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data/34.json

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{
  "definitions" : {
    "P_{1}" : [ {
      "Q43260" : "polynomial (mathematical expression consisting of variables and coefficients)"
    } ],
    "X" : [ {
      "Q3150667" : "Indeterminate "
    } ],
    "P" : [ {
      "Q43260" : "polynomial (mathematical expression consisting of variables and coefficients)"
    } ],
    "\\alpha_{1}" : [ {
      "Q11567" : "complex number (number that can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit )"
    } ]
  },
  "constraints" : [ ],
  "math_inputtex" : "P_1(X)=P(X)/(X-\\alpha_1)",
  "math_inputtex_semantic" : "\\wf{Q43260}{P}_1(\\w{Q3150667}{X}) = \\wf{Q43260}{P}(\\w{Q3150667}{X})/(X-\\w{Q11567}{\\alpha}_1)",
  "correct_tex" : "P_1(X)=P(X)/(X-\\alpha_1)",
  "correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"P_{1}(X)=P(X)/(X-\\alpha_{1})\" display=\"inline\">\n  <semantics id=\"p1.1.m1.1a\">\n    <mrow id=\"p1.1.m1.1.18\" xref=\"p1.1.m1.1.18.cmml\">\n      <mrow id=\"p1.1.m1.1.18.1.2\" xref=\"p1.1.m1.1.18.1.1.cmml\">\n        <msub id=\"p1.1.m1.1.18.1.2.1\" xref=\"p1.1.m1.1.18.1.2.1.cmml\">\n          <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">P</mi>\n          <mn id=\"p1.1.m1.1.2.1\" xref=\"p1.1.m1.1.2.1.cmml\">1</mn>\n        </msub>\n        <mo id=\"p1.1.m1.1.18.1.2a\" xref=\"p1.1.m1.1.18.1.1.cmml\">⁡</mo>\n        <mrow id=\"p1.1.m1.1.18.1.2.2\" xref=\"p1.1.m1.1.18.1.1.cmml\">\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.18.1.1.cmml\">(</mo>\n          <mi id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.4.cmml\">X</mi>\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.5\" xref=\"p1.1.m1.1.18.1.1.cmml\">)</mo>\n        </mrow>\n      </mrow>\n      <mo id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.6.cmml\">=</mo>\n      <mrow id=\"p1.1.m1.1.18.2\" xref=\"p1.1.m1.1.18.2.cmml\">\n        <mrow id=\"p1.1.m1.1.18.2.1.2\" xref=\"p1.1.m1.1.18.2.1.1.cmml\">\n          <mi id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">P</mi>\n          <mo id=\"p1.1.m1.1.18.2.1.2a\" xref=\"p1.1.m1.1.18.2.1.1.cmml\">⁡</mo>\n          <mrow id=\"p1.1.m1.1.18.2.1.2.1\" xref=\"p1.1.m1.1.18.2.1.1.cmml\">\n            <mo stretchy=\"false\" id=\"p1.1.m1.1.8\" xref=\"p1.1.m1.1.18.2.1.1.cmml\">(</mo>\n            <mi id=\"p1.1.m1.1.9\" xref=\"p1.1.m1.1.9.cmml\">X</mi>\n            <mo stretchy=\"false\" id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.18.2.1.1.cmml\">)</mo>\n          </mrow>\n        </mrow>\n        <mo id=\"p1.1.m1.1.11\" xref=\"p1.1.m1.1.11.cmml\">/</mo>\n        <mrow id=\"p1.1.m1.1.18.2.2\" xref=\"p1.1.m1.1.18.2.2.2.cmml\">\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.12\" xref=\"p1.1.m1.1.18.2.2.2.cmml\">(</mo>\n          <mrow id=\"p1.1.m1.1.18.2.2.2\" xref=\"p1.1.m1.1.18.2.2.2.cmml\">\n            <mi id=\"p1.1.m1.1.13\" xref=\"p1.1.m1.1.13.cmml\">X</mi>\n            <mo id=\"p1.1.m1.1.14\" xref=\"p1.1.m1.1.14.cmml\">-</mo>\n            <msub id=\"p1.1.m1.1.18.2.2.2.1\" xref=\"p1.1.m1.1.18.2.2.2.1.cmml\">\n              <mi id=\"p1.1.m1.1.15\" xref=\"p1.1.m1.1.15.cmml\">α</mi>\n              <mn id=\"p1.1.m1.1.16.1\" xref=\"p1.1.m1.1.16.1.cmml\">1</mn>\n            </msub>\n          </mrow>\n          <mo stretchy=\"false\" id=\"p1.1.m1.1.17\" xref=\"p1.1.m1.1.18.2.2.2.cmml\">)</mo>\n        </mrow>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.18.cmml\" xref=\"p1.1.m1.1.18\">\n        <eq id=\"p1.1.m1.1.6.cmml\" xref=\"p1.1.m1.1.6\"/>\n        <apply id=\"p1.1.m1.1.18.1.1.cmml\" xref=\"p1.1.m1.1.18.1.2\">\n          <apply id=\"p1.1.m1.1.18.1.2.1.cmml\" xref=\"p1.1.m1.1.18.1.2.1\">\n            <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.18.1.2.1.1.cmml\" xref=\"p1.1.m1.1.18.1.2.1\">subscript</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">Q43260</csymbol>\n            <cn type=\"integer\" id=\"p1.1.m1.1.2.1.cmml\" xref=\"p1.1.m1.1.2.1\">1</cn>\n          </apply>\n          <csymbol cd=\"latexml\" id=\"p1.1.m1.1.4.cmml\" xref=\"p1.1.m1.1.4\">Q3150667</csymbol>\n        </apply>\n        <apply id=\"p1.1.m1.1.18.2.cmml\" xref=\"p1.1.m1.1.18.2\">\n          <divide id=\"p1.1.m1.1.11.cmml\" xref=\"p1.1.m1.1.11\"/>\n          <apply id=\"p1.1.m1.1.18.2.1.1.cmml\" xref=\"p1.1.m1.1.18.2.1.2\">\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\">Q43260</csymbol>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.9.cmml\" xref=\"p1.1.m1.1.9\">Q3150667</csymbol>\n          </apply>\n          <apply id=\"p1.1.m1.1.18.2.2.2.cmml\" xref=\"p1.1.m1.1.18.2.2\">\n            <minus id=\"p1.1.m1.1.14.cmml\" xref=\"p1.1.m1.1.14\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.13.cmml\" xref=\"p1.1.m1.1.13\">Q3150667</csymbol>\n            <apply id=\"p1.1.m1.1.18.2.2.2.1.cmml\" xref=\"p1.1.m1.1.18.2.2.2.1\">\n              <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.18.2.2.2.1.1.cmml\" xref=\"p1.1.m1.1.18.2.2.2.1\">subscript</csymbol>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.15.cmml\" xref=\"p1.1.m1.1.15\">Q11567</csymbol>\n              <cn type=\"integer\" id=\"p1.1.m1.1.16.1.cmml\" xref=\"p1.1.m1.1.16.1\">1</cn>\n            </apply>\n          </apply>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">P_{1}(X)=P(X)/(X-\\alpha_{1})</annotation>\n  </semantics>\n</math>",
  "uri" : "https://en.formulasearchengine.com/w/index.php?oldid=17497#math17497.55",
  "title" : "Jenkins–Traub_algorithm",
  "type" : "equation"
}