<cn>
Rendering <cn>,<sep/>-Represented Numbers
Strict uses of <cn>
<cn type="hexdouble">7F800000</cn>
Non-Strict uses of <cn>
<cn base="16">7FE0</cn>
<cn base="1000">10F</cn>
<cn type="rational">22<sep/>7</cn>
<cn type="complex-cartesian"> 12.3 <sep/> 5 </cn>
<cn type="complex-polar"> 2 <sep/> 3.1415 </cn>
Rewrite: cn sep
<cn type="rational" base="b">n<sep/>d</cn>
<apply><csymbol cd="nums1">rational</csymbol>
<cn type="integer" base="b">n</cn>
<cn type="integer" base="b">d</cn>
</apply>
Rewrite: cn based_integer
<cn type="integer" base="16">FF60</cn>
<apply><csymbol cd="nums1">based_integer</csymbol>
<cn type="integer">16</cn>
<cs>FF60</cs>
</apply>
Rewrite: cn constant
<cn type="constant">c</cn>
<csymbol cd="nums1">c2</csymbol>
Rewrite: cn presentation mathml
<cn type="rational"><mi>P</mi><sep/><mi>Q</mi></cn>
<apply><csymbol cd="nums1">rational</csymbol>
<semantics>
<ci>p</ci>
<annotation-xml encoding="MathML-Presentation">
<mi>P</mi>
</annotation-xml>
</semantics>
<semantics>
<ci>q</ci>
<annotation-xml encoding="MathML-Presentation">
<mi>Q</mi>
</annotation-xml>
</semantics>
</apply>
Content Identifiers <ci>
<ci>x</ci>
Strict uses of <ci>
<ci type="integer">n</ci>
<semantics>
<ci>n</ci>
<annotation-xml cd="mathmltypes" name="type" encoding="MathML-Content">
<csymbol cd="mathmltypes">integer_type</csymbol>
</annotation-xml>
</semantics>
Non-Strict uses of <ci> Rewrite: ci type annotation
<ci type="T">n</ci>
<semantics>
<ci>n</ci>
<annotation-xml cd="mathmltypes" name="type" encoding="MathML-Content">
<ci>T</ci>
</annotation-xml>
</semantics>
Rewrite: ci presentation mathml
<ci><mi>P</mi></ci>
<semantics>
<ci>p</ci>
<annotation-xml encoding="MathML-Presentation">
<mi>P</mi>
</annotation-xml>
</semantics>
<ci>
<msup><mi>C</mi><mn>2</mn></msup>
</ci>
<semantics>
<ci>C2</ci>
<annotation-xml encoding="MathML-Presentation">
<msup><mi>C</mi><mn>2</mn></msup>
</annotation-xml>
</semantics>
Rendering Content Identifiers
<ci type="vector">V</ci>
Content Symbols <csymbol>
Strict uses of <csymbol>
Non-Strict uses of <csymbol> Rewrite: csymbol type annotation
<csymbol type="T">symbolname</csymbol>
<semantics>
<csymbol>symbolname</csymbol>
<annotation-xml cd="mathmltypes" name="type" encoding="MathML-Content">
<ci>T</ci>
</annotation-xml>
</semantics>
Rendering Symbols
String Literals <cs>
<set>
<cs>A</cs><cs>B</cs><cs> </cs>
</set>
Function Application <apply> Strict Content MathML
<apply><csymbol cd="arith1">plus</csymbol><ci>x</ci><ci>y</ci></apply>
<apply><csymbol cd="arith1">plus</csymbol>
<ci>x</ci>
<ci>y</ci>
<ci>z</ci>
</apply>
<apply><csymbol cd="arith1">plus</csymbol>
<apply><csymbol cd="arith1">times</csymbol>
<ci>a</ci>
<ci>x</ci>
</apply>
<ci>b</ci>
</apply>
<apply><csymbol cd="arith1">times</csymbol>
<apply><csymbol cd="arith1">plus</csymbol>
<ci>F</ci>
<ci>G</ci>
</apply>
<ci>x</ci>
</apply>
<apply><csymbol cd="arith1">plus</csymbol><ci>F</ci><ci>G</ci></apply>
<apply>
<apply><csymbol cd="arith1">plus</csymbol>
<ci>F</ci>
<ci>G</ci>
</apply>
<ci>x</ci>
</apply>
Rendering Applications
<apply><ci>f</ci>
<ci>a1</ci>
<ci>a2</ci>
<ci>...</ci>
<ci>an</ci>
</apply>
<apply><ci>op</ci>
<bvar><ci>x</ci></bvar>
<domainofapplication><ci>d</ci></domainofapplication>
<ci>expression-in-x</ci>
</apply>
Bindings and Bound Variables <bind> and <bvar>
Bindings
Bound Variables
<bind><csymbol cd="quant1">forall</csymbol>
<bvar><ci id="var-x">x</ci></bvar>
<apply><csymbol cd="relation1">lt</csymbol>
<ci xref="var-x">x</ci>
<cn>1</cn>
</apply>
</bind>
<bind><csymbol cd="quant1">forall</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="relation1">eq</csymbol>
<apply><csymbol cd="arith1">plus</csymbol><ci>x</ci><ci>y</ci></apply>
<apply><csymbol cd="arith1">plus</csymbol><ci>y</ci><ci>x</ci></apply>
</apply>
</bind>
Renaming Bound Variables
Rendering Binding Constructions
<bind><ci>b</ci>
<bvar><ci>x1</ci></bvar>
<bvar><ci>...</ci></bvar>
<bvar><ci>xn</ci></bvar>
<ci>s</ci>
</bind>
Structure Sharing <share>
<apply><ci>f</ci>
<apply><ci>f</ci>
<apply><ci>f</ci>
<ci>a</ci>
<ci>a</ci>
</apply>
<apply><ci>f</ci>
<ci>a</ci>
<ci>a</ci>
</apply>
</apply>
<apply><ci>f</ci>
<apply><ci>f</ci>
<ci>a</ci>
<ci>a</ci>
</apply>
<apply><ci>f</ci>
<ci>a</ci>
<ci>a</ci>
</apply>
</apply>
</apply>
<apply><ci>f</ci>
<apply id="t1"><ci>f</ci>
<apply id="t11"><ci>f</ci>
<ci>a</ci>
<ci>a</ci>
</apply>
<share src="#t11"/>
</apply>
<share src="#t1"/>
</apply>
An Acyclicity Constraint
<bind id="outer"><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<apply><ci>f</ci>
<bind id="inner"><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<share id="copy" src="#orig"/>
</bind>
<apply id="orig"><ci>g</ci><ci>x</ci></apply>
</apply>
</bind>
Attribution via semantics
Error Markup <cerror>
<cerror>
<csymbol cd="aritherror">DivisionByZero</csymbol>
<apply><csymbol cd="arith1">divide</csymbol><ci>x</ci><cn>0</cn></apply>
</cerror>
<apply><csymbol cd="relation1">eq</csymbol>
