Merged ASTs

MathML - AST Renderer

referenceMML

<math xmlns="http://www.w3.org/1998/Math/MathML"
      alttext="\displaystyle\overline{F}_{v,i}=\sum_{i\neq j}|\sum_{k=1}^{N_{C}}c_{\mathsf{I}_{U}(i),\mathsf{I}_{C}(k),\mathsf{I}_{U}(j)}\hat{\phi}_{\mathsf{I}_{C}(k)}^{(1)}|"
      class="ltx_Math" display="inline" id="p1.1.m1.1">
  <semantics id="a0">
    <mrow id="a1" xref="a86">
      <msub id="a2" xref="a88">
        <mover accent="true" id="a3" xref="a89">
          <mi id="a4" xref="a91">F</mi>
          <mo id="a5" xref="a90">¯</mo>
        </mover>
        <mrow id="a6" xref="a92">
          <mi id="a7" xref="a93">v</mi>
          <mo id="a8" xref="a92">,</mo>
          <mi id="a9" xref="a94">i</mi>
        </mrow>
      </msub>
      <mo id="a10" xref="a87">=</mo>
      <mrow id="a11" xref="a95">
        <mstyle displaystyle="true" id="a12" xref="a96">
          <munder id="a13" xref="a96">
            <mo id="a14" largeop="true" movablelimits="false" symmetric="true" xref="a97">∑</mo>
            <mrow id="a15" xref="a98">
              <mi id="a16" xref="a100">i</mi>
              <mo id="a17" xref="a99">≠</mo>
              <mi id="a18" xref="a101">j</mi>
            </mrow>
          </munder>
        </mstyle>
        <mrow id="a19" xref="a102">
          <mo id="a20" stretchy="false" xref="a103">|</mo>
          <mrow id="a21" xref="a104">
            <mstyle displaystyle="true" id="a22" xref="a105">
              <munderover id="a23" xref="a105">
                <mo id="a24" largeop="true" movablelimits="false" symmetric="true" xref="a106">∑</mo>
                <mrow id="a25" xref="a105">
                  <mi id="a26" xref="a107">k</mi>
                  <mo id="a27" xref="a106">=</mo>
                  <mn id="a28" xref="a108">1</mn>
                </mrow>
                <msub id="a29" xref="a109">
                  <mi id="a30" xref="a110">N</mi>
                  <mi id="a31" xref="a111">C</mi>
                </msub>
              </munderover>
            </mstyle>
            <mo id="a32" xref="a104">⁡</mo>
            <mrow id="a33" xref="a112">
              <msub id="a34" xref="a114">
                <mi id="a35" xref="a115">c</mi>
                <mrow id="a36" xref="a116">
                  <mrow id="a37" xref="a117">
                    <msub id="a38" xref="a119">
                      <mi id="a39" xref="a120">𝖨</mi>
                      <mi id="a40" xref="a121">U</mi>
                    </msub>
                    <mo id="a41" xref="a118">⁢</mo>
                    <mrow id="a42" xref="a117">
                      <mo id="a43" stretchy="false" xref="a117">(</mo>
                      <mi id="a44" xref="a122">i</mi>
                      <mo id="a45" stretchy="false" xref="a117">)</mo>
                    </mrow>
                  </mrow>
                  <mo id="a46" xref="a116">,</mo>
                  <mrow id="a47" xref="a123">
                    <msub id="a48" xref="a125">
                      <mi id="a49" xref="a126">𝖨</mi>
                      <mi id="a50" xref="a127">C</mi>
                    </msub>
                    <mo id="a51" xref="a124">⁢</mo>
                    <mrow id="a52" xref="a123">
                      <mo id="a53" stretchy="false" xref="a123">(</mo>
                      <mi id="a54" xref="a128">k</mi>
                      <mo id="a55" stretchy="false" xref="a123">)</mo>
                    </mrow>
                  </mrow>
                  <mo id="a56" xref="a116">,</mo>
                  <mrow id="a57" xref="a129">
                    <msub id="a58" xref="a131">
                      <mi id="a59" xref="a132">𝖨</mi>
                      <mi id="a60" xref="a133">U</mi>
                    </msub>
                    <mo id="a61" xref="a130">⁢</mo>
                    <mrow id="a62" xref="a129">
                      <mo id="a63" stretchy="false" xref="a129">(</mo>
                      <mi id="a64" xref="a134">j</mi>
                      <mo id="a65" stretchy="false" xref="a129">)</mo>
                    </mrow>
                  </mrow>
                </mrow>
              </msub>
              <mo id="a66" xref="a113">⁢</mo>
              <msubsup id="a67" xref="a135">
                <mover accent="true" id="a68" xref="a138">
                  <mi id="a69" xref="a140">ϕ</mi>
                  <mo id="a70" stretchy="false" xref="a139">^</mo>
                </mover>
                <mrow id="a71" xref="a141">
                  <msub id="a72" xref="a143">
                    <mi id="a73" xref="a144">𝖨</mi>
                    <mi id="a74" xref="a145">C</mi>
                  </msub>
                  <mo id="a75" xref="a142">⁢</mo>
                  <mrow id="a76" xref="a141">
                    <mo id="a77" stretchy="false" xref="a141">(</mo>
                    <mi id="a78" xref="a146">k</mi>
                    <mo id="a79" stretchy="false" xref="a141">)</mo>
                  </mrow>
                </mrow>
                <mrow id="a80" xref="a135">
                  <mo id="a81" stretchy="false" xref="a135">(</mo>
                  <mn id="a82" xref="a147">1</mn>
                  <mo id="a83" stretchy="false" xref="a135">)</mo>
                </mrow>
              </msubsup>
            </mrow>
          </mrow>
          <mo id="a84" stretchy="false" xref="a103">|</mo>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="a85">
      <apply id="a86" xref="a1">
        <eq id="a87" xref="a10"/>
        <apply id="a88" xref="a2">
          <apply id="a89" xref="a3">
            <ci id="a90" xref="a5">¯</ci>
            <ci id="a91" xref="a4">𝐹</ci>
          </apply>
          <ci id="a93" xref="a7">𝑣</ci>
          <ci id="a94" xref="a9">𝑖</ci>
        </apply>
        <apply id="a95" xref="a11">
          <apply id="a96" xref="a12">
            <sum id="a97" xref="a14"/>
            <apply id="a98" xref="a15">
              <neq id="a99" xref="a17"/>
              <ci id="a100" xref="a16">𝑖</ci>
              <ci id="a101" xref="a18">𝑗</ci>
            </apply>
          </apply>
          <apply id="a102" xref="a19">
            <abs id="a103" xref="a20"/>
            <apply id="a104" xref="a21">
              
