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    <metadata lang="rus">
      <title>Поиск функции от матрицы (Формула Сильвестра)</title>
      <author>Кирилл Николаев</author>
      <description>Вычисление определённой пользователем функции от заданной матрицы по формуле Сильвестра.
В примере также показывается метод получения коэффициентов характеристического многочлена (векового уравнения) по методу Леверрье-Фаддеева.</description>
      <keywords>Примеры, Матрицы, Формула Сильвестра, Метод Леверрье-Фаддеева, Собственные числа, Характеристический многочлен, Вековое уравнение</keywords>
    </metadata>
    <metadata lang="ind">
      <title>Fungsi dari matriks (Formula Sylvester)</title>
      <author>Kirill Nikolaev</author>
      <translator>Waluyo Adi Siswanto</translator>
      <description>Menghitung fungsi dari suatu matriks menggunakan formula Sylvester. Fungsi matriks ini merupakan fungsi yang dapat didefinisikan sendiri.
Pada contoh ini, penentuan koefisien karakteristik polinomial dari matriks menggunakan metode Leverrie-Faddeev.</description>
      <keywords>Contoh, Matriks,  Formula Sylvester,  Metode Leverrie-Faddeev, Angka Eigen, Karakteristik polinomial</keywords>
    </metadata>
    <metadata lang="eng">
      <title>Function of the matrix (Sylvester's formula)</title>
      <author>Kirill Nikolaev</author>
      <translator>Andrey Ivashov</translator>
      <description>Computing the user-defined function of the matrix using Sylvester's formula.
Example also shows how to get the coefficients of matrix characteristic polynomial with Leverrie-Faddeev method.</description>
      <keywords>Examples, Matrices, Sylvester's formula, Leverrie-Faddeev method, Eigenvalues, Characteristic polynomial</keywords>
    </metadata>
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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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  <region id="0" left="9" top="9" width="449" height="28" color="#0000ff" bgColor="#ffffff" fontSize="12">
    <text lang="rus">
      <p bold="true">Поиск функции от матрицы (Формула Сильвестра)</p>
    </text>
    <text lang="ind">
      <p bold="true">Fungsi dari matriks (Formula Sylvester)</p>
    </text>
    <text lang="eng">
      <p bold="true">Function of the matrix (Sylvester's formula)</p>
    </text>
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    <text lang="rus">
      <p>Входные данные:</p>
    </text>
    <text lang="ind">
      <p>Data masukan:</p>
    </text>
    <text lang="eng">
      <p>Input data:</p>
    </text>
  </region>
  <region id="2" left="9" top="63" width="102" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Right" lang="rus">
        <p>Задание матрицы</p>
      </description>
      <description active="true" position="Right" lang="ind">
        <p>Data matriks</p>
      </description>
      <description active="true" position="Right" lang="eng">
        <p>Considered matrix</p>
      </description>
      <input>
        <e type="operand">A</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">7</e>
        <e type="operand">5</e>
        <e type="operand">2</e>
        <e type="operand">9</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
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  <region id="3" left="9" top="126" width="75" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Right" lang="rus">
        <p>Искомая функция</p>
      </description>
      <description active="true" position="Right" lang="ind">
        <p>Definisi fungsi</p>
      </description>
      <description active="true" position="Right" lang="eng">
        <p>Function to proceed</p>
      </description>
      <input>
        <e type="operand">α</e>
        <e type="function" args="1">φ</e>
        <e type="operand">α</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="4" left="9" top="171" width="111" height="24" border="true" color="#000000" bgColor="#dddddd" fontSize="10">
    <text lang="rus">
      <p>Расчёт:</p>
    </text>
    <text lang="ind">
      <p>Perhitungan:</p>
    </text>
    <text lang="eng">
      <p>Calculation:</p>
    </text>
  </region>
  <region id="5" left="9" top="198" width="434" height="48" color="#0000ff" bgColor="#ffffff" fontSize="12">
    <text lang="rus">
      <p bold="true">Нахождение коэффициентов векового уравнения
методом Леверрье-Фаддеева</p>
    </text>
    <text lang="ind">
      <p bold="true">Menghitung karakteristik polinomial menggunakan
metode Leverrie-Faddee</p>
    </text>
    <text lang="eng">
      <p bold="true">Computing the characteristic polynomial of 
the matrix with Leverrie-Faddeev method</p>
    </text>
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    <math>
      <input>
        <e type="operand">m</e>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">cols</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="9" top="279" width="199" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">A</e>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">tr</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="1">identity</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="8" left="9" top="315" width="85" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">q</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">tr</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="9" top="351" width="224" height="147" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">n</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
        <e type="operand">n</e>
        <e type="operand">m</e>
        <e type="operator" args="2">≤</e>
