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="Subscript 3 Baseline phi 2 left-parenthesis StartLayout 1st Row a comma b comma q Superscript negative n Baseline 2nd Row c comma a b q Superscript 1 minus n Baseline slash c EndLayout semicolon q comma q right-parenthesis equals StartFraction left-parenthesis c slash a comma c slash b semicolon q right-parenthesis Subscript n Baseline Over left-parenthesis c comma c slash left-parenthesis a b right-parenthesis semicolon q right-parenthesis Subscript n Baseline EndFraction"> <semantics> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="87" data-semantic-children="86,84" data-semantic-content="46"> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="86" data-semantic-children="7,45" data-semantic-content="85" data-semantic-parent="87"> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="7" 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data-semantic-role="comma" data-semantic-id="12" data-semantic-parent="18" data-semantic-operator="punctuated">,</mo> <msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="17" data-semantic-children="13,16" data-semantic-parent="18"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="13" data-semantic-parent="17">q</mi> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="16" data-semantic-children="15" data-semantic-content="14" data-semantic-parent="17"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="14" data-semantic-parent="16" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="15" data-semantic-parent="16">n</mi> </mrow> </msup> </mrow> </mrow> <mrow data-semantic-added="true" data-semantic-type="line" data-semantic-role="binomial" data-semantic-id="37" data-semantic-children="35" data-semantic-parent="38"> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="35" data-semantic-children="19,20,34" data-semantic-content="20" data-semantic-parent="37"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="19" data-semantic-parent="35">c</mi> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="20" data-semantic-parent="35" data-semantic-operator="punctuated">,</mo> <mrow data-semantic-type="infixop" data-semantic-role="division" data-semantic-id="34" data-semantic-children="33,30" data-semantic-content="29" data-semantic-parent="35"> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="33" data-semantic-children="21,22,28" data-semantic-content="31,32" data-semantic-parent="34"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="21" data-semantic-parent="33">a</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="31" data-semantic-parent="33" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="22" data-semantic-parent="33">b</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="32" data-semantic-parent="33" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <msup data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-id="28" data-semantic-children="23,27" data-semantic-parent="33"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="23" data-semantic-parent="28">q</mi> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="27" data-semantic-children="24,26" data-semantic-content="25" data-semantic-parent="28"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="24" data-semantic-parent="27">1</mn> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="25" data-semantic-parent="27" data-semantic-operator="infixop,−"><!-- − --> </mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="26" data-semantic-parent="27">n</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="29" data-semantic-parent="34" data-semantic-operator="infixop,/">/</mo> </mrow> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="30" data-semantic-parent="34">c</mi> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="39" data-semantic-parent="43" data-semantic-operator="punctuated">;</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="40" data-semantic-parent="43">q</mi> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="41" data-semantic-parent="43" data-semantic-operator="punctuated">,</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="42" data-semantic-parent="43">q</mi> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="44" data-semantic-parent="45" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="46" data-semantic-parent="87" data-semantic-operator="relseq,=">=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="84" data-semantic-children="63,83" data-semantic-parent="87"> <msub data-semantic-type="subscript" data-semantic-role="leftright" data-semantic-id="63" data-semantic-children="61,62" data-semantic-parent="84"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="61" data-semantic-children="59" data-semantic-content="47,60" data-semantic-parent="63"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="47" data-semantic-parent="61" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="59" data-semantic-children="57,51,58,55,56" data-semantic-content="51,55" data-semantic-parent="61"> <mrow data-semantic-type="infixop" data-semantic-role="division" data-semantic-id="57" data-semantic-children="48,50" data-semantic-content="49" data-semantic-parent="59"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="48" data-semantic-parent="57">c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="49" data-semantic-parent="57" data-semantic-operator="infixop,/">/</mo> </mrow> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="50" data-semantic-parent="57">a</mi> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="51" data-semantic-parent="59" data-semantic-operator="punctuated">,</mo> <mrow data-semantic-type="infixop" data-semantic-role="division" data-semantic-id="58" data-semantic-children="52,54" data-semantic-content="53" data-semantic-parent="59"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="52" data-semantic-parent="58">c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="53" data-semantic-parent="58" data-semantic-operator="infixop,/">/</mo> </mrow> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="54" data-semantic-parent="58">b</mi> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="55" data-semantic-parent="59" data-semantic-operator="punctuated">;</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="56" data-semantic-parent="59">q</mi> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="60" data-semantic-parent="61" data-semantic-operator="fenced">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="62" data-semantic-parent="63">n</mi> </mrow> </msub> <msub data-semantic-type="subscript" data-semantic-role="leftright" data-semantic-id="83" data-semantic-children="81,82" data-semantic-parent="84"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="81" data-semantic-children="79" data-semantic-content="64,80" data-semantic-parent="83"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="64" data-semantic-parent="81" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="79" data-semantic-children="65,66,78,73,74" data-semantic-content="66,73" data-semantic-parent="81"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="65" data-semantic-parent="79">c</mi> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="66" data-semantic-parent="79" data-semantic-operator="punctuated">,</mo> <mrow data-semantic-type="infixop" data-semantic-role="division" data-semantic-id="78" data-semantic-children="67,77" data-semantic-content="68" data-semantic-parent="79"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="67" data-semantic-parent="78">c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo data-semantic-type="operator" data-semantic-role="division" data-semantic-id="68" data-semantic-parent="78" data-semantic-operator="infixop,/">/</mo> </mrow> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="77" data-semantic-children="76" data-semantic-content="69,72" data-semantic-parent="78"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="69" data-semantic-parent="77" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="76" data-semantic-children="70,71" data-semantic-content="75" data-semantic-parent="77"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="70" data-semantic-parent="76">a</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="75" data-semantic-parent="76" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="71" data-semantic-parent="76">b</mi> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="72" data-semantic-parent="77" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mo data-semantic-type="punctuation" data-semantic-role="unknown" data-semantic-id="73" data-semantic-parent="79" data-semantic-operator="punctuated">;</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="74" data-semantic-parent="79">q</mi> </mrow> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="80" data-semantic-parent="81" data-semantic-operator="fenced">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="82" data-semantic-parent="83">n</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <annotation encoding="application/x-tex">{{}_{3}\phi _{2}}\left({a,b,q^{-n} \atop c,abq^{1-n}/c};q,q\right)={\frac {\left(c/a,c/b;q\right)_{n}}{\left(c,c/(ab);q\right)_{n}}}</annotation> </semantics> </math>