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<div><h1>PrimaryDecomposition</h1>
<div class="single"><h2>Description</h2>
<div>This package provides computations with components of ideals, including minimal and associated primes, radicals, and primary decompositions of ideals.</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_primary__Decomposition.html" title="irredundant primary decomposition of an ideal">primaryDecomposition(Ideal)</a> -- irredundant primary decomposition of an ideal</span></li>
</ul>
</div>
<div class="single"><h2>Author</h2>
<ul><li><div class="single">Michael E. Stillman<span> <<a href="mailto:mike@math.cornell.edu">mike@math.cornell.edu</a>></span></div>
</li>
</ul>
</div>
<div class="single"><h2>Version</h2>
This documentation describes version <b>1.0</b> of PrimaryDecomposition.</div>
<div class="single"><h2>Source code</h2>
The source code from which this documentation is derived is in the file <a href="../../../../Macaulay2/PrimaryDecomposition.m2">PrimaryDecomposition.m2</a>. The auxiliary files accompanying it are in the directory <a href="../../../../Macaulay2/PrimaryDecomposition/">PrimaryDecomposition/</a>.</div>
<div class="single"><h2>Exports</h2>
<ul><li><div class="single">Types<ul><li><span>Hybrid, see <span><a href="_primary__Decomposition_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">primaryDecomposition(..., Strategy => ...)</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Functions<ul><li><span>irreducibleDecomposition, see <span><a href="_irreducible__Decomposition_lp__Monomial__Ideal_rp.html" title="express a monomial ideal as an intersection of irreducible monomial ideals">irreducibleDecomposition(MonomialIdeal)</a> -- express a monomial ideal as an intersection of irreducible monomial ideals</span></span></li>
<li><span><a href="_is__Primary.html" title="determine whether an ideal is primary">isPrimary</a> -- determine whether an ideal is primary</span></li>
<li><span>localize, see <span><a href="_localize_lp__Ideal_cm__Ideal_rp.html" title="localize an ideal at a prime ideal">localize(Ideal,Ideal)</a> -- localize an ideal at a prime ideal</span></span></li>
<li><span>primaryComponent, see <span><a href="_primary__Component_lp__Ideal_cm__Ideal_rp.html" title="find a primary component corresponding to an associated prime">primaryComponent(Ideal,Ideal)</a> -- find a primary component corresponding to an associated prime</span></span></li>
<li><span><a href="_primary__Decomposition.html" title="irredundant primary decomposition of an ideal">primaryDecomposition</a> -- irredundant primary decomposition of an ideal</span></li>
</ul>
</div>
</li>
<li><div class="single">Symbols<ul><li><span>Increment, see <span><a href="_primary__Component_lp..._cm_sp__Increment_sp_eq_gt_sp..._rp.html" title="">primaryComponent(..., Increment => ...)</a></span></span></li>
<li><span>EisenbudHunekeVasconcelos, see <span><a href="_primary__Decomposition_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">primaryDecomposition(..., Strategy => ...)</a></span></span></li>
<li><span>GTZ, see <span><a href="_primary__Decomposition_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">primaryDecomposition(..., Strategy => ...)</a></span></span></li>
<li><span>ShimoyamaYokoyama, see <span><a href="_primary__Decomposition_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">primaryDecomposition(..., Strategy => ...)</a></span></span></li>
</ul>
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</li>
</ul>
</div>
<div><h3>Menu</h3>
<ul><li><span><a href="_associated__Primes_lp__Ideal_rp.html" title="find the associated primes of an ideal">associatedPrimes(Ideal)</a> -- find the associated primes of an ideal</span></li>
<li><span><a href="_localize_lp__Ideal_cm__Ideal_rp.html" title="localize an ideal at a prime ideal">localize(Ideal,Ideal)</a> -- localize an ideal at a prime ideal</span></li>
<li><span><a href="_localize_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">localize(..., Strategy => ...)</a></span></li>
<li><span><a href="_primary__Component_lp__Ideal_cm__Ideal_rp.html" title="find a primary component corresponding to an associated prime">primaryComponent(Ideal,Ideal)</a> -- find a primary component corresponding to an associated prime</span></li>
<li><span><a href="_primary__Component_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">primaryComponent(..., Strategy => ...)</a></span></li>
<li><span><a href="_primary__Component_lp..._cm_sp__Increment_sp_eq_gt_sp..._rp.html" title="">primaryComponent(..., Increment => ...)</a></span></li>
<li><span>primaryDecomposition(Ideal), see <span><a href="_primary__Decomposition.html" title="irredundant primary decomposition of an ideal">primaryDecomposition</a> -- irredundant primary decomposition of an ideal</span></span></li>
<li><span><a href="_primary__Decomposition_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html" title="">primaryDecomposition(..., Strategy => ...)</a></span></li>
</ul>
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