<cerror>
<csymbol cd="aritherror">DivisionByZero</csymbol>
<apply><csymbol cd="arith1">divide</csymbol><ci>x</ci><cn>0</cn></apply>
</cerror>
<cn>0</cn>
</apply>
<cerror>
<csymbol cd="aritherror">DivisionByZero</csymbol>
<apply><csymbol cd="arith1">divide</csymbol><ci>x</ci><cn>0</cn></apply>
</cerror>
<cerror>
<csymbol cd="error">Illegal bound variable</csymbol>
<cs> <bvar><plus/></bvar> </cs>
</cerror>
Encoded Bytes <cbytes>
Content MathML for Specific Structures Container Markup Container Markup for Constructor Symbols
<set><ci>a</ci><ci>b</ci><ci>c</ci></set>
<apply><csymbol cd="set1">set</csymbol><ci>a</ci><ci>b</ci><ci>c</ci></apply>
<set>
<bvar><ci>x</ci></bvar>
<domainofapplication><integers/></domainofapplication>
<apply><times/><cn>2</cn><ci>x</ci></apply>
</set>
<apply><csymbol cd="set1">map</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="arith1">times</csymbol>
<cn>2</cn>
<ci>x</ci>
</apply>
</bind>
<csymbol cd="setname1">Z</csymbol>
</apply>
Container Markup for Binding Constructors
<lambda><bvar><ci>x</ci></bvar><ci>x</ci></lambda>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar><ci>x</ci>
</bind>
Bindings with <apply>
<apply><forall/>
<bvar><ci>x</ci></bvar>
<apply><geq/><ci>x</ci><ci>x</ci></apply>
</apply>
<bind><csymbol cd="logic1">forall</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="relation1">geq</csymbol><ci>x</ci><ci>x</ci></apply>
</bind>
<apply><sum/>
<bvar><ci>i</ci></bvar>
<lowlimit><cn>0</cn></lowlimit>
<uplimit><cn>100</cn></uplimit>
<apply><power/><ci>x</ci><ci>i</ci></apply>
</apply>
<apply><csymbol cd="arith1">sum</csymbol>
<apply><csymbol cd="interval1">integer_interval</csymbol>
<cn>0</cn>
<cn>100</cn>
</apply>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>i</ci></bvar>
<apply><csymbol cd="arith1">power</csymbol>
<ci>x</ci>
<ci>i</ci>
</apply>
</bind>
</apply>
Qualifiers Uses of <domainofapplication>, <interval>, <condition>, <lowlimit> and <uplimit>
<apply><int/>
<domainofapplication>
<ci type="set">C</ci>
</domainofapplication>
<ci type="function">f</ci>
</apply>
<apply><int/>
<bvar><ci>x</ci></bvar>
<interval><cn>0</cn><cn>1</cn></interval>
<apply><power/><ci>x</ci><cn>2</cn></apply>
</apply>
<apply><int/>
<bvar><ci>x</ci></bvar>
<lowlimit><cn>0</cn></lowlimit>
<uplimit><cn>1</cn></uplimit>
<apply><power/><ci>x</ci><cn>2</cn></apply>
</apply>
<apply><int/>
<bvar><ci>x</ci></bvar>
<condition>
<apply><and/>
<apply><leq/><cn>0</cn><ci>x</ci></apply>
<apply><leq/><ci>x</ci><cn>1</cn></apply>
</apply>
</condition>
<apply><power/><ci>x</ci><cn>2</cn></apply>
</apply>
<apply><int/>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<domainofapplication>
<set>
<bvar><ci>t</ci></bvar>
<bvar><ci>u</ci></bvar>
<condition>
<apply><and/>
<apply><leq/><cn>0</cn><ci>t</ci></apply>
<apply><leq/><ci>t</ci><cn>1</cn></apply>
<apply><leq/><cn>0</cn><ci>u</ci></apply>
<apply><leq/><ci>u</ci><cn>1</cn></apply>
</apply>
</condition>
<list><ci>t</ci><ci>u</ci></list>
</set>
</domainofapplication>
<apply><times/>
<apply><power/><ci>x</ci><cn>2</cn></apply>
<apply><power/><ci>y</ci><cn>3</cn></apply>
</apply>
</apply>
Rewrite: interval qualifier
<apply><ci>H</ci>
<bvar><ci>x</ci></bvar>
<lowlimit><ci>a</ci></lowlimit>
<uplimit><ci>b</ci></uplimit>
<ci>C</ci>
</apply>
<apply><ci>H</ci>
<bvar><ci>x</ci></bvar>
<domainofapplication>
<apply><csymbol cd="interval1">interval</csymbol>
<ci>a</ci>
<ci>b</ci>
</apply>
</domainofapplication>
<ci>C</ci>
</apply>
Rewrite: condition
Rewrite: restriction
<apply><ci>F</ci>
<domainofapplication>
<ci>C</ci>
</domainofapplication>
<ci>a1</ci>
<ci>an</ci>
</apply>
<apply>
<apply><csymbol cd="fns1">restriction</csymbol>
<ci>F</ci>
<ci>C</ci>
</apply>
<ci>a1</ci>
<ci>an</ci>
</apply>
Rewrite: apply bvar domainofapplication
Uses of <degree>
<apply><diff/>
<bvar>
<ci>x</ci>
<degree><cn>2</cn></degree>
</bvar>
<apply><power/><ci>x</ci><cn>4</cn></apply>
</apply>
Uses of <momentabout> and <logbase>
Operator Classes Rewrite: element
<plus/>
<csymbol cd="arith1">plus</csymbol>
N-ary Operators (classes nary-arith, nary-functional, nary-logical, nary-linalg, nary-set, nary-constructor)
Schema Patterns
Rewriting to Strict Content MathML Rewrite: n-ary domainofapplication
<apply><union/>
<bvar><ci>x</ci></bvar>
<domainofapplication><ci>D</ci></domainofapplication>
<ci>expression-in-x</ci>
</apply>
<apply><csymbol cd="fns2">apply_to_list</csymbol>
<csymbol cd="set1">union</csymbol>
<apply><csymbol cd="list1">map</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
<ci>D</ci>
</apply>
</apply>
N-ary Constructors for set and list (class nary-setlist-constructor)
Schema Patterns
Rewriting to Strict Content MathML Rewrite: n-ary setlist domainofapplication
<set>
<bvar><ci>x</ci></bvar>
<domainofapplication><ci>D</ci></domainofapplication>
<ci>expression-in-x</ci>
</set>
<apply><csymbol cd="set1">map</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