              <csymbol cd="dlmf" id="a106" xref="a24">semantic-sum</csymbol>
              <ci id="a107" xref="a26">𝑘</ci>
              <cn id="a108" type="integer" xref="a28">1</cn>
              <ci id="a110" xref="a29">Nc</ci>
              
              <apply id="a112" xref="a33">
                <times id="a113" xref="a66"/>
                <apply id="a114" xref="a34">
                  <ci id="a115" xref="a35">𝑐</ci>
                  <apply id="a117" xref="a37">
                    <apply id="a119" xref="a38">
                      <ci id="a120" xref="a39">𝖨</ci>
                      <ci id="a121" xref="a40">𝑈</ci>
                    </apply>
                    <ci id="a122" xref="a44">𝑖</ci>
                  </apply>
                  <apply id="a123" xref="a47">
                    <apply id="a125" xref="a48">
                      <ci id="a126" xref="a49">𝖨</ci>
                      <ci id="a127" xref="a50">𝐶</ci>
                    </apply>
                    <ci id="a128" xref="a54">𝑘</ci>
                  </apply>
                  <apply id="a129" xref="a57">
                    <apply id="a131" xref="a58">
                      <ci id="a132" xref="a59">𝖨</ci>
                      <ci id="a133" xref="a60">𝑈</ci>
                    </apply>
                    <ci id="a134" xref="a64">𝑗</ci>
                  </apply>
                </apply>
                <apply id="a135" xref="a67">
                  <partialdiff/>
                  <cn id="a147" type="integer" xref="a80">1</cn>
                  <apply id="a137" xref="a67">
                    <apply id="a138" xref="a68">
                      <ci id="a139" xref="a70">^</ci>
                      <ci id="a140" xref="a69">italic-ϕ</ci>
                    </apply>
                    <apply id="a141" xref="a71">
                      <apply id="a143" xref="a72">
                        <ci id="a144" xref="a73">𝖨</ci>
                        <ci id="a145" xref="a74">𝐶</ci>
                      </apply>
                      <ci id="a146" xref="a78">𝑘</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="a148">\displaystyle\overline{F}_{v,i}=\sum_{i\neq
      j}|\sum_{k=1}^{N_{C}}c_{\mathsf{I}_{U}(i),\mathsf{I}_{C}(k),\mathsf{I}_{U}(j)}\hat{\phi}_{\mathsf{I}_{C}(k)}^{(1)}|
    </annotation>
  </semantics>
</math>

