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<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>Basic Functions</title>
<para xml:id="S1.p1">
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<equation xml:id="S1.Ex3">
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<XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
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</equation>
<equation xml:id="S1.Ex4">
<Math mode="display" tex="\sin f(a)" text="sine@(f@(a))" xml:id="S1.Ex4.m1">
<XMath>
<XMApp>
<XMTok meaning="sine" role="TRIGFUNCTION">sin</XMTok>
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</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>Trigonometric functions</title>
<para xml:id="S2.p1">
<equation xml:id="S2.Ex5">
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</equation>
<equation xml:id="S2.Ex6">
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<equation xml:id="S2.Ex7">
<Math mode="display" tex="\sin 2\pi\neq\log 2x^{2}" text="sine@(2 * pi) not-equals logarithm@(2 * x ^ 2)" xml:id="S2.Ex7.m1">
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<XMTok meaning="not-equals" name="neq" role="RELOP">≠</XMTok>
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<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
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<XMTok meaning="times" role="MULOP"></XMTok>
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<XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
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<equation xml:id="S2.Ex8">
<Math mode="display" tex="\log\sin x" text="logarithm@(sine@(x))" xml:id="S2.Ex8.m1">
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<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
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<XMTok meaning="sine" role="TRIGFUNCTION">sin</XMTok>
<XMTok font="italic" role="ID">x</XMTok>
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<equation xml:id="S2.Ex9">
<Math mode="display" tex="\sin\log x" text="sine@(logarithm@(x))" xml:id="S2.Ex9.m1">
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<XMTok meaning="sine" role="TRIGFUNCTION">sin</XMTok>
<XMApp>
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMTok font="italic" role="ID">x</XMTok>
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<equation xml:id="S2.Ex10">
<Math mode="display" tex="\nabla\log x" text="(nabla@(logarithm))@(x)" xml:id="S2.Ex10.m1">
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<XMApp>
<XMTok name="nabla" role="OPERATOR">∇</XMTok>
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<XMTok font="italic" role="ID">x</XMTok>
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</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>Probability functions</title>
<para xml:id="S3.p1">
<equation xml:id="S3.Ex11">
<Math mode="display" tex="p(x,y|\Theta)" text="p@(x, conditional@(y, Theta))" xml:id="S3.Ex11.m1">
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<XMTok font="italic" role="FUNCTION" xml:id="S3.Ex11.m1.1">p</XMTok>
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<XMTok role="OPEN" stretchy="false">(</XMTok>
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<XMTok meaning="conditional" role="MODIFIEROP" stretchy="false">|</XMTok>
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<XMTok name="Theta" role="UNKNOWN">Θ</XMTok>
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<XMTok role="CLOSE" stretchy="false">)</XMTok>
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<Math mode="display" tex="p(y|x,\Theta)" text="p@(conditional@(y, list@(x, Theta)))" xml:id="S3.Ex12.m1">
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<XMTok font="italic" role="ID" xml:id="S3.Ex12.m1.1">x</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok name="Theta" role="UNKNOWN" xml:id="S3.Ex12.m1.2">Θ</XMTok>
