD4">
<text>sign</text>
</declare>
<equation xml:id="S4.Ex9">
<Math mode="display" tex="\varepsilon,\varepsilon_{1},\mathcal{T}_{\varepsilon},\mathcal{T}_{\varepsilon% _{1}},\mathcal{T}_{\varepsilon_{1},\varepsilon_{2},\varepsilon_{3}}" text="list@(varepsilon, varepsilon _ 1, T _ varepsilon, T _ varepsilon _ 1, T _ (list@(varepsilon _ 1, varepsilon _ 2, varepsilon _ 3)))" xml:id="S4.Ex9.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S4.Ex9.m1.9"/>
<XMRef idref="S4.Ex9.m1.10"/>
<XMRef idref="S4.Ex9.m1.11"/>
<XMRef idref="S4.Ex9.m1.12"/>
<XMRef idref="S4.Ex9.m1.13"/>
</XMApp>
<XMWrap>
<XMTok font="italic" name="varepsilon" role="UNKNOWN" xml:id="S4.Ex9.m1.9">ε</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S4.Ex9.m1.10">
<XMApp>
<XMTok decl_id="S4.XMD4"/>
<XMRef idref="S4.Ex9.m1.1"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="70%" meaning="1" role="NUMBER" xml:id="S4.Ex9.m1.1">1</XMTok>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S4.Ex9.m1.11">
<XMApp>
<XMTok decl_id="S4.XMD3"/>
<XMRef idref="S4.Ex9.m1.6"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="caligraphic" role="UNKNOWN">T</XMTok>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN" xml:id="S4.Ex9.m1.6">ε</XMTok>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S4.Ex9.m1.12">
<XMApp>
<XMTok decl_id="S4.XMD3"/>
<XMRef idref="S4.Ex9.m1.7"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="caligraphic" role="UNKNOWN">T</XMTok>
<XMDual role="ID" xml:id="S4.Ex9.m1.7">
<XMApp>
<XMTok decl_id="S4.XMD4"/>
<XMRef idref="S4.Ex9.m1.2"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="50%" meaning="1" role="NUMBER" xml:id="S4.Ex9.m1.2">1</XMTok>
</XMApp>
</XMDual>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S4.Ex9.m1.13">
<XMApp>
<XMTok decl_id="S4.XMD3"/>
<XMRef idref="S4.Ex9.m1.8"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="caligraphic" role="UNKNOWN">T</XMTok>
<XMDual xml:id="S4.Ex9.m1.8">
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S4.Ex9.m1.8.1"/>
<XMRef idref="S4.Ex9.m1.8.2"/>
<XMRef idref="S4.Ex9.m1.8.3"/>
</XMApp>
<XMWrap>
<XMDual role="ID" xml:id="S4.Ex9.m1.8.1">
<XMApp>
<XMTok decl_id="S4.XMD4"/>
<XMRef idref="S4.Ex9.m1.3"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="50%" meaning="1" role="NUMBER" xml:id="S4.Ex9.m1.3">1</XMTok>
</XMApp>
</XMDual>
<XMTok fontsize="70%" role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S4.Ex9.m1.8.2">
<XMApp>
<XMTok decl_id="S4.XMD4"/>
<XMRef idref="S4.Ex9.m1.4"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="50%" meaning="2" role="NUMBER" xml:id="S4.Ex9.m1.4">2</XMTok>
</XMApp>
</XMDual>
<XMTok fontsize="70%" role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S4.Ex9.m1.8.3">
<XMApp>
<XMTok decl_id="S4.XMD4"/>
<XMRef idref="S4.Ex9.m1.5"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="50%" meaning="3" role="NUMBER" xml:id="S4.Ex9.m1.5">3</XMTok>
</XMApp>
</XMDual>
</XMWrap>
</XMDual>
</XMApp>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S5">
<tags>
<tag>5</tag>
<tag role="refnum">5</tag>
<tag role="typerefnum">§5</tag>
</tags>
<title><tag close=" ">5</tag>Declaration order</title>
<declare xml:id="S5.XMD1">
<text>sign</text>
</declare>
<declare xml:id="S5.XMD2">
<text>transformation</text>
</declare>
<para xml:id="S5.p1">
<equation xml:id="S5.Ex10">
<Math mode="display" tex="\varepsilon,\varepsilon_{1},\mathcal{T}_{\varepsilon},\mathcal{T}_{\varepsilon% _{1}},\mathcal{T}_{\varepsilon_{1},\varepsilon_{2},\varepsilon_{3}}" text="list@(varepsilon, varepsilon _ 1, T _ varepsilon, T _ varepsilon _ 1, T _ (list@(varepsilon _ 1, varepsilon _ 2, varepsilon _ 3)))" xml:id="S5.Ex10.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S5.Ex10.m1.5"/>
<XMRef idref="S5.Ex10.m1.6"/>
<XMRef idref="S5.Ex10.m1.7"/>