comparisonMML

<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"
      alttext="\displaystyle\overline{F}_{v}(i)=\sum_{i\neq j}|\sum_{k=1}^{N_{C}}c_{N_{U}(i),N_{C}(k),N_{U}(j)}\hat{\ddot{\phi}}_{N_{C}(k)}|"
      class="ltx_Math" display="inline" id="p1.1.m1.1">
  <semantics id="b1">
    <mrow id="b2" xref="b87">
      <mrow id="b3" xref="b89">
        <msub id="b4" xref="undefined">
          <mover accent="true" id="b5" xref="b90">
            <mi id="b6" xref="b92">F</mi>
            <mo id="b7" xref="b91">¯</mo>
          </mover>
          <mi id="b8" xref="b93">v</mi>
        </msub>
        <mo id="b9" xref="undefined">⁢</mo>
        <mrow id="b10" xref="b89">
          <mo id="b11" stretchy="false" xref="b89">(</mo>
          <mi id="b12" xref="b94">i</mi>
          <mo id="b13" stretchy="false" xref="b89">)</mo>
        </mrow>
      </mrow>
      <mo id="b14" xref="b88">=</mo>
      <mrow id="b15" xref="b95">
        <mstyle displaystyle="true" id="b16" xref="b96">
          <munder id="b17" xref="b96">
            <mo id="b18" largeop="true" movablelimits="false" symmetric="true" xref="b97">∑</mo>
            <mrow id="b19" xref="b98">
              <mi id="b20" xref="b100">i</mi>
              <mo id="b21" xref="b99">≠</mo>
              <mi id="b22" xref="b101">j</mi>
            </mrow>
          </munder>
        </mstyle>
        <mrow id="b23" xref="b102">
          <mo id="b24" stretchy="false" xref="b103">|</mo>
          <mrow id="b25" xref="b104">
            <mstyle displaystyle="true" id="b26" xref="b105">
              <munderover id="b27" xref="b105">
                <mo id="b28" largeop="true" movablelimits="false" symmetric="true" xref="b108">∑</mo>
                <mrow id="b29" xref="b109">
                  <mi id="b30" xref="b111">k</mi>
                  <mo id="b31" xref="b110">=</mo>
                  <mn id="b32" xref="b112">1</mn>
                </mrow>
                <msub id="b33" xref="b113">
                  <mi id="b34" xref="b114">N</mi>
                  <mi id="b35" xref="b115">C</mi>
                </msub>
              </munderover>
            </mstyle>
            <mrow id="b36" xref="b116">
              <msub id="b37" xref="b118">
                <mi id="b38" xref="b119">c</mi>
                <mrow id="b39" xref="b120">
                  <mrow id="b40" xref="b121">
                    <msub id="b41" xref="b123">
                      <mi id="b42" xref="b124">N</mi>
                      <mi id="b43" xref="b125">U</mi>
                    </msub>
                    <mo id="b44" xref="b122">⁢</mo>
                    <mrow id="b45" xref="b121">
                      <mo id="b46" stretchy="false" xref="b121">(</mo>
                      <mi id="b47" xref="b126">i</mi>
                      <mo id="b48" stretchy="false" xref="b121">)</mo>
                    </mrow>
                  </mrow>
                  <mo id="b49" xref="b120">,</mo>
                  <mrow id="b50" xref="b127">
                    <msub id="b51" xref="b129">
                      <mi id="b52" xref="b130">N</mi>
                      <mi id="b53" xref="b131">C</mi>
                    </msub>
                    <mo id="b54" xref="b128">⁢</mo>
                    <mrow id="b55" xref="b127">
                      <mo id="b56" stretchy="false" xref="b127">(</mo>
                      <mi id="b57" xref="b132">k</mi>
                      <mo id="b58" stretchy="false" xref="b127">)</mo>
                    </mrow>
                  </mrow>
                  <mo id="b59" xref="b120">,</mo>
                  <mrow id="b60" xref="b133">
                    <msub id="b61" xref="b135">
                      <mi id="b62" xref="b136">N</mi>
                      <mi id="b63" xref="b137">U</mi>
                    </msub>
                    <mo id="b64" xref="b134">⁢</mo>
                    <mrow id="b65" xref="b133">
                      <mo id="b66" stretchy="false" xref="b133">(</mo>
                      <mi id="b67" xref="b138">j</mi>
                      <mo id="b68" stretchy="false" xref="b133">)</mo>
                    </mrow>
                  </mrow>
                </mrow>
              </msub>
              <mo id="b69" xref="b117">⁢</mo>