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</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S3.Ex13">
<Math mode="display" tex="f\left(a\middle|b\right)" text="f@(a, b)" xml:id="S3.Ex13.m1">
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<XMApp>
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<XMApp>
<XMTok font="italic" role="FUNCTION" xml:id="S3.Ex13.m1.1">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="true">(</XMTok>
<XMTok font="italic" role="ID" xml:id="S3.Ex13.m1.2">a</XMTok>
<XMTok role="MIDDLE" stretchy="true">|</XMTok>
<XMTok font="italic" role="ID" xml:id="S3.Ex13.m1.3">b</XMTok>
<XMTok role="CLOSE" stretchy="true">)</XMTok>
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</Math>
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</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>Missing arguments</title>
<para xml:id="S4.p1">
<equation xml:id="S4.Ex14">
<Math mode="display" tex="fgh" text="f * g * h" xml:id="S4.Ex14.m1">
<XMath>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="FUNCTION">f</XMTok>
<XMTok font="italic" role="FUNCTION">g</XMTok>
<XMTok font="italic" role="FUNCTION">h</XMTok>
</XMApp>
</XMath>
</Math>
</equation>
<equation xml:id="S4.Ex15">
<Math mode="display" tex="fgha" text="f * g * h * a" xml:id="S4.Ex15.m1">
<XMath>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="FUNCTION">f</XMTok>
<XMTok font="italic" role="FUNCTION">g</XMTok>
<XMTok font="italic" role="FUNCTION">h</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
</XMApp>
</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>Operator-like functions</title>
<para xml:id="S5.p1">
<equation xml:id="S5.Ex16">
<Math mode="display" tex="FGH" text="F@(G@(H))" xml:id="S5.Ex16.m1">
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<XMApp>
<XMTok font="italic" role="OPFUNCTION">F</XMTok>
<XMApp>
<XMTok font="italic" role="OPFUNCTION">G</XMTok>
<XMTok font="italic" role="OPFUNCTION">H</XMTok>
</XMApp>
</XMApp>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex17">
<Math mode="display" tex="FGHa" text="F@(G@(H@(a)))" xml:id="S5.Ex17.m1">
<XMath>
<XMApp>
<XMTok font="italic" role="OPFUNCTION">F</XMTok>
<XMApp>
<XMTok font="italic" role="OPFUNCTION">G</XMTok>
<XMApp>
<XMTok font="italic" role="OPFUNCTION">H</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</Math>
</equation>
</para>
<para xml:id="S5.p2">
<equation xml:id="S5.Ex18">
<Math mode="display" tex="f^{\prime}(a)=a^{2}" text="(f ^ prime)@(a) = a ^ 2" xml:id="S5.Ex18.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMDual>
<XMApp>
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<XMRef idref="S5.Ex18.m1.1"/>
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<XMApp>
<XMApp xml:id="S5.Ex18.m1.2">
<XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="FUNCTION">f</XMTok>
<XMTok fontsize="70%" name="prime" role="SUPOP">′</XMTok>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="ID" xml:id="S5.Ex18.m1.1">a</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex19">
<Math mode="display" tex="f^{2}(a)=g^{b}(2)" text="(f ^ 2)@(a) = (g ^ b)@(2)" xml:id="S5.Ex19.m1">
<XMath>
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMDual>
<XMApp>
<XMRef idref="S5.Ex19.m1.3"/>
<XMRef idref="S5.Ex19.m1.1"/>
</XMApp>
<XMApp>
<XMApp xml:id="S5.Ex19.m1.3">
<XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="FUNCTION">f</XMTok>
<XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="ID" xml:id="S5.Ex19.m1.1">a</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
<XMDual>
<XMApp>
<XMRef idref="S5.Ex19.m1.4"/>
<XMRef idref="S5.Ex19.m1.2"/>
</XMApp>
<XMApp>
<XMApp xml:id="S5.Ex19.m1.4">
<XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="FUNCTION">g</XMTok>
<XMTok font="italic" fontsize="70%" role="ID">b</XMTok>
</XMApp>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok meaning="2" role="NUMBER" xml:id="S5.Ex19.m1.2">2</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMApp>
