ag-gipp/GoUldI

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data/213.json

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{
  "definitions" : {
    "N" : [ {
      "Q28920052" : "Non-negative integer"
    } ],
    "M" : [ {
      "Q28920052" : "Non-negative integer"
    } ],
    "a" : [ {
      "Q28920052" : "Non-negative integer"
    } ],
    "b" : [ {
      "Q28920052" : "Non-negative integer"
    } ],
    "j" : [ {
      "Q28920052" : "Non-negative integer"
    } ],
    "Q" : [ {
      "Q11348" : "function"
    } ],
    "q" : [ "q as in q-analog", { } ]
  },
  "constraints" : [ "2⁢a ≥ b ≥ 0", "N ≥ |(a−b)j|" ],
  "math_inputtex" : "Q(N,M,aj,bj,q)=Q(M,N,bj,aj,q),",
  "math_inputtex_semantic" : "\\wf{Q11348}{Q}(\\w{Q28920052}{N},\\w{Q28920052}{M}, \\w{Q28920052}{a} \\w{Q28920052}{j},\\w{Q28920052}{b} j,\\w{Q28920052}{q}) = Q(M,N,bj,aj,q)",
  "correct_tex" : "Q(N,M,aj,bj,q)=Q(M,N,bj,aj,q)",
  "correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"Q(N,M,aj,bj,q)=Q(M,N,bj,aj,q)\" display=\"inline\">\n  <semantics id=\"p1.1.m1.1a\">\n    <mrow id=\"p1.1.m1.1.30\" xref=\"p1.1.m1.1.30.cmml\">\n      <mrow id=\"p1.1.m1.1.30.1.2\" xref=\"p1.1.m1.1.30.1.1.cmml\">\n        <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">Q</mi>\n        <mo id=\"p1.1.m1.1.30.1.2a\" xref=\"p1.1.m1.1.30.1.1.cmml\">⁡</mo>\n        <mrow id=\"p1.1.m1.1.30.1.2.3\" xref=\"p1.1.m1.1.30.1.1.cmml\">\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.2\" xref=\"p1.1.m1.1.30.1.1.cmml\">(</mo>\n          <mi id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">N</mi>\n          <mo id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.30.1.1.cmml\">,</mo>\n          <mi id=\"p1.1.m1.1.5\" xref=\"p1.1.m1.1.5.cmml\">M</mi>\n          <mo id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.30.1.1.cmml\">,</mo>\n          <mrow id=\"p1.1.m1.1.30.1.2.1\" xref=\"p1.1.m1.1.30.1.2.1.cmml\">\n            <mi id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">a</mi>\n            <mo id=\"p1.1.m1.1.30.1.2.1.1\" xref=\"p1.1.m1.1.30.1.2.1.1.cmml\">⁢</mo>\n            <mi id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.8.cmml\">j</mi>\n          </mrow>\n          <mo id=\"p1.1.m1.1.9\" xref=\"p1.1.m1.1.30.1.1.cmml\">,</mo>\n          <mrow id=\"p1.1.m1.1.30.1.2.2\" xref=\"p1.1.m1.1.30.1.2.2.cmml\">\n            <mi id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.10.cmml\">b</mi>\n            <mo id=\"p1.1.m1.1.30.1.2.2.1\" xref=\"p1.1.m1.1.30.1.2.2.1.cmml\">⁢</mo>\n            <mi id=\"p1.1.m1.1.11\" xref=\"p1.1.m1.1.11.cmml\">j</mi>\n          </mrow>\n          <mo id=\"p1.1.m1.1.12\" xref=\"p1.1.m1.1.30.1.1.cmml\">,</mo>\n          <mi id=\"p1.1.m1.1.13\" xref=\"p1.1.m1.1.13.cmml\">q</mi>\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.14\" xref=\"p1.1.m1.1.30.1.1.cmml\">)</mo>\n        </mrow>\n      </mrow>\n      <mo id=\"p1.1.m1.1.15\" xref=\"p1.1.m1.1.15.cmml\">=</mo>\n      <mrow id=\"p1.1.m1.1.30.2.2\" xref=\"p1.1.m1.1.30.2.1.cmml\">\n        <mi id=\"p1.1.m1.1.16\" xref=\"p1.1.m1.1.16.cmml\">Q</mi>\n        <mo id=\"p1.1.m1.1.30.2.2a\" xref=\"p1.1.m1.1.30.2.1.cmml\">⁡</mo>\n        <mrow id=\"p1.1.m1.1.30.2.2.3\" xref=\"p1.1.m1.1.30.2.1.cmml\">\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.17\" xref=\"p1.1.m1.1.30.2.1.cmml\">(</mo>\n          <mi id=\"p1.1.m1.1.18\" xref=\"p1.1.m1.1.18.cmml\">M</mi>\n          <mo id=\"p1.1.m1.1.19\" xref=\"p1.1.m1.1.30.2.1.cmml\">,</mo>\n          <mi id=\"p1.1.m1.1.20\" xref=\"p1.1.m1.1.20.cmml\">N</mi>\n          <mo id=\"p1.1.m1.1.21\" xref=\"p1.1.m1.1.30.2.1.cmml\">,</mo>\n          <mrow id=\"p1.1.m1.1.30.2.2.1\" xref=\"p1.1.m1.1.30.2.2.1.cmml\">\n            <mi id=\"p1.1.m1.1.22\" xref=\"p1.1.m1.1.22.cmml\">b</mi>\n            <mo id=\"p1.1.m1.1.30.2.2.1.1\" xref=\"p1.1.m1.1.30.2.2.1.1.cmml\">⁢</mo>\n            <mi id=\"p1.1.m1.1.23\" xref=\"p1.1.m1.1.23.cmml\">j</mi>\n          </mrow>\n          <mo id=\"p1.1.m1.1.24\" xref=\"p1.1.m1.1.30.2.1.cmml\">,</mo>\n          <mrow id=\"p1.1.m1.1.30.2.2.2\" xref=\"p1.1.m1.1.30.2.2.2.cmml\">\n            <mi id=\"p1.1.m1.1.25\" xref=\"p1.1.m1.1.25.cmml\">a</mi>\n            <mo id=\"p1.1.m1.1.30.2.2.2.1\" xref=\"p1.1.m1.1.30.2.2.2.1.cmml\">⁢</mo>\n            <mi id=\"p1.1.m1.1.26\" xref=\"p1.1.m1.1.26.cmml\">j</mi>\n          </mrow>\n          <mo id=\"p1.1.m1.1.27\" xref=\"p1.1.m1.1.30.2.1.cmml\">,</mo>\n          <mi id=\"p1.1.m1.1.28\" xref=\"p1.1.m1.1.28.cmml\">q</mi>\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.29\" xref=\"p1.1.m1.1.30.2.1.cmml\">)</mo>\n        </mrow>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.30.cmml\" xref=\"p1.1.m1.1.30\">\n        <eq id=\"p1.1.m1.1.15.cmml\" xref=\"p1.1.m1.1.15\"/>\n        <apply id=\"p1.1.m1.1.30.1.1.cmml\" xref=\"p1.1.m1.1.30.1.2\">\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q11348</csymbol>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\">Q28920052</csymbol>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.5.cmml\" xref=\"p1.1.m1.1.5\">Q28920052</csymbol>\n          <apply id=\"p1.1.m1.1.30.1.2.1.cmml\" xref=\"p1.1.m1.1.30.1.2.1\">\n            <times id=\"p1.1.m1.1.30.1.2.1.1.cmml\" xref=\"p1.1.m1.1.30.1.2.1.1\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\">Q28920052</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.8.cmml\" xref=\"p1.1.m1.1.8\">Q28920052</csymbol>\n          </apply>\n          <apply id=\"p1.1.m1.1.30.1.2.2.cmml\" xref=\"p1.1.m1.1.30.1.2.2\">\n            <times id=\"p1.1.m1.1.30.1.2.2.1.cmml\" xref=\"p1.1.m1.1.30.1.2.2.1\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.10.cmml\" xref=\"p1.1.m1.1.10\">Q28920052</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.11.cmml\" xref=\"p1.1.m1.1.11\">Q28920052</csymbol>\n          </apply>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.13.cmml\" xref=\"p1.1.m1.1.13\">Q28920052</csymbol>\n        </apply>\n        <apply id=\"p1.1.m1.1.30.2.1.cmml\" xref=\"p1.1.m1.1.30.2.2\">\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.16.cmml\" xref=\"p1.1.m1.1.16\">Q11348</csymbol>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.18.cmml\" xref=\"p1.1.m1.1.18\">Q28920052</csymbol>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.20.cmml\" xref=\"p1.1.m1.1.20\">Q28920052</csymbol>\n          <apply id=\"p1.1.m1.1.30.2.2.1.cmml\" xref=\"p1.1.m1.1.30.2.2.1\">\n            <times id=\"p1.1.m1.1.30.2.2.1.1.cmml\" xref=\"p1.1.m1.1.30.2.2.1.1\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.22.cmml\" xref=\"p1.1.m1.1.22\">Q28920052</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.23.cmml\" xref=\"p1.1.m1.1.23\">Q28920052</csymbol>\n          </apply>\n          <apply id=\"p1.1.m1.1.30.2.2.2.cmml\" xref=\"p1.1.m1.1.30.2.2.2\">\n            <times id=\"p1.1.m1.1.30.2.2.2.1.cmml\" xref=\"p1.1.m1.1.30.2.2.2.1\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.25.cmml\" xref=\"p1.1.m1.1.25\">Q28920052</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.26.cmml\" xref=\"p1.1.m1.1.26\">Q28920052</csymbol>\n          </apply>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.28.cmml\" xref=\"p1.1.m1.1.28\">Q28920052</csymbol>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">Q(N,M,aj,bj,q)=Q(M,N,bj,aj,q)</annotation>\n  </semantics>\n</math>",
  "uri" : "https://arxiv.org/abs/math/0109141",
  "title" : "Swap",
  "comment" : "constraints on page 14. this one is difficult",
  "type" : "definition",
  "ntcir12-type" : "13",
  "formula" : "1_136.2",
  "page" : "18",
  "ntcir12-relevance" : "1"
}