<ci>D</ci>
</apply>
N-ary Relations (classes nary-reln, nary-set-reln)
Schema Patterns
Rewriting to Strict Content MathML Rewrite: n-ary relations
<apply><lt/>
<ci>a</ci><ci>b</ci><ci>c</ci><ci>d</ci>
</apply>
<apply><csymbol cd="fns2">predicate_on_list</csymbol>
<csymbol cd="reln1">lt</csymbol>
<apply><csymbol cd="list1">list</csymbol>
<ci>a</ci><ci>b</ci><ci>c</ci><ci>d</ci>
</apply>
</apply>
Rewrite: n-ary relations bvar
<apply><lt/>
<bvar><ci>x</ci></bvar>
<domainofapplication><ci>R</ci></domainofapplication>
<ci>expression-in-x</ci>
</apply>
<apply><csymbol cd="fns2">predicate_on_list</csymbol>
<csymbol cd="reln1">lt</csymbol>
<apply><csymbol cd="list1">map</csymbol>
<ci>R</ci>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
</apply>
</apply>
N-ary/Unary Operators (classes nary-minmax, nary-stats)
Schema Patterns
Rewriting to Strict Content MathML Rewrite: n-ary unary set
<apply><max/><ci>a1</ci><ci>a2</ci><ci>an</ci></apply>
<apply><csymbol cd="minmax1">max</csymbol>
<apply><csymbol cd="set1">set</csymbol>
<ci>a1</ci><ci>a2</ci><ci>an</ci>
</apply>
</apply>
Rewrite: n-ary unary domainofapplication
<apply><max/>
<bvar><ci>x</ci></bvar>
<domainofapplication><ci>D</ci></domainofapplication>
<ci>expression-in-x</ci>
</apply>
<apply><csymbol cd="minmax1">max</csymbol>
<apply><csymbol cd="set1">map</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
<ci>D</ci>
</apply>
</apply>
Rewrite: n-ary unary single
<apply><max/><ci>a</ci></apply>
<apply><csymbol cd="minmax1">max</csymbol> <ci>a</ci> </apply>
Binary Operators (classes binary-arith, binary-logical, binary-reln, binary-linalg, binary-set)
Schema Patterns
Unary Operators (classes unary-arith, unary-linalg, unary-functional, unary-set, unary-elementary, unary-veccalc)
Schema Patterns
Constants (classes constant-arith, constant-set)
Schema Patterns
Quantifiers (class quantifier)
Schema Patterns
Rewriting to Strict Content MathML Rewrite: quantifier
<apply><exists/>
<bvar><ci>x</ci></bvar>
<domainofapplication><ci>D</ci></domainofapplication>
<ci>expression-in-x</ci>
</apply>
<bind><csymbol cd="quant1">exists</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="set1">in</csymbol><ci>x</ci><ci>D</ci></apply>
<ci>expression-in-x</ci>
</apply>
</bind>
Other Operators (classes lambda, interval, int, diff partialdiff, sum, product, limit)
Schema Patterns
Non-strict Attributes Rewrite: attributes
<ci class="foo" xmlns:other="http://example.com" other:att="bla">x</ci>
<semantics>
<ci>x</ci>
<annotation cd="mathmlattr"
name="class" encoding="text/plain">foo</annotation>
<annotation-xml cd="mathmlattr" name="foreign" encoding="MathML-Content">
<apply><csymbol cd="mathmlattr">foreign_attribute</csymbol>
<cs>http://example.com</cs>
<cs>other</cs>
<cs>att</cs>
<cs>bla</cs>
</apply>
</annotation-xml>
</semantics>
Content MathML for Specific Operators and Constants Functions and Inverses Interval <interval>
<interval closure="open"><ci>x</ci><cn>1</cn></interval>
<interval closure="closed"><cn>0</cn><cn>1</cn></interval>
<interval closure="open-closed"><cn>0</cn><cn>1</cn></interval>
<interval closure="closed-open"><cn>0</cn><cn>1</cn></interval>
Inverse <inverse>
<apply><inverse/>
<ci> f </ci>
</apply>
<apply>
<apply><inverse/><ci type="matrix">A</ci></apply>
<ci>a</ci>
</apply>
Lambda <lambda>
<lambda>
<bvar><ci> x </ci></bvar>
<domainofapplication><integers/></domainofapplication>
<apply><sin/><ci> x </ci></apply>
</lambda>
<lambda>
<domainofapplication><integers/></domainofapplication>
<sin/>
</lambda>
<lambda>
<bvar><ci>x</ci></bvar>
<apply><sin/>
<apply><plus/><ci>x</ci><cn>1</cn></apply>
</apply>
</lambda>
Rewrite: lambda
<lambda>
<bvar><ci>x1</ci></bvar><bvar><ci>xn</ci></bvar>
<ci>expression-in-x1-xn</ci>
</lambda>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x1</ci></bvar><bvar><ci>xn</ci></bvar>
<ci>expression-in-x1-xn</ci>
</bind>
Rewrite: lambda domainofapplication
<lambda>
<bvar><ci>x1</ci></bvar><bvar><ci>xn</ci></bvar>
<domainofapplication><ci>D</ci></domainofapplication>
<ci>expression-in-x1-xn</ci>
</lambda>
<apply><csymbol cd="fns1">restriction</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x1</ci></bvar><bvar><ci>xn</ci></bvar>
<ci>expression-in-x1-xn</ci>
</bind>
<ci>D</ci>
</apply>
Function composition <compose/>
<apply><compose/><ci>f</ci><ci>g</ci><ci>h</ci></apply>
<apply><eq/>
<apply>
<apply><compose/><ci>f</ci><ci>g</ci></apply>
<ci>x</ci>
</apply>
<apply><ci>f</ci><apply><ci>g</ci><ci>x</ci></apply></apply>
</apply>
Identity function <ident/>
<apply><eq/>
<apply><compose/>
<ci type="function">f</ci>
<apply><inverse/>
<ci type="function">f</ci>
</apply>
</apply>
<ident/>
</apply>
Domain <domain/>
<apply><eq/>
<apply><domain/><ci>f</ci></apply>
<reals/>
</apply>
codomain <codomain/>
<apply><eq/>
<apply><codomain/><ci>f</ci></apply>
<rationals/>
</apply>
Image <image/>
<apply><eq/>
<apply><image/><sin/></apply>
