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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>determ</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="determ"> determinant of polynomial matrix</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>res=determ(W [,k])  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>W</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: real square polynomial matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>k</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: integer (upper bound for the degree of the determinant of W)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    returns the determinant of a real polynomial matrix 
    (computation made by FFT if W size is greater than 2*2).</P>
    <P><VERB>res=determ(W [,k])</VERB><VERB>k</VERB> is an integer larger than the actual degree of the determinant
    of <VERB>W</VERB>.</P>
    <P>
    The default value of <VERB>k</VERB> is the smallest power of 2 which is larger
    than <VERB>n*maxi(degree(W))</VERB>.</P>
    <P>
    Method (Only if W size is greater than 2*2) : evaluate the determinant of <VERB>W</VERB> for the Fourier frequencies
    and apply inverse FFT to the coefficients of the determinant.</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
s=poly(0,'s');
w=s*rand(10,10);
determ(w)
det(coeff(w,1))*s^10
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>det</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>detr</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>coffg</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
  <AUTHOR>F.D.  </AUTHOR>
</MAN>
