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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_ideals.html" title="">ideals</a></div>
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<div><h1>ideals</h1>
<div><h2>An overview</h2>
In Macaulay2, once a ring (see <a href="_rings.html" title="">rings</a>) is defined, ideals are constructed in the usual way by giving a set of generators.<p/>
For those operations where we consider an ideal as a module, such as computing Hilbert functions and polynomials, syzygies, free resolutions, see <a href="_modules.html" title="">modules</a>.<p/>
For additional common operations and a comprehensive list of all routines in Macaulay2 which return or use ideals, see <a href="___Ideal.html" title="the class of all ideals">Ideal</a>.<p/>
The following link differs from the previous one in case only: <a href="_ideal.html" title="make an ideal">ideal</a>.</div>
<div><h3>Menu</h3>
<ul><li><span><a href="_creating_span_spideal.html" title="">creating an ideal</a></span></li>
</ul>
<h4>conversions</h4>
<ul><li><span><a href="_ideals_spto_spand_spfrom_spmatrices.html" title="">ideals to and from matrices</a></span></li>
<li><span><a href="_ideals_spto_spand_spfrom_spmodules.html" title="">ideals to and from modules</a></span></li>
</ul>
<h4>basic operations on ideals</h4>
<ul><li><span><a href="_sums_cm_spproducts_cm_spand_sppowers_spof_spideals.html" title="">sums, products, and powers of ideals</a></span></li>
<li><span><a href="_equality_spand_spcontainment.html" title="">equality and containment</a></span></li>
<li><span><a href="_extracting_spgenerators_spof_span_spideal.html" title="">extracting generators of an ideal</a></span></li>
<li><span><a href="_dimension_cm_spcodimension_cm_spand_spdegree.html" title="">dimension, codimension, and degree</a></span></li>
</ul>
<h4>components of ideals</h4>
<ul><li><span><a href="_intersection_spof_spideals.html" title="">intersection of ideals</a></span></li>
<li><span><a href="_ideal_spquotients_spand_spsaturation.html" title="">ideal quotients and saturation</a></span></li>
<li><span><a href="_radical_spof_span_spideal.html" title="">radical of an ideal</a></span></li>
<li><span><a href="_minimal_spprimes_spof_span_spideal.html" title="">minimal primes of an ideal</a></span></li>
<li><span><a href="_associated_spprimes_spof_span_spideal.html" title="">associated primes of an ideal</a></span></li>
<li><span><a href="_primary_spdecomposition.html" title="">primary decomposition</a></span></li>
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