<XMRef idref="S5.Ex10.m1.8"/>
<XMRef idref="S5.Ex10.m1.9"/>
</XMApp>
<XMWrap>
<XMTok font="italic" name="varepsilon" role="UNKNOWN" xml:id="S5.Ex10.m1.5">ε</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S5.Ex10.m1.6">
<XMApp>
<XMTok decl_id="S5.XMD1"/>
<XMRef idref="S5.Ex10.m1.4"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="70%" meaning="1" role="NUMBER" xml:id="S5.Ex10.m1.4">1</XMTok>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S5.Ex10.m1.7">
<XMApp>
<XMTok decl_id="S5.XMD2"/>
<XMRef idref="S5.Ex10.m1.1"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="caligraphic" role="UNKNOWN">T</XMTok>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN" xml:id="S5.Ex10.m1.1">ε</XMTok>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S5.Ex10.m1.8">
<XMApp>
<XMTok decl_id="S5.XMD2"/>
<XMRef idref="S5.Ex10.m1.2"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="caligraphic" role="UNKNOWN">T</XMTok>
<XMDual role="ID" xml:id="S5.Ex10.m1.2">
<XMApp>
<XMTok decl_id="S5.XMD1"/>
<XMRef idref="S5.Ex10.m1.2.1"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="50%" meaning="1" role="NUMBER" xml:id="S5.Ex10.m1.2.1">1</XMTok>
</XMApp>
</XMDual>
</XMApp>
</XMDual>
<XMTok role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S5.Ex10.m1.9">
<XMApp>
<XMTok decl_id="S5.XMD2"/>
<XMRef idref="S5.Ex10.m1.3"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="caligraphic" role="UNKNOWN">T</XMTok>
<XMDual xml:id="S5.Ex10.m1.3">
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S5.Ex10.m1.3.4"/>
<XMRef idref="S5.Ex10.m1.3.5"/>
<XMRef idref="S5.Ex10.m1.3.6"/>
</XMApp>
<XMWrap>
<XMDual role="ID" xml:id="S5.Ex10.m1.3.4">
<XMApp>
<XMTok decl_id="S5.XMD1"/>
<XMRef idref="S5.Ex10.m1.3.1"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="50%" meaning="1" role="NUMBER" xml:id="S5.Ex10.m1.3.1">1</XMTok>
</XMApp>
</XMDual>
<XMTok fontsize="70%" role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S5.Ex10.m1.3.5">
<XMApp>
<XMTok decl_id="S5.XMD1"/>
<XMRef idref="S5.Ex10.m1.3.2"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="50%" meaning="2" role="NUMBER" xml:id="S5.Ex10.m1.3.2">2</XMTok>
</XMApp>
</XMDual>
<XMTok fontsize="70%" role="PUNCT">,</XMTok>
<XMDual role="ID" xml:id="S5.Ex10.m1.3.6">
<XMApp>
<XMTok decl_id="S5.XMD1"/>
<XMRef idref="S5.Ex10.m1.3.3"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok font="italic" fontsize="70%" name="varepsilon" role="UNKNOWN">ε</XMTok>
<XMTok fontsize="50%" meaning="3" role="NUMBER" xml:id="S5.Ex10.m1.3.3">3</XMTok>
</XMApp>
</XMDual>
</XMWrap>
</XMDual>
</XMApp>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S6">
<tags>
<tag>6</tag>
<tag role="refnum">6</tag>
<tag role="typerefnum">§6</tag>
</tags>
<title><tag close=" ">6</tag>Notations?</title>
<declare xml:id="S6.XMD1">
<text>Baz</text>
</declare>
<declare xml:id="S6.XMD2">
<text>Plus</text>
</declare>
<declare xml:id="S6.XMD3">
<text>Foo</text>
</declare>
<declare xml:id="S6.XMD4">
<text>Oddball</text>
</declare>
<declare xml:id="S6.XMD5">
<text>Weird</text>
</declare>
<para xml:id="S6.p1">
<equation xml:id="S6.Ex11">
<Math content-tex="a\plus b;\baz,\foo{x},\foo{j}" mode="display" tex="a+b;\mathbf{baz},\mathbf{foo}{x},\mathbf{foo}{j}" text="list@(a + b, foo, foo * x, foo * j)" xml:id="S6.Ex11.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S6.Ex11.m1.2"/>
<XMRef idref="S6.Ex11.m1.1"/>
<XMRef idref="S6.Ex11.m1.3"/>
<XMRef idref="S6.Ex11.m1.4"/>
</XMApp>
<XMWrap>
<XMApp xml:id="S6.Ex11.m1.2">
<XMTok decl_id="S6.XMD2" name="plus" role="ADDOP">+</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
<XMTok role="PUNCT">;</XMTok>