<interval><cn>-1</cn><cn> 1</cn></interval>
</apply>
Piecewise declaration <piecewise>, <piece>, <otherwise>
<piecewise>
<piece>
<apply><minus/><ci>x</ci></apply>
<apply><lt/><ci>x</ci><cn>0</cn></apply>
</piece>
<piece>
<cn>0</cn>
<apply><eq/><ci>x</ci><cn>0</cn></apply>
</piece>
<piece>
<ci>x</ci>
<apply><gt/><ci>x</ci><cn>0</cn></apply>
</piece>
</piecewise>
<piecewise>
<piece>
<cn>0</cn>
<apply><lt/><ci>x</ci><cn>0</cn></apply>
</piece>
<piece>
<cn>1</cn>
<apply><gt/><ci>x</ci><cn>1</cn></apply>
</piece>
<otherwise>
<ci>x</ci>
</otherwise>
</piecewise>
<apply><csymbol cd="piece1">piecewise</csymbol>
<apply><csymbol cd="piece1">piece</csymbol>
<cn>0</cn>
<apply><csymbol cd="relation1">lt</csymbol><ci>x</ci><cn>0</cn></apply>
</apply>
<apply><csymbol cd="piece1">piece</csymbol>
<cn>1</cn>
<apply><csymbol cd="relation1">gt</csymbol><ci>x</ci><cn>1</cn></apply>
</apply>
<apply><csymbol cd="piece1">otherwise</csymbol>
<ci>x</ci>
</apply>
</apply>
Arithmetic, Algebra and Logic Quotient <quotient/>
<apply><quotient/><ci>a</ci><ci>b</ci></apply>
Factorial <factorial/>
<apply><factorial/><ci>n</ci></apply>
Division <divide/>
<apply><divide/>
<ci>a</ci>
<ci>b</ci>
</apply>
Maximum <max/>
<apply><max/><cn>2</cn><cn>3</cn><cn>5</cn></apply>
<apply><max/>
<bvar><ci>y</ci></bvar>
<condition>
<apply><in/>
<ci>y</ci>
<interval><cn>0</cn><cn>1</cn></interval>
</apply>
</condition>
<apply><power/><ci>y</ci><cn>3</cn></apply>
</apply>
Minimum <min/>
<apply><min/><ci>a</ci><ci>b</ci></apply>
<apply><min/>
<bvar><ci>x</ci></bvar>
<condition>
<apply><notin/><ci>x</ci><ci type="set">B</ci></apply>
</condition>
<apply><power/><ci>x</ci><cn>2</cn></apply>
</apply>
Subtraction <minus/>
<apply><minus/><cn>3</cn></apply>
<apply><minus/><ci>x</ci><ci>y</ci></apply>
Addition <plus/>
<apply><plus/><ci>x</ci><ci>y</ci><ci>z</ci></apply>
Exponentiation <power/>
<apply><power/><ci>x</ci><cn>3</cn></apply>
Remainder <rem/>
<apply><rem/><ci> a </ci><ci> b </ci></apply>
Multiplication <times/>
<apply><times/><ci>a</ci><ci>b</ci></apply>
Root <root/>
<apply><root/>
<degree><ci type="integer">n</ci></degree>
<ci>a</ci>
</apply>
<apply><root/><ci>x</ci></apply>
<apply><csymbol cd="arith1">root</csymbol>
<ci>x</ci>
<cn type="integer">2</cn>
</apply>
<apply><root/>
<degree><ci type="integer">n</ci></degree>
<ci>a</ci>
</apply>
<apply><csymbol cd="arith1">root</csymbol>
<ci>a</ci>
<cn type="integer">n</cn>
</apply>
Greatest common divisor <gcd/>
<apply><gcd/><ci>a</ci><ci>b</ci><ci>c</ci></apply>
And <and/>
<apply><and/><ci>a</ci><ci>b</ci></apply>
<apply><and/>
<bvar><ci>i</ci></bvar>
<lowlimit><cn>0</cn></lowlimit>
<uplimit><ci>n</ci></uplimit>
<apply><gt/><apply><selector/><ci>a</ci><ci>i</ci></apply><cn>0</cn></apply>
</apply>
<apply><csymbol cd="fns2">apply_to_list</csymbol>
<csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="list1">map</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>i</ci></bvar>
<apply><csymbol cd="relation1">gt</csymbol>
<apply><csymbol cd="linalg1">vector_selector</csymbol>
<ci>i</ci>
<ci>a</ci>
</apply>
<cn>0</cn>
</apply>
</bind>
<apply><csymbol cd="interval1">integer_interval</csymbol>
<cn type="integer">0</cn>
<ci>n</ci>
</apply>
</apply>
</apply>
Or <or/>
<apply><or/><ci>a</ci><ci>b</ci></apply>
Exclusive Or <xor/>
<apply><xor/><ci>a</ci><ci>b</ci></apply>
Not <not/>
<apply><not/><ci>a</ci></apply>
Implies <implies/>
<apply><implies/><ci>A</ci><ci>B</ci></apply>
Universal quantifier <forall/>
<bind><forall/>
<bvar><ci>x</ci></bvar>
<apply><eq/>
<apply><minus/><ci>x</ci><ci>x</ci></apply>
<cn>0</cn>
</apply>
</bind>
<bind><forall/>
<bvar><ci>p</ci></bvar>
<bvar><ci>q</ci></bvar>
<condition>
<apply><and/>
<apply><in/><ci>p</ci><rationals/></apply>
<apply><in/><ci>q</ci><rationals/></apply>
<apply><lt/><ci>p</ci><ci>q</ci></apply>
</apply>
</condition>
<apply><lt/>
<ci>p</ci>
<apply><power/><ci>q</ci><cn>2</cn></apply>
</apply>
</bind>
<bind><csymbol cd="quant1">forall</csymbol>
<bvar><ci>p</ci></bvar>
<bvar><ci>q</ci></bvar>
<apply><csymbol cd="logic1">implies</csymbol>
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="set1">in</csymbol>
<ci>p</ci>
<csymbol cd="setname1">Q</csymbol>
</apply>
<apply><csymbol cd="set1">in</csymbol>
<ci>q</ci>
<csymbol cd="setname1">Q</csymbol>
</apply>
<apply><csymbol cd="relation1">lt</csymbol><ci>p</ci><ci>q</ci></apply>
</apply>
<apply><csymbol cd="relation1">lt</csymbol>
<ci>p</ci>
<apply><csymbol cd="arith1">power</csymbol>
<ci>q</ci>
<cn>2</cn>
</apply>
</apply>
</apply>
</bind>
Existential quantifier <exists/>
<bind><exists/>
<bvar><ci>x</ci></bvar>
<apply><eq/>
<apply><ci>f</ci><ci>x</ci></apply>
<cn>0</cn>
</apply>
</bind>
<apply><exists/>
<bvar><ci>x</ci></bvar>
<domainofapplication>
<integers/>
</domainofapplication>
<apply><eq/>
<apply><ci>f</ci><ci>x</ci></apply>
<cn>0</cn>
</apply>
</apply>
<bind><csymbol cd="quant1">exists</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="set1">in</csymbol>
