UNPKG

mathmlben

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Visualization for goldstandard

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="Start 2 By 3 Matrix 1st Row 1st Column j 1 2nd Column j 2 3rd Column j 3 2nd Row 1st Column one-half 2nd Column j 3 minus one-half 3rd Column j 2 minus one-half EndMatrix equals left-parenthesis negative 1 right-parenthesis Superscript upper J Baseline left-parenthesis StartFraction left-parenthesis j 2 plus j 3 minus j 1 right-parenthesis left-parenthesis j 1 plus j 2 plus j 3 plus 1 right-parenthesis Over 2 j 2 left-parenthesis 2 j 2 plus 1 right-parenthesis 2 j 3 left-parenthesis 2 j 3 plus 1 right-parenthesis EndFraction right-parenthesis Superscript one-half"> <semantics> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="132" data-semantic-children="37,131" data-semantic-content="40"> <mrow class="MJX-TeXAtom-ORD"> <mrow data-semantic-type="matrix" data-semantic-role="unknown" data-semantic-id="37" data-semantic-children="13,36" data-semantic-content="0,38" data-semantic-parent="132"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="0" data-semantic-parent="37">{</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr data-semantic-type="row" data-semantic-role="matrix" data-semantic-id="13" data-semantic-children="4,8,12" data-semantic-parent="37"> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="13"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="3" data-semantic-children="1,2" data-semantic-parent="4"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="1" data-semantic-parent="3">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="2" data-semantic-parent="3">1</mn> </mrow> </msub> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="8" data-semantic-children="7" data-semantic-parent="13"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="7" data-semantic-children="5,6" data-semantic-parent="8"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="5" data-semantic-parent="7">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="6" data-semantic-parent="7">2</mn> </mrow> </msub> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="12" data-semantic-children="11" data-semantic-parent="13"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="11" data-semantic-children="9,10" data-semantic-parent="12"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="9" 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</mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="26" data-semantic-children="25" data-semantic-parent="36"> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="25" data-semantic-children="20,24" data-semantic-content="21" data-semantic-parent="26"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="20" data-semantic-children="18,19" data-semantic-parent="25"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="18" data-semantic-parent="20">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="19" data-semantic-parent="20">3</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="21" data-semantic-parent="25" data-semantic-operator="infixop,−"><!-- − --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-id="24" data-semantic-children="22,23" data-semantic-parent="25"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="22" data-semantic-parent="24">1</mn> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="23" data-semantic-parent="24">2</mn> </mfrac> </mrow> </mrow> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="35" data-semantic-children="34" data-semantic-parent="36"> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="34" data-semantic-children="29,33" data-semantic-content="30" data-semantic-parent="35"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="29" data-semantic-children="27,28" data-semantic-parent="34"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="27" data-semantic-parent="29">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="28" data-semantic-parent="29">2</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="30" data-semantic-parent="34" data-semantic-operator="infixop,−"><!-- − --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-id="33" data-semantic-children="31,32" data-semantic-parent="34"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="31" data-semantic-parent="33">1</mn> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="32" data-semantic-parent="33">2</mn> </mfrac> </mrow> </mrow> </mtd> </mtr> </mtable> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="38" data-semantic-parent="37">}</mo> </mrow> </mrow> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="40" data-semantic-parent="132" data-semantic-operator="relseq,=">=</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="131" data-semantic-children="46,127" data-semantic-content="130" data-semantic-parent="132"> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="46" data-semantic-children="129,45" data-semantic-parent="131" data-semantic-fencepointer="44"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="129" data-semantic-children="128" data-semantic-content="41,44" data-semantic-parent="46"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="41" data-semantic-parent="129">(</mo> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="128" data-semantic-children="43" data-semantic-content="42" data-semantic-parent="129"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="42" data-semantic-parent="128" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="43" data-semantic-parent="128">1</mn> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="44" data-semantic-parent="129">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="45" data-semantic-parent="46">J</mi> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="130" data-semantic-parent="131" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="127" data-semantic-children="123,126" data-semantic-parent="131"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="123" data-semantic-children="121" data-semantic-content="47,122" data-semantic-parent="127"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="47" data-semantic-parent="123" data-semantic-operator="fenced">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="121" data-semantic-children="82,120" data-semantic-parent="123"> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="82" data-semantic-children="78,80" data-semantic-content="81" data-semantic-parent="121"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="78" data-semantic-children="77" data-semantic-content="48,60" data-semantic-parent="82"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="48" data-semantic-parent="78" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="77" data-semantic-children="76,59" data-semantic-content="56" data-semantic-parent="78"> <mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="76" data-semantic-children="51,55" data-semantic-content="52" data-semantic-parent="77"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="51" data-semantic-children="49,50" data-semantic-parent="76"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="49" data-semantic-parent="51">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="50" data-semantic-parent="51">2</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="52" data-semantic-parent="76" data-semantic-operator="infixop,+">+</mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="55" data-semantic-children="53,54" data-semantic-parent="76"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="53" data-semantic-parent="55">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="54" data-semantic-parent="55">3</mn> </mrow> </msub> </mrow> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="56" data-semantic-parent="77" data-semantic-operator="infixop,−"><!