<XMTok decl_id="S6.XMD1" font="bold" meaning="foo" name="baz" role="UNKNOWN" xml:id="S6.Ex11.m1.1">baz</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S6.Ex11.m1.3">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok decl_id="S6.XMD3" font="bold" meaning="foo" role="UNKNOWN">foo</XMTok>
<XMTok font="italic" role="UNKNOWN">x</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S6.Ex11.m1.4">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok decl_id="S6.XMD3" font="bold" meaning="foo" role="UNKNOWN">foo</XMTok>
<XMTok font="italic" role="UNKNOWN">j</XMTok>
</XMApp>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S6.Ex12">
<Math content-tex="\oddball{a}{j};\oddball{abc}{j}" mode="display" tex="\left|\left(a\right)_{j}\right|;\left|\left(abc\right)_{j}\right|" text="list@(oddball@(a, j), oddball@(a * b * c, j))" xml:id="S6.Ex12.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S6.Ex12.m1.7"/>
<XMRef idref="S6.Ex12.m1.8"/>
</XMApp>
<XMWrap>
<XMDual xml:id="S6.Ex12.m1.7">
<XMApp>
<XMTok decl_id="S6.XMD4" name="oddball" role="UNKNOWN"/>
<XMRef idref="S6.Ex12.m1.1"/>
<XMRef idref="S6.Ex12.m1.2"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">|</XMTok>
<XMApp xml:id="S6.Ex12.m1.5">
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMWrap>
<XMTok role="OPEN" stretchy="true">(</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S6.Ex12.m1.1">a</XMTok>
<XMTok role="CLOSE" stretchy="true">)</XMTok>
</XMWrap>
<XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S6.Ex12.m1.2">j</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">|</XMTok>
</XMWrap>
</XMDual>
<XMTok role="PUNCT">;</XMTok>
<XMDual xml:id="S6.Ex12.m1.8">
<XMApp>
<XMTok decl_id="S6.XMD4" name="oddball" role="UNKNOWN"/>
<XMRef idref="S6.Ex12.m1.3"/>
<XMRef idref="S6.Ex12.m1.4"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">|</XMTok>
<XMApp xml:id="S6.Ex12.m1.6">
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMWrap>
<XMTok role="OPEN" stretchy="true">(</XMTok>
<XMApp xml:id="S6.Ex12.m1.3">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
<XMTok font="italic" role="UNKNOWN">c</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">)</XMTok>
</XMWrap>
<XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S6.Ex12.m1.4">j</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">|</XMTok>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S6.Ex13">
<Math content-tex="\weird{a}{j};\weird{abc}{j}" mode="display" tex="\left(\left[a\right]_{j}\right);\left(\left[abc\right]_{j}\right)" text="list@(weird@(a, j), weird@(a * b * c, j))" xml:id="S6.Ex13.m1">
<XMath>
<XMDual>
<XMApp>
<XMTok meaning="list"/>
<XMRef idref="S6.Ex13.m1.7"/>
<XMRef idref="S6.Ex13.m1.8"/>
</XMApp>
<XMWrap>
<XMDual decl_id="S6.XMD5" xml:id="S6.Ex13.m1.7">
<XMApp>
<XMTok name="weird" role="UNKNOWN"/>
<XMRef idref="S6.Ex13.m1.1"/>
<XMRef idref="S6.Ex13.m1.2"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">(</XMTok>
<XMApp xml:id="S6.Ex13.m1.5">
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMWrap>
<XMTok role="OPEN" stretchy="true">[</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S6.Ex13.m1.1">a</XMTok>
<XMTok role="CLOSE" stretchy="true">]</XMTok>
</XMWrap>
<XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S6.Ex13.m1.2">j</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">)</XMTok>
</XMWrap>
</XMDual>
<XMTok role="PUNCT">;</XMTok>
<XMDual decl_id="S6.XMD5" xml:id="S6.Ex13.m1.8">
<XMApp>
<XMTok name="weird" role="UNKNOWN"/>
<XMRef idref="S6.Ex13.m1.3"/>
<XMRef idref="S6.Ex13.m1.4"/>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="true">(</XMTok>
<XMApp xml:id="S6.Ex13.m1.6">
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMWrap>
<XMTok role="OPEN" stretchy="true">[</XMTok>
<XMApp xml:id="S6.Ex13.m1.3">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
<XMTok font="italic" role="UNKNOWN">c</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">]</XMTok>
