mathmlben/data/84.json

Visualization for goldstandard

{
  "definitions": {
    "F": [
      "set",
      {}
    ],
    "x": [
      {
        "Q12916": "real number (quantity along a continuous line)"
      }
    ],
    "y": [
      {
        "Q12916": "real number (quantity along a continuous line)"
      }
    ],
    "\\mathcal{R}": [
      {
        "Q12916": "real number (quantity along a continuous line)"
      }
    ],
    "b": [
      {
        "Q12503": "integer (number that can be written without a fractional or decimal component)"
      }
    ],
    "n": [
      {
        "Q12503": "integer (number that can be written without a fractional or decimal component)"
      }
    ]
  },
  "constraints": [],
  "math_inputtex": " F = \\{ (x,y) : x \\in \\mathcal{R}^b,\\, y \\in \\mathcal{R}^n,\\; x=y \\}.",
  "math_inputtex_semantic": "\\w{Q36161}{F} = \\{ (\\w{Q12916}{x},\\w{Q12916}{y}) : x \\in {\\mathcal{R}^{\\w{Q12503}{b}},\\, y \\in \\mathcal{R}^{\\w{Q12503}{n}},\\; x=y \\}",
  "correct_tex": "F = \\{ (x,y) : x \\in \\mathcal{R}^b,\\, y \\in \\mathcal{R}^n,\\; x=y \\}",
  "correct_mml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"F=\\{(x,y):x\\in{\\mathcal{R}^{b},\\,y\\in\\mathcal{R}^{n},\\;x=y\\}\\)\\@add@PDF@RDFa@triples\\end{document}}\" display=\"inline\">\n  <semantics id=\"p1.1.m1.1a\">\n    <mrow id=\"p1.1.m1.1.26\" xref=\"p1.1.m1.1.26.cmml\">\n      <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">F</mi>\n      <mo id=\"p1.1.m1.1.2\" xref=\"p1.1.m1.1.2.cmml\">=</mo>\n      <mrow id=\"p1.1.m1.1.26.1\" xref=\"p1.1.m1.1.26.1.1.cmml\">\n        <mo stretchy=\"false\" id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.26.1.1.1.cmml\">{</mo>\n        <mrow id=\"p1.1.m1.1.26.1.2\" xref=\"p1.1.m1.1.26.1.2.1.cmml\">\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.26.1.2.1.cmml\">(</mo>\n          <mi id=\"p1.1.m1.1.5\" xref=\"p1.1.m1.1.5.cmml\">x</mi>\n          <mo id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.26.1.2.1.cmml\">,</mo>\n          <mi id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">y</mi>\n  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xref=\"p1.1.m1.1.26.1.3.3.2.cmml\">\n              <mi id=\"p1.1.m1.1.16\" xref=\"p1.1.m1.1.16.cmml\">y</mi>\n              <mo id=\"p1.1.m1.1.17\" xref=\"p1.1.m1.1.17.cmml\">∈</mo>\n              <msup id=\"p1.1.m1.1.26.1.3.3.2.1\" xref=\"p1.1.m1.1.26.1.3.3.2.1.cmml\">\n                <mi class=\"ltx_font_mathcaligraphic\" id=\"p1.1.m1.1.18\" xref=\"p1.1.m1.1.18.cmml\">ℛ</mi>\n                <mi id=\"p1.1.m1.1.19.1\" xref=\"p1.1.m1.1.19.1.cmml\">n</mi>\n              </msup>\n            </mrow>\n            <mo rspace=\"5.3pt\" id=\"p1.1.m1.1.20\" xref=\"p1.1.m1.1.26.1.3.3.1a.cmml\">,</mo>\n            <mrow id=\"p1.1.m1.1.26.1.3.3.3\" xref=\"p1.1.m1.1.26.1.3.3.3.cmml\">\n              <mi id=\"p1.1.m1.1.22\" xref=\"p1.1.m1.1.22.cmml\">x</mi>\n              <mo id=\"p1.1.m1.1.23\" xref=\"p1.1.m1.1.23.cmml\">=</mo>\n              <mi id=\"p1.1.m1.1.24\" xref=\"p1.1.m1.1.24.cmml\">y</mi>\n            </mrow>\n          </mrow>\n        </mrow>\n        <mo stretchy=\"false\" id=\"p1.1.m1.1.25\" xref=\"p1.1.m1.1.26.1.1.1.cmml\">}</mo>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.26.cmml\" xref=\"p1.1.m1.1.26\">\n        <eq id=\"p1.1.m1.1.2.cmml\" xref=\"p1.1.m1.1.2\"/>\n        <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q36161</csymbol>\n        <apply id=\"p1.1.m1.1.26.1.1.cmml\" xref=\"p1.1.m1.1.26.1\">\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.26.1.1.1.cmml\" xref=\"p1.1.m1.1.3\">conditional-set</csymbol>\n          <interval closure=\"open\" id=\"p1.1.m1.1.26.1.2.1.cmml\" xref=\"p1.1.m1.1.26.1.2\">\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.5.cmml\" xref=\"p1.1.m1.1.5\">Q12916</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\">Q12916</csymbol>\n          </interval>\n          <apply id=\"p1.1.m1.1.26.1.3.1.cmml\" xref=\"p1.1.m1.1.26.1.3\">\n            <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.26.1.3.1a.cmml\" xref=\"p1.1.m1.1.14\">formulae-sequence</csymbol>\n            <apply id=\"p1.1.m1.1.26.1.3.2.cmml\" xref=\"p1.1.m1.1.26.1.3.2\">\n              <in id=\"p1.1.m1.1.11.cmml\" xref=\"p1.1.m1.1.11\"/>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.10.cmml\" xref=\"p1.1.m1.1.10\">Q12916</csymbol>\n              <apply id=\"p1.1.m1.1.26.1.3.2.1.cmml\" xref=\"p1.1.m1.1.26.1.3.2.1\">\n                <power xmlns:m=\"http://www.w3.org/1998/Math/MathML\" xref=\"p1.1.m1.1.26.1.3.2.1\"/>\n                <ci id=\"p1.1.m1.1.12.cmml\" xref=\"p1.1.m1.1.12\">ℛ</ci>\n                <csymbol cd=\"latexml\" id=\"p1.1.m1.1.13.1.cmml\" xref=\"p1.1.m1.1.13.1\">Q12503</csymbol>\n              </apply>\n            </apply>\n            <apply id=\"p1.1.m1.1.26.1.3.3.1.cmml\" xref=\"p1.1.m1.1.26.1.3.3\">\n              <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.26.1.3.3.1a.cmml\" xref=\"p1.1.m1.1.20\">formulae-sequence</csymbol>\n              <apply id=\"p1.1.m1.1.26.1.3.3.2.cmml\" xref=\"p1.1.m1.1.26.1.3.3.2\">\n                <in id=\"p1.1.m1.1.17.cmml\" xref=\"p1.1.m1.1.17\"/>\n                <csymbol cd=\"latexml\" id=\"p1.1.m1.1.16.cmml\" xref=\"p1.1.m1.1.16\">Q12916</csymbol>\n                <apply id=\"p1.1.m1.1.26.1.3.3.2.1.cmml\" xref=\"p1.1.m1.1.26.1.3.3.2.1\">\n                  <power xmlns:m=\"http://www.w3.org/1998/Math/MathML\" xref=\"p1.1.m1.1.26.1.3.3.2.1\"/>\n                  <ci id=\"p1.1.m1.1.18.cmml\" xref=\"p1.1.m1.1.18\">ℛ</ci>\n                  <csymbol cd=\"latexml\" id=\"p1.1.m1.1.19.1.cmml\" xref=\"p1.1.m1.1.19.1\">Q12503</csymbol>\n                </apply>\n              </apply>\n              <apply id=\"p1.1.m1.1.26.1.3.3.3.cmml\" xref=\"p1.1.m1.1.26.1.3.3.3\">\n                <eq id=\"p1.1.m1.1.23.cmml\" xref=\"p1.1.m1.1.23\"/>\n                <csymbol cd=\"latexml\" id=\"p1.1.m1.1.22.cmml\" xref=\"p1.1.m1.1.22\">Q12916</csymbol>\n                <csymbol cd=\"latexml\" id=\"p1.1.m1.1.24.cmml\" xref=\"p1.1.m1.1.24\">Q12916</csymbol>\n              </apply>\n            </apply>\n          </apply>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">F=\\{(x,y):x\\in{\\mathcal{R}^{b},\\,y\\in\\mathcal{R}^{n},\\;x=y\\}\\)\\@add@PDF@RDFa@triples\\end{document}}</annotation>\n  </semantics>\n</math>",
  "uri": "https://en.formulasearchengine.com/w/index.php?oldid=28184#math28184.6",
  "title": "Projections_onto_convex_sets",
  "type": "definition",
  "check": {
    "tree": false
  }
}