<ci>x</ci>
<csymbol cd="setname1">Z</csymbol>
</apply>
<apply><csymbol cd="relation1">eq</csymbol>
<apply><ci>f</ci><ci>x</ci></apply>
<cn>0</cn>
</apply>
</apply>
</bind>
Absolute Value <abs/>
<apply><abs/><ci>x</ci></apply>
Complex conjugate <conjugate/>
<apply><conjugate/>
<apply><plus/>
<ci>x</ci>
<apply><times/><cn>ⅈ</cn><ci>y</ci></apply>
</apply>
</apply>
Argument <arg/>
<apply><arg/>
<apply><plus/>
<ci> x </ci>
<apply><times/><imaginaryi/><ci>y</ci></apply>
</apply>
</apply>
Real part <real/>
<apply><real/>
<apply><plus/>
<ci>x</ci>
<apply><times/><imaginaryi/><ci>y</ci></apply>
</apply>
</apply>
Imaginary part <imaginary/>
<apply><imaginary/>
<apply><plus/>
<ci>x</ci>
<apply><times/><imaginaryi/><ci>y</ci></apply>
</apply>
</apply>
Lowest common multiple <lcm/>
<apply><lcm/><ci>a</ci><ci>b</ci><ci>c</ci></apply>
Floor <floor/>
<apply><floor/><ci>a</ci></apply>
Ceiling <ceiling/>
<apply><ceiling/><ci>a</ci></apply>
Relations Equals <eq/>
<apply><eq/>
<cn type="rational">2<sep/>4</cn>
<cn type="rational">1<sep/>2</cn>
</apply>
Not Equals <neq/>
<apply><neq/><cn>3</cn><cn>4</cn></apply>
Greater than <gt/>
<apply><gt/><cn>3</cn><cn>2</cn></apply>
Less Than <lt/>
<apply><lt/><cn>2</cn><cn>3</cn><cn>4</cn></apply>
Greater Than or Equal <geq/>
<apply><geq/><cn>4</cn><cn>3</cn><cn>3</cn></apply>
<apply><csymbol cd="fns2">predicate_on_list</csymbol>
<csymbol cd="reln1">geq</csymbol>
<apply><csymbol cd="list1">list</csymbol>
<cn>4</cn><cn>3</cn><cn>3</cn>
</apply>
</apply>
Less Than or Equal <leq/>
<apply><leq/><cn>3</cn><cn>3</cn><cn>4</cn></apply>
Equivalent <equivalent/>
<apply><equivalent/>
<ci>a</ci>
<apply><not/><apply><not/><ci>a</ci></apply></apply>
</apply>
Approximately <approx/>
<apply><approx/>
<pi/>
<cn type="rational">22<sep/>7</cn>
</apply>
Factor Of <factorof/>
<apply><factorof/><ci>a</ci><ci>b</ci></apply>
Calculus and Vector Calculus Integral <int/>
<apply><eq/>
<apply><int/><sin/></apply>
<cos/>
</apply>
<apply><int/>
<interval><ci>a</ci><ci>b</ci></interval>
<cos/>
</apply>
<apply><int/>
<bvar><ci>x</ci></bvar>
<lowlimit><cn>0</cn></lowlimit>
<uplimit><cn>1</cn></uplimit>
<apply><power/><ci>x</ci><cn>2</cn></apply>
</apply>
Rewrite: int
<apply><int/>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</apply>
<apply>
<apply><csymbol cd="calculus1">int</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
</apply>
<ci>x</ci>
</apply>
<apply><int/>
<bvar><ci>x</ci></bvar>
<apply><cos/><ci>x</ci></apply>
</apply>
<apply>
<apply><csymbol cd="calculus1">int</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<apply><cos/><ci>x</ci></apply>
</bind>
</apply>
<ci>x</ci>
</apply>
<apply><int/>
<domainofapplication><ci>C</ci></domainofapplication>
<ci>f</ci>
</apply>
<apply><csymbol cd="calculus1">defint</csymbol><ci>C</ci><ci>f</ci></apply>
Rewrite: defint
<apply><int/>
<bvar><ci>x</ci></bvar>
<domainofapplication><ci>D</ci></domainofapplication>
<ci>expression-in-x</ci>
</apply>
<apply><csymbol cd="calculus1">defint</csymbol>
<ci>D</ci>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
</apply>
Rewrite: defint limits
<apply><int/>
<bvar><ci>x</ci></bvar>
<lowlimit><ci>a</ci></lowlimit>
<uplimit><ci>b</ci></uplimit>
<ci>expression-in-x</ci>
</apply>
<apply><csymbol cd="calculus1">defint</csymbol>
<apply><csymbol cd="interval1">oriented_interval</csymbol>
<ci>a</ci> <ci>b</ci>
</apply>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
</apply>
<bind><int/>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<condition>
<apply><and/>
<apply><leq/><cn>0</cn><ci>x</ci></apply>
<apply><leq/><ci>x</ci><cn>1</cn></apply>
<apply><leq/><cn>0</cn><ci>y</ci></apply>
<apply><leq/><ci>y</ci><cn>1</cn></apply>
</apply>
</condition>
<apply><times/>
<apply><power/><ci>x</ci><cn>2</cn></apply>
<apply><power/><ci>y</ci><cn>3</cn></apply>
</apply>
</bind>
<apply><csymbol cd="calculus1">defint</csymbol>
<apply><csymbol cd="set1">suchthat</csymbol>
<apply><csymbol cd="set1">cartesianproduct</csymbol>
<csymbol cd="setname1">R</csymbol>
<csymbol cd="setname1">R</csymbol>
</apply>
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="arith1">leq</csymbol><cn>0</cn><ci>x</ci></apply>
<apply><csymbol cd="arith1">leq</csymbol><ci>x</ci><cn>1</cn></apply>
<apply><csymbol cd="arith1">leq</csymbol><cn>0</cn><ci>y</ci></apply>
<apply><csymbol cd="arith1">leq</csymbol><ci>y</ci><cn>1</cn></apply>
</apply>
<bind><csymbol cd="fns11">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<apply><csymbol cd="arith1">times</csymbol>
<apply><csymbol cd="arith1">power</csymbol><ci>x</ci><cn>2</cn></apply>
<apply><csymbol cd="arith1">power</csymbol><ci>y</ci><cn>3</cn></apply>
</apply>
</bind>
</apply>
</apply>
Differentiation <diff/>
<apply><diff/><ci>f</ci></apply>
<apply><eq/>
<apply><diff/>
<bvar><ci>x</ci></bvar>
<apply><sin/><ci>x</ci></apply>
</apply>
<apply><cos/><ci>x</ci></apply>
</apply>
<apply><diff/>