              <msub id="b70" xref="b139">
                <mover accent="true" id="b71" xref="b140">
                  <mover accent="true" id="b72" xref="b142">
                    <mi id="b73" xref="b144">ϕ</mi>
                    <mo id="b75" stretchy="false" xref="b141">^</mo>
                  </mover>
                  <mo id="b74" xref="b143">¨</mo>
                </mover>
                <mrow id="b76" xref="b145">
                  <msub id="b77" xref="b147">
                    <mi id="b78" xref="b148">N</mi>
                    <mi id="b79" xref="b149">C</mi>
                  </msub>
                  <mo id="b80" xref="b146">⁢</mo>
                  <mrow id="b81" xref="b145">
                    <mo id="b82" stretchy="false" xref="b145">(</mo>
                    <mi id="b83" xref="b150">k</mi>
                    <mo id="b84" stretchy="false" xref="b145">)</mo>
                  </mrow>
                </mrow>
              </msub>
            </mrow>
          </mrow>
          <mo id="b85" stretchy="false" xref="b103">|</mo>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="b86">
      <apply id="b87" xref="b2">
        <eq id="b88" xref="b14"/>
        <apply id="b89" xref="b3">
          <apply id="b90" xref="b5">
            <ci id="b91" xref="b7">¯</ci>
            <ci id="b92" xref="b6">𝐹</ci>
          </apply>
          <ci id="b93" xref="b8">𝑣</ci>
          <ci id="b94" xref="b12">𝑖</ci>
        </apply>
        <apply id="b95" xref="b15">
          <apply id="b96" xref="b16">
            <sum id="b97" xref="b18"/>
            <apply id="b98" xref="b19">
              <neq id="b99" xref="b21"/>
              <ci id="b100" xref="b20">𝑖</ci>
              <ci id="b101" xref="b22">𝑗</ci>
            </apply>
          </apply>
          <apply id="b102" xref="b23">
            <abs id="b103" xref="b24"/>
            <apply id="b104" xref="b25">
              <sum id="b108" xref="b28"/>
              <ci id="b111" xref="b30">𝑘</ci>
              <cn id="b112" type="integer" xref="b32">1</cn>
              <ci id="b114" xref="b33">Nc</ci>
              <apply id="b116" xref="b36">
                <times/>
                <apply id="b118" xref="b37">
                  <ci id="b119" xref="b38">𝑐</ci>
                  <apply id="b121" xref="b40">
                    <apply id="b123" xref="b41">
                      <ci id="b124" xref="b42">𝑁</ci>
                      <ci id="b125" xref="b43">𝑈</ci>
                    </apply>
                    <ci id="b126" xref="b47">𝑖</ci>
                  </apply>
                  <apply id="b127" xref="b50">
                    <apply id="b129" xref="b51">
                      <ci id="b130" xref="b52">𝑁</ci>
                      <ci id="b131" xref="b53">𝐶</ci>
                    </apply>
                    <ci id="b132" xref="b57">𝑘</ci>
                  </apply>
                  <apply id="b133" xref="b60">
                    <apply id="b135" xref="b61">
                      <ci id="b136" xref="b62">𝑁</ci>
                      <ci id="b137" xref="b63">𝑈</ci>
                    </apply>
                    <ci id="b138" xref="b67">𝑗</ci>
                  </apply>
                </apply>
                <apply id="b139" xref="b70">
                  <partialdiff id="b140" xref="b71"/>
                  <cn id="b143" xref="b74">2</cn>
                  
                  <apply id="b145" xref="b76">
                    <apply id="b142" xref="b72">
                      <ci id="b141" xref="b75">^</ci>
                      <ci id="b144" xref="b73">italic-ϕ</ci>
                    </apply>
                    <apply id="corr" xref="b77">
                      <apply id="b147" xref="b77">
                        <ci id="b148" xref="b78">𝑁</ci>
                        <ci id="b149" xref="b79">𝐶</ci>
                      </apply>
                      <ci id="b150" xref="b83">𝑘</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="b151">\displaystyle\overline{F}_{v}(i)=\sum_{i\neq
      j}|\sum_{k=1}^{N_{C}}c_{N_{U}(i),N_{C}(k),N_{U}(j)}\hat{\ddot{\phi}}_{N_{C}(k)}|
    </annotation>
  </semantics>
</math>

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