</XMWrap>
<XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S6.Ex13.m1.4">j</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="true">)</XMTok>
</XMWrap>
</XMDual>
</XMWrap>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
<section inlist="toc" xml:id="S7">
<tags>
<tag>7</tag>
<tag role="refnum">7</tag>
<tag role="typerefnum">§7</tag>
</tags>
<title><tag close=" ">7</tag>More detail</title>
<declare xml:id="S7.XMD1">
<tags>
<tag role="term"><Math mode="inline" tex="x" text="x" xml:id="S7.XMD1.m1">
<XMath>
<XMTok decl_id="S7.XMD1" font="italic" role="ID">x</XMTok>
</XMath>
</Math></tag>
<tag role="short">variable</tag>
</tags>
<text> a real variable</text>
</declare>
<declare xml:id="S7.XMD2">
<tags>
<tag role="term"><Math mode="inline" tex="i" text="i" xml:id="S7.XMD2.m1">
<XMath>
<XMTok decl_id="S7.XMD2" font="italic" role="ID">i</XMTok>
</XMath>
</Math></tag>
<tag role="short"> an integer variable</tag>
</tags>
<text> an integer variable</text>
</declare>
<declare xml:id="S7.XMD3">
<tags>
<tag role="term"><Math mode="inline" tex="f(x)" text="f@(x)" xml:id="S7.XMD3.m1">
<XMath>
<XMDual>
<XMApp>
<XMRef idref="S7.XMD3.m1.1"/>
<XMRef idref="S7.XMD3.m1.2"/>
</XMApp>
<XMApp>
<XMTok decl_id="S7.XMD3" font="italic" role="FUNCTION" xml:id="S7.XMD3.m1.1">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok decl_id="S7.XMD1" font="italic" role="ID" xml:id="S7.XMD3.m1.2">x</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMath>
</Math></tag>
<tag role="short">function</tag>
</tags>
<text> a function of reals</text>
</declare>
<declare xml:id="S7.XMD4">
<tags>
<tag role="term"><Math mode="inline" tex="f_{i}" text="f _ i" xml:id="S7.XMD4.m1">
<XMath>
<XMDual role="ID">
<XMApp>
<XMTok decl_id="S7.XMD4"/>
<XMRef idref="S7.XMD4.m1.1"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">f</XMTok>
<XMTok decl_id="S7.XMD2" font="italic" fontsize="70%" role="ID" xml:id="S7.XMD4.m1.1">i</XMTok>
</XMApp>
</XMDual>
</XMath>
</Math></tag>
<tag role="short">coefficient</tag>
</tags>
<text> expansion coefficient</text>
</declare>
<para xml:id="S7.p1">
<equation xml:id="S7.Ex14">
<Math mode="display" tex="f(x)=\sum_{i=0}^{\infty}f_{i}x^{i}" text="f@(x) = ((sum _ (i = 0)) ^ infinity)@(f _ i * x ^ i)" xml:id="S7.Ex14.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMDual>
<XMApp>
<XMRef idref="S7.Ex14.m1.2"/>
<XMRef idref="S7.Ex14.m1.3"/>
</XMApp>
<XMApp>
<XMTok decl_id="S7.XMD3" font="italic" role="FUNCTION" xml:id="S7.Ex14.m1.2">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok decl_id="S7.XMD1" font="italic" role="ID" xml:id="S7.Ex14.m1.3">x</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMApp>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="mid1"/>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="mid1"/>
<XMTok mathstyle="display" meaning="sum" role="SUMOP" scriptpos="mid">∑</XMTok>
<XMApp>
<XMTok fontsize="70%" meaning="equals" role="RELOP">=</XMTok>
<XMTok decl_id="S7.XMD2" font="italic" fontsize="70%" role="ID">i</XMTok>
<XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
</XMApp>
</XMApp>
<XMTok fontsize="70%" meaning="infinity" name="infty" role="ID">∞</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMDual role="ID">
<XMApp>
<XMTok decl_id="S7.XMD4"/>
<XMRef idref="S7.Ex14.m1.1"/>
</XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">f</XMTok>
<XMTok decl_id="S7.XMD2" font="italic" fontsize="70%" role="ID" xml:id="S7.Ex14.m1.1">i</XMTok>
</XMApp>
</XMDual>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
<XMTok decl_id="S7.XMD1" font="italic" role="ID">x</XMTok>
<XMTok decl_id="S7.XMD2" font="italic" fontsize="70%" role="ID">i</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</Math>
</equation>
</para>
</section>
</document>