<bvar><ci>x</ci><degree><cn>2</cn></degree></bvar>
<apply><power/><ci>x</ci><cn>4</cn></apply>
</apply>
Rewrite: diff
<apply><diff/>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</apply>
<apply>
<apply><csymbol cd="calculus1">diff</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>E</ci>
</bind>
</apply>
<ci>x</ci>
</apply>
<apply><diff/>
<bvar><ci>x</ci></bvar>
<apply><sin/><ci>x</ci></apply>
</apply>
<apply>
<apply><csymbol cd="calculus1">diff</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="transc1">sin</csymbol><ci>x</ci></apply>
</bind>
</apply>
<ci>x</ci>
</apply>
Rewrite: nthdiff
<apply><diff/>
<bvar><ci>x</ci><degree><ci>n</ci></degree></bvar>
<ci>expression-in-x</ci>
</apply>
<apply>
<apply><csymbol cd="calculus1">nthdiff</csymbol>
<ci>n</ci>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
</apply>
<ci>x</ci>
</apply>
<apply><diff/>
<bvar><degree><cn>2</cn></degree><ci>x</ci></bvar>
<apply><sin/><ci>x</ci></apply>
</apply>
<apply>
<apply><csymbol cd="calculus1">nthdiff</csymbol>
<cn>2</cn>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="transc1">sin</csymbol><ci>x</ci></apply>
</bind>
</apply>
<ci>x</ci>
</apply>
Partial Differentiation <partialdiff/>
<apply><partialdiff/>
<list><cn>1</cn><cn>1</cn><cn>3</cn></list>
<ci type="function">f</ci>
</apply>
<apply><partialdiff/>
<list><cn>1</cn><cn>1</cn><cn>3</cn></list>
<lambda>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<bvar><ci>z</ci></bvar>
<apply><ci>f</ci><ci>x</ci><ci>y</ci><ci>z</ci></apply>
</lambda>
</apply>
<apply><partialdiff/>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<apply><ci type="function">f</ci><ci>x</ci><ci>y</ci></apply>
</apply>
<apply><partialdiff/>
<bvar><ci>x</ci><degree><ci>m</ci></degree></bvar>
<bvar><ci>y</ci><degree><ci>n</ci></degree></bvar>
<degree><ci>k</ci></degree>
<apply><ci type="function">f</ci>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
Rewrite: partialdiffdegree
<apply><partialdiff/>
<bvar><ci>x1</ci><degree><ci>n1</ci></degree></bvar>
<bvar><ci>xk</ci><degree><ci>nk</ci></degree></bvar>
<degree><ci>total-n1-nk</ci></degree>
<ci>expression-in-x1-xk</ci>
</apply>
<apply>
<apply><csymbol cd="calculus1">partialdiffdegree</csymbol>
<apply><csymbol cd="list1">list</csymbol>
<ci>n1</ci> <ci>nk</ci>
</apply>
<ci>total-n1-nk</ci>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x1</ci></bvar>
<bvar><ci>xk</ci></bvar>
<ci>expression-in-x1-xk</ci>
</bind>
</apply>
<ci>x1</ci>
<ci>xk</ci>
</apply>
<apply><csymbol cd="arith1">plus</csymbol>
<ci>n1</ci> <ci>nk</ci>
</apply>
<apply><partialdiff/>
<bvar><ci>x</ci><degree><ci>n</ci></degree></bvar>
<bvar><ci>y</ci><degree><ci>m</ci></degree></bvar>
<apply><sin/>
<apply><times/><ci>x</ci><ci>y</ci></apply>
</apply>
</apply>
<apply>
<apply><csymbol cd="calculus1">partialdiffdegree</csymbol>
<apply><csymbol cd="list1">list</csymbol>
<ci>n</ci><ci>m</ci>
</apply>
<apply><csymbol cd="arith1">plus</csymbol>
<ci>n</ci><ci>m</ci>
</apply>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<apply><csymbol cd="transc1">sin</csymbol>
<apply><csymbol cd="arith1">times</csymbol>
<ci>x</ci><ci>y</ci>
</apply>
</apply>
</bind>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
Divergence <divergence/>
<apply><divergence/><ci>a</ci></apply>
<apply><divergence/>
<ci type="vector">E</ci>
</apply>
<apply><divergence/>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<bvar><ci>z</ci></bvar>
<vector>
<apply><plus/><ci>x</ci><ci>y</ci></apply>
<apply><plus/><ci>x</ci><ci>z</ci></apply>
<apply><plus/><ci>z</ci><ci>y</ci></apply>
</vector>
</apply>
Gradient <grad/>
<apply><grad/><ci type="function">f</ci></apply>
<apply><grad/>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<bvar><ci>z</ci></bvar>
<apply><times/><ci>x</ci><ci>y</ci><ci>z</ci></apply>
</apply>
Curl <curl/>
<apply><curl/><ci>a</ci></apply>
Laplacian <laplacian/>
<apply><laplacian/><ci type="vector">E</ci></apply>
<apply><laplacian/>
<bvar><ci>x</ci></bvar>
<bvar><ci>y</ci></bvar>
<bvar><ci>z</ci></bvar>
<apply><ci>f</ci><ci>x</ci><ci>y</ci></apply>
</apply>
Theory of Sets Set <set>
<set>
<ci>a</ci><ci>b</ci><ci>c</ci>
</set>
<set>
<bvar><ci>x</ci></bvar>
<condition>
<apply><lt/><ci>x</ci><cn>5</cn></apply>
</condition>
<ci>x</ci>
</set>
<set>
<bvar><ci type="set">S</ci></bvar>
<condition>
<apply><in/><ci>S</ci><ci type="list">T</ci></apply>
</condition>
<ci>S</ci>
</set>
<set>
<bvar><ci> x </ci></bvar>
<condition>
<apply><and/>
<apply><lt/><ci>x</ci><cn>5</cn></apply>
<apply><in/><ci>x</ci><naturalnumbers/></apply>
</apply>
</condition>
<ci>x</ci>
</set>
List <list>
<list>
<ci>a</ci><ci>b</ci><ci>c</ci>
</list>
<list order="numeric">
<bvar><ci>x</ci></bvar>
<condition>
<apply><lt/><ci>x</ci><cn>5</cn></apply>
</condition>
</list>
Union <union/>
<apply><union/><ci>A</ci><ci>B</ci></apply>
<apply><union/>
<bvar><ci type="set">S</ci></bvar>
<domainofapplication>
<ci type="list">L</ci>