-- − --> </mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="59" data-semantic-children="57,58" data-semantic-parent="77"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="57" data-semantic-parent="59">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="58" data-semantic-parent="59">1</mn> </mrow> </msub> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="60" data-semantic-parent="78" data-semantic-operator="fenced">)</mo> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="81" data-semantic-parent="82" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="80" data-semantic-children="79" data-semantic-content="61,75" data-semantic-parent="82"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="61" data-semantic-parent="80" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="79" data-semantic-children="64,68,72,74" data-semantic-content="65,69,73" data-semantic-parent="80"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="64" data-semantic-children="62,63" data-semantic-parent="79"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="62" data-semantic-parent="64">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="63" data-semantic-parent="64">1</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="65" data-semantic-parent="79" data-semantic-operator="infixop,+">+</mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="68" data-semantic-children="66,67" data-semantic-parent="79"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="66" data-semantic-parent="68">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="67" data-semantic-parent="68">2</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="69" data-semantic-parent="79" data-semantic-operator="infixop,+">+</mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="72" data-semantic-children="70,71" data-semantic-parent="79"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="70" data-semantic-parent="72">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="71" data-semantic-parent="72">3</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="73" data-semantic-parent="79" data-semantic-operator="infixop,+">+</mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="74" data-semantic-parent="79">1</mn> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="75" data-semantic-parent="80" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="120" data-semantic-children="83,86,110,95,98,114" data-semantic-content="115,116,117,118,119" data-semantic-parent="121"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="83" data-semantic-parent="120">2</mn> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="115" data-semantic-parent="120" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="86" data-semantic-children="84,85" data-semantic-parent="120"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="84" data-semantic-parent="86">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="85" data-semantic-parent="86">2</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="116" data-semantic-parent="120" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="110" data-semantic-children="109" data-semantic-content="87,94" data-semantic-parent="120"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="87" data-semantic-parent="110" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="109" data-semantic-children="108,93" data-semantic-content="92" data-semantic-parent="110"> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="108" data-semantic-children="88,91" data-semantic-content="107" data-semantic-parent="109"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="88" data-semantic-parent="108">2</mn> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="107" data-semantic-parent="108" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="91" data-semantic-children="89,90" data-semantic-parent="108"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="89" data-semantic-parent="91">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="90" data-semantic-parent="91">2</mn> </mrow> </msub> </mrow> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="92" data-semantic-parent="109" data-semantic-operator="infixop,+">+</mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="93" data-semantic-parent="109">1</mn> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="94" data-semantic-parent="110" data-semantic-operator="fenced">)</mo> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="117" data-semantic-parent="120" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="95" data-semantic-parent="120">2</mn> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="118" data-semantic-parent="120" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="98" data-semantic-children="96,97" data-semantic-parent="120"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="96" data-semantic-parent="98">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="97" data-semantic-parent="98">3</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="119" data-semantic-parent="120" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="114" data-semantic-children="113" data-semantic-content="99,106" data-semantic-parent="120"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="99" data-semantic-parent="114" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="113" data-semantic-children="112,105" data-semantic-content="104" data-semantic-parent="114"> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="112" data-semantic-children="100,103" data-semantic-content="111" data-semantic-parent="113"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="100" data-semantic-parent="112">2</mn> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="111" data-semantic-parent="112" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="103" data-semantic-children="101,102" data-semantic-parent="112"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="101" data-semantic-parent="103">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="102" data-semantic-parent="103">3</mn> </mrow> </msub> </mrow> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="104" data-semantic-parent="113" data-semantic-operator="infixop,+">+</mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="105" data-semantic-parent="113">1</mn> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="106" data-semantic-parent="114" data-semantic-operator="fenced">)</mo> </mrow> </mrow> </mfrac> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="122" data-semantic-parent="123" data-semantic-operator="fenced">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-id="126" data-semantic-children="124,125" data-semantic-parent="127"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="124" data-semantic-parent="126">1</mn> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="125" data-semantic-parent="126">2</mn> </mfrac> </mrow> </msup> </mrow> </mrow> <annotation encoding="application/x-tex">{\begin{Bmatrix}j_{1}&amp;j_{2}&amp;j_{3}\\{\frac {1}{2}}&amp;j_{3}-{\frac {1}{2}}&amp;j_{2}-{\frac {1}{2}}\end{Bmatrix}}=(-1)^{J}\left({\frac {(j_{2}+j_{3}-j_{1})(j_{1}+j_{2}+j_{3}+1)}{2j_{2}(2j_{2}+1)2j_{3}(2j_{3}+1)}}\right)^{\frac {1}{2}}</annotation> </semantics> </math>