</XMath>
</Math>
</equation>
</para>
<para xml:id="S5.p3">
<equation xml:id="S5.Ex20">
<Math mode="display" tex="fgx" text="f@(g * x)" xml:id="S5.Ex20.m1">
<XMath>
<XMApp>
<XMTok font="italic" role="FUNCTION">f</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok font="italic" role="FUNCTION">g</XMTok>
<XMTok font="italic" role="ID">x</XMTok>
</XMApp>
</XMApp>
</XMath>
</Math>
</equation>
<equation xml:id="S5.Ex21">
<Math mode="display" tex="f(x)" text="f@(x)" xml:id="S5.Ex21.m1">
<XMath>
<XMDual>
<XMApp>
<XMRef idref="S5.Ex21.m1.1"/>
<XMRef idref="S5.Ex21.m1.2"/>
</XMApp>
<XMApp>
<XMTok font="italic" role="FUNCTION" xml:id="S5.Ex21.m1.1">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok font="italic" role="ID" xml:id="S5.Ex21.m1.2">x</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</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>Scripts</title>
<para xml:id="S6.p1">
<equation xml:id="S6.Ex22">
<Math mode="display" tex="\ln a=\log_{e}a=\ln_{+}b" text="natural-logarithm@(a) = (logarithm _ e)@(a) = (natural-logarithm _ +)@(b)" xml:id="S6.Ex22.m1">
<XMath>
<XMApp>
<XMTok meaning="multirelation"/>
<XMApp>
<XMTok meaning="natural-logarithm" role="OPFUNCTION">ln</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
</XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMTok font="italic" fontsize="70%" role="ID">e</XMTok>
</XMApp>
<XMTok font="italic" role="ID">a</XMTok>
</XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok meaning="natural-logarithm" role="OPFUNCTION">ln</XMTok>
<XMTok fontsize="70%" meaning="plus" role="ADDOP">+</XMTok>
</XMApp>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
</XMApp>
</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>Advanced argument patterns</title>
<para xml:id="S7.p1">
<equation xml:id="S7.Ex23">
<Math mode="display" tex="f(a<b)" text="f@(a < b)" xml:id="S7.Ex23.m1">
<XMath>
<XMDual>
<XMApp>
<XMRef idref="S7.Ex23.m1.1"/>
<XMRef idref="S7.Ex23.m1.2"/>
</XMApp>
<XMApp>
<XMTok font="italic" role="FUNCTION" xml:id="S7.Ex23.m1.1">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S7.Ex23.m1.2">
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S7.Ex24">
<Math mode="display" tex="f(a:b)" text="f@(a colon b)" xml:id="S7.Ex24.m1">
<XMath>
<XMDual>
<XMApp>
<XMRef idref="S7.Ex24.m1.1"/>
<XMRef idref="S7.Ex24.m1.2"/>
</XMApp>
<XMApp>
<XMTok font="italic" role="FUNCTION" xml:id="S7.Ex24.m1.1">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S7.Ex24.m1.2">
<XMTok name="colon" role="METARELOP">:</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S7.Ex25">
<Math mode="display" tex="f(a\leftrightarrow b)" text="f@(a leftrightarrow b)" xml:id="S7.Ex25.m1">
<XMath>
<XMDual>
<XMApp>
<XMRef idref="S7.Ex25.m1.1"/>
<XMRef idref="S7.Ex25.m1.2"/>
</XMApp>
<XMApp>
<XMTok font="italic" role="FUNCTION" xml:id="S7.Ex25.m1.1">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMApp xml:id="S7.Ex25.m1.2">
<XMTok name="leftrightarrow" role="METARELOP">↔</XMTok>
<XMTok font="italic" role="ID">a</XMTok>
<XMTok font="italic" role="ID">b</XMTok>
</XMApp>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMath>
</Math>
</equation>
<equation xml:id="S7.Ex26">
<Math mode="display" tex="f(\rightarrow,\leftarrow)" text="f@(rightarrow, leftarrow)" xml:id="S7.Ex26.m1">
<XMath>
<XMDual>
<XMApp>
<XMRef idref="S7.Ex26.m1.1"/>
<XMRef idref="S7.Ex26.m1.2"/>
<XMRef idref="S7.Ex26.m1.3"/>
</XMApp>
<XMApp>
<XMTok font="italic" role="FUNCTION" xml:id="S7.Ex26.m1.1">f</XMTok>
<XMWrap>
<XMTok role="OPEN" stretchy="false">(</XMTok>
<XMTok name="rightarrow" role="ARROW" xml:id="S7.Ex26.m1.2">→</XMTok>
<XMTok role="PUNCT">,</XMTok>
<XMTok name="leftarrow" role="ARROW" xml:id="S7.Ex26.m1.3">←</XMTok>
<XMTok role="CLOSE" stretchy="false">)</XMTok>
</XMWrap>
</XMApp>
</XMDual>
</XMath>
</Math>
</equation>
</para>
</section>
</document>