        <e type="operand">n</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">C</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">A</e>
        <e type="operand">B</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
        <e type="operand">q</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">C</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="1">tr</e>
        <e type="operand">n</e>
        <e type="operator" args="2">/</e>
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        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">C</e>
        <e type="operand">n</e>
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        <e type="operand">n</e>
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        <e type="function" preserve="true" args="2">el</e>
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        <e type="operator" args="2">:</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
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        <e type="function" preserve="true" args="4">for</e>
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    <math>
      <input>
        <e type="operand">p</e>
        <e type="operand">m</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
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    <math>
      <input>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
        <e type="operand">j</e>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">cols</e>
        <e type="operator" args="2">≤</e>
        <e type="operand">j</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">p</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">q</e>
        <e type="operand">m</e>
        <e type="operand">j</e>
        <e type="operator" args="2">-</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="4">for</e>
      </input>
    </math>
  </region>
  <region id="12" left="9" top="594" width="88" height="80" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Right" lang="rus">
        <p>Коэффициенты характеристического
многочлена</p>
      </description>
      <description active="true" position="Right" lang="ind">
        <p>Koefisien karakteristik polinomial</p>
      </description>
      <description active="true" position="Right" lang="eng">
        <p>Characteristic polynomial
coefficients</p>
      </description>
      <input>
        <e type="operand">p</e>
      </input>
      <result action="numeric">
        <e type="operand">204</e>
        <e type="operator" args="1">-</e>
        <e type="operand">85</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">mat</e>
      </result>
    </math>
  </region>
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    <math>
      <input>
        <e type="operand">λ</e>
        <e type="operand">p</e>
        <e type="function" preserve="true" args="1">polyroots</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="14" left="9" top="711" width="112" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Right" lang="rus">
        <p>Собственные числа матрцы А</p>
      </description>
      <description active="true" position="Right" lang="ind">
        <p>Angka Eigen dari matriks A</p>
      </description>
      <description active="true" position="Right" lang="eng">
        <p>Eigenvalues of A matrix</p>
      </description>
      <input>
        <e type="operand">λ</e>
      </input>
      <result action="numeric">
        <e type="operand">2.358</e>
        <e type="operator" args="1">-</e>
        <e type="operand">8.9858</e>
        <e type="operand">9.6278</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
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    <math optimize="2">
      <input>
        <e type="operand">ξ</e>
        <e type="operand">λ</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">φ</e>
        <e type="operand">k</e>
        <e type="operand">j</e>
        <e type="operator" args="2">≠</e>
        <e type="operand">A</e>
        <e type="operand">λ</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">cols</e>
        <e type="function" preserve="true" args="1">identity</e>
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        <e type="operand">λ</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">λ</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">/</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">if</e>
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        <e type="operand">1</e>
        <e type="operand">A</e>
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        <e type="function" preserve="true" args="4">product</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">cols</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">:</e>
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    <text lang="rus">
      <p>Результат:</p>
    </text>
    <text lang="ind">
      <p>Hasil:</p>
    </text>
    <text lang="eng">
      <p>Result:</p>
    </text>
  </region>
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    <math>
      <input>
        <e type="operand">ξ</e>
      </input>
      <result action="numeric">
        <e type="operand">53</e>
        <e type="operand">23</e>
        <e type="operand">17</e>
        <e type="operator" args="1">-</e>
        <e type="operand">59</e>
        <e type="operand">41</e>
        <e type="operand">17</e>
        <e type="operand">15</e>
        <e type="operator" args="1">-</e>
        <e type="operand">6</e>
        <e type="operand">85</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
      </result>
    </math>
  </region>
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