</domainofapplication>
<ci type="set"> S</ci>
</apply>
Intersect <intersect/>
<apply><intersect/>
<ci type="set"> A </ci>
<ci type="set"> B </ci>
</apply>
<apply><intersect/>
<bvar><ci type="set">S</ci></bvar>
<domainofapplication><ci type="list">L</ci></domainofapplication>
<ci type="set"> S </ci>
</apply>
Set inclusion <in/>
<apply><in/><ci>a</ci><ci type="set">A</ci></apply>
Set exclusion <notin/>
<apply><notin/><ci>a</ci><ci type="set">A</ci></apply>
Subset <subset/>
<apply><subset/>
<ci type="set">A</ci>
<ci type="set">B</ci>
</apply>
Proper Subset <prsubset/>
<apply><prsubset/>
<ci type="set">A</ci>
<ci type="set">B</ci>
</apply>
Not Subset <notsubset/>
<apply><notsubset/>
<ci type="set">A</ci>
<ci type="set">B</ci>
</apply>
Not Proper Subset <notprsubset/>
<apply><notprsubset/>
<ci type="set">A</ci>
<ci type="set">B</ci>
</apply>
Set Difference <setdiff/>
<apply><setdiff/>
<ci type="set">A</ci>
<ci type="set">B</ci>
</apply>
Cardinality <card/>
<apply><eq/>
<apply><card/><ci>A</ci></apply>
<cn>5</cn>
</apply>
Cartesian product <cartesianproduct/>
<apply><cartesianproduct/><ci>A</ci><ci>B</ci></apply>
Sequences and Series Sum <sum/>
<apply><sum/>
<bvar><ci>x</ci></bvar>
<lowlimit><ci>a</ci></lowlimit>
<uplimit><ci>b</ci></uplimit>
<apply><ci>f</ci><ci>x</ci></apply>
</apply>
<apply><sum/>
<bvar><ci>x</ci></bvar>
<condition>
<apply><in/><ci>x</ci><ci type="set">B</ci></apply>
</condition>
<apply><ci type="function">f</ci><ci>x</ci></apply>
</apply>
<apply><sum/>
<domainofapplication>
<ci type="set">B</ci>
</domainofapplication>
<ci type="function">f</ci>
</apply>
<apply><sum/>
<bvar><ci>i</ci></bvar>
<lowlimit><cn>0</cn></lowlimit>
<uplimit><cn>100</cn></uplimit>
<apply><power/><ci>x</ci><ci>i</ci></apply>
</apply>
<apply><csymbol cd="arith1">sum</csymbol>
<apply><csymbol cd="interval1">integer_interval</csymbol>
<cn>0</cn>
<cn>100</cn>
</apply>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>i</ci></bvar>
<apply><csymbol cd="arith1">power</csymbol><ci>x</ci><ci>i</ci></apply>
</bind>
</apply>
Product <product/>
<apply><product/>
<bvar><ci>x</ci></bvar>
<lowlimit><ci>a</ci></lowlimit>
<uplimit><ci>b</ci></uplimit>
<apply><ci type="function">f</ci>
<ci>x</ci>
</apply>
</apply>
<apply><product/>
<bvar><ci>x</ci></bvar>
<condition>
<apply><in/>
<ci>x</ci>
<ci type="set">B</ci>
</apply>
</condition>
<apply><ci>f</ci><ci>x</ci></apply>
</apply>
<apply><product/>
<bvar><ci>i</ci></bvar>
<lowlimit><cn>0</cn></lowlimit>
<uplimit><cn>100</cn></uplimit>
<apply><power/><ci>x</ci><ci>i</ci></apply>
</apply>
<apply><csymbol cd="arith1">product</csymbol>
<apply><csymbol cd="interval1">integer_interval</csymbol>
<cn>0</cn>
<cn>100</cn>
</apply>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>i</ci></bvar>
<apply><csymbol cd="arith1">power</csymbol><ci>x</ci><ci>i</ci></apply>
</bind>
</apply>
Limits <limit/>
<apply><limit/>
<bvar><ci>x</ci></bvar>
<lowlimit><cn>0</cn></lowlimit>
<apply><sin/><ci>x</ci></apply>
</apply>
<apply><limit/>
<bvar><ci>x</ci></bvar>
<condition>
<apply><tendsto/><ci>x</ci><cn>0</cn></apply>
</condition>
<apply><sin/><ci>x</ci></apply>
</apply>
<apply><limit/>
<bvar><ci>x</ci></bvar>
<condition>
<apply><tendsto type="above"/><ci>x</ci><ci>a</ci></apply>
</condition>
<apply><sin/><ci>x</ci></apply>
</apply>
Rewrite: limits condition
<apply><limit/>
<bvar><ci>x</ci></bvar>
<condition>
<apply><tendsto/><ci>x</ci><cn>0</cn></apply>
</condition>
<ci>expression-in-x</ci>
</apply>
<apply><csymbol cd="limit1">limit</csymbol>
<cn>0</cn>
<csymbol cd="limit1">null</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<ci>expression-in-x</ci>
</bind>
</apply>
Tends To <tendsto/>
<apply><tendsto type="above"/>
<apply><power/><ci>x</ci><cn>2</cn></apply>
<apply><power/><ci>a</ci><cn>2</cn></apply>
</apply>
<apply><tendsto/>
<vector><ci>x</ci><ci>y</ci></vector>
<vector>
<apply><ci type="function">f</ci><ci>x</ci><ci>y</ci></apply>
<apply><ci type="function">g</ci><ci>x</ci><ci>y</ci></apply>
</vector>
</apply>
Rewrite: tendsto
<tendsto/>
<semantics>
<ci>tendsto</ci>
<annotation-xml encoding="MathML-Content">
<tendsto/>
</annotation-xml>
</semantics>
Elementary classical functions Common trigonometric functions <sin/>, <cos/>, <tan/>, <sec/>, <csc/>, <cot/>
<apply><sin/><ci>x</ci></apply>
<apply><sin/>
<apply><plus/>
<apply><cos/><ci>x</ci></apply>
<apply><power/><ci>x</ci><cn>3</cn></apply>
</apply>
</apply>
Common inverses of trigonometric functions <arcsin/>, <arccos/>, <arctan/>, <arcsec/>, <arccsc/>, <arccot/>
<apply><arcsin/><ci>x</ci></apply>
<mrow>
<mi>arcsin</mi>
<mo>⁡</mo>
<mi>x</mi>
</mrow>
<mrow>
<msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup>
<mo>⁡</mo>
<mi>x</mi>
</mrow>
Common hyperbolic functions <sinh/>, <cosh/>, <tanh/>, <sech/>, <csch/>, <coth/>
<apply><sinh/><ci>x</ci></apply>
Common inverses of hyperbolic functions <arcsinh/>, <arccosh/>, <arctanh/>, <arcsech/>, <arccsch/>, <arccoth/>
