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<head><title>determinant(..., Strategy => ...) -- choose between Bareiss and Cofactor algorithms</title>
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<div><h1>determinant(..., Strategy => ...) -- choose between Bareiss and Cofactor algorithms</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>determinant(M, Strategy => s)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
<li><span><tt>s</tt>, <span>a <a href="___Symbol.html">symbol</a></span>, either <tt>Bareiss</tt> or <tt>Cofactor</tt></span></li>
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<li><div class="single">Consequences:<ul><li>If <tt>s</tt> is <a href="___Bareiss.html" title="">Bareiss</a>, then the Bareiss algorithm is used; if <tt>s</tt> is <a href="___Cofactor.html" title="">Cofactor</a>, then cofactor expansion is used.</li>
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<div class="single"><h2>Description</h2>
<div>The <a href="___Ring.html">ring</a> of <tt>M</tt> determines the default strategy. If the ring is a <a href="___Polynomial__Ring.html">polynomial ring</a> or a field (as identified by <a href="_is__Field.html" title="whether something is a field">isField</a>) then the <a href="___Bareiss.html" title="">Bareiss</a> algorithm is used. If the ring is a <a href="___Quotient__Ring.html">quotient ring</a> (which has not been declared a field by <a href="_to__Field_lp__Ring_rp.html" title="declare that a ring is a field">toField</a>), then the <a href="___Cofactor.html" title="">Cofactor</a> algorithm is used.<p/>
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<h2>Further information</h2>
<ul><li><span>Default value: <a href="_null.html" title="the unique member of the empty class">null</a></span></li>
<li><span>Function: <span><a href="_determinant.html" title="determinant of a matrix">determinant</a> -- determinant of a matrix</span></span></li>
<li><span>Option name: <span><a href="___Strategy.html" title="name for an optional argument">Strategy</a> -- name for an optional argument</span></span></li>
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<div class="single"><h2>Caveat</h2>
<div>The <a href="___Bareiss.html" title="">Bareiss</a> algorithm returns a ring element that may differ from the actual determinant by a zero divisor in the ring. Thus, an <em>incorrect</em> answer may be computed if the ring contains zero divisors.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_exterior__Power.html" title="exterior power">exteriorPower</a> -- exterior power</span></li>
<li><span><a href="_minors_lp__Z__Z_cm__Matrix_rp.html" title="ideal generated by minors">minors</a> -- ideal generated by minors</span></li>
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