data/mathoid/233.mml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="alpha 1 equals StartFraction upper X left-parenthesis tau 1 right-parenthesis y Over parallel-to upper X left-parenthesis tau 1 right-parenthesis parallel-to EndFraction ellipsis alpha Subscript j plus 1 Baseline equals StartFraction upper X left-parenthesis alpha Subscript j plus 1 Baseline right-parenthesis y Over parallel-to upper X left-parenthesis tau Subscript j plus 1 Baseline right-parenthesis parallel-to EndFraction comma alpha Subscript j plus 2 Baseline equals StartFraction upper X left-parenthesis tau Subscript j plus 2 Baseline right-parenthesis y Over parallel-to upper X left-parenthesis tau Subscript j plus 2 Baseline right-parenthesis parallel-to EndFraction">
<semantics>
<mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="115" data-semantic-children="113,70,114" data-semantic-content="70">
<mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="113" data-semantic-children="2,112,69" data-semantic-content="3,37" data-semantic-parent="115">
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="2" data-semantic-children="0,1" data-semantic-parent="113">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="0" data-semantic-parent="2">α
<!-- α -->
</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="1" data-semantic-parent="2">1</mn>
</mrow>
</msub>
<mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="3" data-semantic-parent="113" data-semantic-operator="relseq,=">=</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="112" data-semantic-children="29,30,36" data-semantic-content="110,111" data-semantic-parent="113">
<mrow class="MJX-TeXAtom-ORD">
<mfrac data-semantic-type="fraction" data-semantic-role="division" data-semantic-id="29" data-semantic-children="15,28" data-semantic-parent="112">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="15" data-semantic-children="13,10" data-semantic-content="14" data-semantic-parent="29">
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="13" data-semantic-children="4,11" data-semantic-content="12,4" data-semantic-parent="15">
<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="4" data-semantic-parent="13" data-semantic-operator="appl">X</mi>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="5" data-semantic-parent="11" data-semantic-operator="fenced">(</mo>
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="8" data-semantic-children="6,7" data-semantic-parent="11">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="6" data-semantic-parent="8">τ
<!-- τ -->
</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="7" data-semantic-parent="8">1</mn>
</mrow>
</msub>
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</mrow>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="14" data-semantic-parent="15" 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="10" data-semantic-parent="15">y</mi>
</mrow>
<mrow data-semantic-type="postfixop" data-semantic-role="unknown" data-semantic-id="28" data-semantic-children="27" data-semantic-content="23" data-semantic-parent="29">
<mrow data-semantic-type="prefixop" data-semantic-role="unknown" data-semantic-id="27" data-semantic-children="26" data-semantic-content="16" data-semantic-parent="28">
<mo stretchy="false" data-semantic-type="operator" data-semantic-role="unknown" data-semantic-id="16" data-semantic-parent="27" data-semantic-operator="prefixop,∥">∥
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</mo>
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="26" data-semantic-children="17,24" data-semantic-content="25,17" data-semantic-parent="27">
<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="17" data-semantic-parent="26" data-semantic-operator="appl">X</mi>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="18" data-semantic-parent="24" data-semantic-operator="fenced">(</mo>
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="21" data-semantic-children="19,20" data-semantic-parent="24">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="19" data-semantic-parent="21">τ
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<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="20" data-semantic-parent="21">1</mn>
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</mrow>
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</mrow>
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</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="110" data-semantic-parent="112" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mo data-semantic-type="punctuation" data-semantic-role="ellipsis" data-semantic-id="30" data-semantic-parent="112">…
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</mo>
<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="greekletter" data-semantic-id="36" data-semantic-children="31,35" data-semantic-parent="112">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="31" data-semantic-parent="36">α
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<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="33" data-semantic-parent="35" data-semantic-operator="infixop,+">+</mo>
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<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="52" data-semantic-children="50,47" data-semantic-content="51" data-semantic-parent="69">
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="50" data-semantic-children="38,48" data-semantic-content="49,38" data-semantic-parent="52">
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="39" data-semantic-parent="48" data-semantic-operator="fenced">(</mo>
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</mrow>
</msub>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="51" data-semantic-parent="52" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mrow data-semantic-type="postfixop" data-semantic-role="unknown" data-semantic-id="68" data-semantic-children="67" data-semantic-content="63" data-semantic-parent="69">
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<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="64" data-semantic-children="61" data-semantic-content="55,62" data-semantic-parent="66">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="55" data-semantic-parent="64" data-semantic-operator="fenced">(</mo>
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="61" data-semantic-children="56,60" data-semantic-parent="64">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="56" data-semantic-parent="61">τ
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="57" data-semantic-parent="60">j</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="58" data-semantic-parent="60" data-semantic-operator="infixop,+">+</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="59" data-semantic-parent="60">1</mn>
</mrow>
</msub>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="62" data-semantic-parent="64" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
</mrow>
<mo stretchy="false" data-semantic-type="operator" data-semantic-role="unknown" data-semantic-id="63" data-semantic-parent="68" data-semantic-operator="postfixop,∥">∥
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</mrow>
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</mrow>
</mrow>
<mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="70" data-semantic-parent="115" data-semantic-operator="punctuated">,</mo>
<mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="114" data-semantic-children="76,109" data-semantic-content="77" data-semantic-parent="115">
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="76" data-semantic-children="71,75" data-semantic-parent="114">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="71" data-semantic-parent="76">α
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<mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="75" data-semantic-children="72,74" data-semantic-content="73" data-semantic-parent="76">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="72" data-semantic-parent="75">j</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="73" data-semantic-parent="75" data-semantic-operator="infixop,+">+</mo>
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<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="92" data-semantic-children="90,87" data-semantic-content="91" data-semantic-parent="109">
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="90" data-semantic-children="78,88" data-semantic-content="89,78" data-semantic-parent="92">
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</msub>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="91" data-semantic-parent="92" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mrow data-semantic-type="postfixop" data-semantic-role="unknown" data-semantic-id="108" data-semantic-children="107" data-semantic-content="103" data-semantic-parent="109">
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<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="96" data-semantic-parent="101">τ
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="97" data-semantic-parent="100">j</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="98" data-semantic-parent="100" data-semantic-operator="infixop,+">+</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="99" data-semantic-parent="100">2</mn>
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</msub>
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<annotation encoding="application/x-tex">\alpha _{1}={\frac {X(\tau _{1})y}{\parallel X(\tau _{1})\parallel }}\dots \alpha _{j+1}={\frac {X(\alpha _{j+1})y}{\parallel X(\tau _{j+1})\parallel }},\alpha _{j+2}={\frac {X(\tau _{j+2})y}{\parallel X(\tau _{j+2})\parallel }}</annotation>
</semantics>
</math>