<apply><arcsinh/><ci>x</ci></apply>
<mrow>
<mi>arcsinh</mi>
<mo>⁡</mo>
<mi>x</mi>
</mrow>
<mrow>
<msup><mi>sinh</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup>
<mo>⁡</mo>
<mi>x</mi>
</mrow>
Exponential <exp/>
<apply><exp/><ci>x</ci></apply>
Natural Logarithm <ln/>
<apply><ln/><ci>a</ci></apply>
Logarithm <log/> , <logbase>
<apply><log/>
<logbase><cn>3</cn></logbase>
<ci>x</ci>
</apply>
<apply><log/><ci>x</ci></apply>
<apply><plus/>
<apply>
<log/>
<logbase><cn>2</cn></logbase>
<ci>x</ci>
</apply>
<apply>
<log/>
<ci>y</ci>
</apply>
</apply>
<apply>
<csymbol cd="arith1">plus</csymbol>
<apply>
<csymbol cd="transc1">log</csymbol>
<cn>2</cn>
<ci>x</ci>
</apply>
<apply>
<csymbol cd="transc1">log</csymbol>
<cn>10</cn>
<ci>y</ci>
</apply>
</apply>
Statistics Mean <mean/>
<apply><mean/>
<cn>3</cn><cn>4</cn><cn>3</cn><cn>7</cn><cn>4</cn>
</apply>
<apply><mean/><ci>X</ci></apply>
Standard Deviation <sdev/>
<apply><sdev/>
<cn>3</cn><cn>4</cn><cn>2</cn><cn>2</cn>
</apply>
<apply><sdev/>
<ci type="discrete_random_variable">X</ci>
</apply>
Variance <variance/>
<apply><variance/>
<cn>3</cn><cn>4</cn><cn>2</cn><cn>2</cn>
</apply>
<apply><variance/>
<ci type="discrete_random_variable"> X</ci>
</apply>
Median <median/>
<apply><median/>
<cn>3</cn><cn>4</cn><cn>2</cn><cn>2</cn>
</apply>
Mode <mode/>
<apply><mode/>
<cn>3</cn><cn>4</cn><cn>2</cn><cn>2</cn>
</apply>
Moment <moment/>, <momentabout>
<apply><moment/>
<degree><cn>3</cn></degree>
<momentabout><mean/></momentabout>
<cn>6</cn><cn>4</cn><cn>2</cn><cn>2</cn><cn>5</cn>
</apply>
<apply><moment/>
<degree><cn>3</cn></degree>
<momentabout><ci>p</ci></momentabout>
<ci>X</ci>
</apply>
<apply><moment/>
<degree><cn>3</cn></degree>
<momentabout><ci>p</ci></momentabout>
<ci>X</ci>
</apply>
<apply><csymbol cd="s_dist1">moment</csymbol>
<cn>3</cn>
<ci>p</ci>
<ci>X</ci>
</apply>
Linear Algebra Vector <vector>
<vector>
<apply><plus/><ci>x</ci><ci>y</ci></apply>
<cn>3</cn>
<cn>7</cn>
</vector>
Matrix <matrix>
<matrix>
<bvar><ci type="integer">i</ci></bvar>
<bvar><ci type="integer">j</ci></bvar>
<condition>
<apply><and/>
<apply><in/>
<ci>i</ci>
<interval><ci>1</ci><ci>5</ci></interval>
</apply>
<apply><in/>
<ci>j</ci>
<interval><ci>5</ci><ci>9</ci></interval>
</apply>
</apply>
</condition>
<apply><power/><ci>i</ci><ci>j</ci></apply>
</matrix>
Matrix row <matrixrow>
Determinant <determinant/>
<apply><determinant/>
<ci type="matrix">A</ci>
</apply>
Transpose <transpose/>
<apply><transpose/>
<ci type="matrix">A</ci>
</apply>
Selector <selector/>
<apply><selector/><ci type="vector">V</ci><cn>1</cn></apply>
<apply><eq/>
<apply><selector/>
<matrix>
<matrixrow><cn>1</cn><cn>2</cn></matrixrow>
<matrixrow><cn>3</cn><cn>4</cn></matrixrow>
</matrix>
<cn>1</cn>
</apply>
<matrix>
<matrixrow><cn>1</cn><cn>2</cn></matrixrow>
</matrix>
</apply>
Vector product <vectorproduct/>
<apply><eq/>
<apply><vectorproduct/>
<ci type="vector"> A </ci>
<ci type="vector"> B </ci>
</apply>
<apply><times/>
<ci>a</ci>
<ci>b</ci>
<apply><sin/><ci>θ</ci></apply>
<ci type="vector"> N </ci>
</apply>
</apply>
Scalar product <scalarproduct/>
<apply><eq/>
<apply><scalarproduct/>
<ci type="vector">A</ci>
<ci type="vector">B</ci>
</apply>
<apply><times/>
<ci>a</ci>
<ci>b</ci>
<apply><cos/><ci>θ</ci></apply>
</apply>
</apply>
Outer product <outerproduct/>
<apply><outerproduct/>
<ci type="vector">A</ci>
<ci type="vector">B</ci>
</apply>
Constant and Symbol Elements integers <integers/>
<apply><in/>
<cn type="integer"> 42 </cn>
<integers/>
</apply>
reals <reals/>
<apply><in/>
<cn type="real"> 44.997</cn>
<reals/>
</apply>
Rational Numbers <rationals/>
<apply><in/>
<cn type="rational"> 22 <sep/>7</cn>
<rationals/>
</apply>
Natural Numbers <naturalnumbers/>
<apply><in/>
<cn type="integer">1729</cn>
<naturalnumbers/>
</apply>
complexes <complexes/>
<apply><in/>
<cn type="complex-cartesian">17<sep/>29</cn>
<complexes/>
</apply>
primes <primes/>
<apply><in/>
<cn type="integer">17</cn>
<primes/>
</apply>
Exponential e <exponentiale/>
<apply><eq/>
<apply><ln/><exponentiale/></apply>
<cn>1</cn>
</apply>
Imaginary i <imaginaryi/>
<apply><eq/>
<apply><power/><imaginaryi/><cn>2</cn></apply>
<cn>-1</cn>
</apply>
Not A Number <notanumber/>
<apply><eq/>
<apply><divide/><cn>0</cn><cn>0</cn></apply>
<notanumber/>
</apply>
True <true/>
<apply><eq/>
<apply><or/>
<true/>
<ci type="boolean">P</ci>
</apply>
<true/>
</apply>
False <false/>
<apply><eq/>
<apply><and/>
<false/>
<ci type="boolean">P</ci>
</apply>
<false/>
</apply>
Empty Set <emptyset/>
<apply><neq/>
<integers/>
<emptyset/>
</apply>
pi <pi/>
<apply><approx/>
<pi/>
<cn type="rational">22<sep/>7</cn>
</apply>
Euler gamma <eulergamma/>
<apply><approx/>
<eulergamma/>
<cn>0.5772156649</cn>
</apply>
infinity <infinity/>
<infinity/>
Deprecated Content Elements
Declare <declare>
Relation <reln>
Relation <fn>
The Strict Content MathML Transformation
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