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<head><title>PolynomialRing -- the class of all ordered monoid rings</title>
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<div><h1>PolynomialRing -- the class of all ordered monoid rings</h1>
<div class="single"><h2>Description</h2>
<div>Every element of a polynomial ring is also a <a href="___Ring__Element.html" title="the class of all ring elements handled by the engine">RingElement</a>.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_polynomial_springs.html" title="">polynomial rings</a></span></li>
</ul>
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<div class="waystouse"><h2>Functions and methods returning a polynomial ring :</h2>
<ul><li><span>degreesMonoid(PolynomialRing), see <span><a href="_degrees__Monoid.html" title="get the monoid of degrees">degreesMonoid</a> -- get the monoid of degrees</span></span></li>
<li><span><a href="_degrees__Ring_lp__List_rp.html" title="the ring of degrees">degreesRing(List)</a> -- the ring of degrees</span></li>
<li><span>degreesRing(ZZ), see <span><a href="_degrees__Ring_lp__List_rp.html" title="the ring of degrees">degreesRing(List)</a> -- the ring of degrees</span></span></li>
<li><span><a href="___Ring_sp__Array.html" title="the standard way to make a polynomial ring">Ring Array</a> -- the standard way to make a polynomial ring</span></li>
<li><span><a href="___Ring_sp__List.html" title="make a local polynomial ring">Ring List</a> -- make a local polynomial ring</span></li>
<li><span><a href="___Ring_sp__Ordered__Monoid.html" title="make a polynomial ring">Ring OrderedMonoid</a> -- make a polynomial ring</span></li>
</ul>
<h2>Methods that use a polynomial ring :</h2>
<ul><li><span>ambient(PolynomialRing), see <span><a href="_ambient_lp__Ring_rp.html" title="ambient polynomial ring">ambient(Ring)</a> -- ambient polynomial ring</span></span></li>
<li><span>codim(PolynomialRing), see <span><a href="_codim_lp__Quotient__Ring_rp.html" title="compute the codimension">codim(QuotientRing)</a> -- compute the codimension</span></span></li>
<li><span>describe(PolynomialRing), see <span><a href="_describe.html" title="real description">describe</a> -- real description</span></span></li>
<li><span>dim(PolynomialRing), see <span><a href="_dim_lp__Ring_rp.html" title="compute the Krull dimension">dim(Ring)</a> -- compute the Krull dimension</span></span></li>
<li><span>Grassmannian(ZZ,ZZ,PolynomialRing), see <span><a href="___Grassmannian_lp__Z__Z_cm__Z__Z_rp.html" title="the Grassmannian of linear subspaces of a vector space">Grassmannian(ZZ,ZZ)</a> -- the Grassmannian of linear subspaces of a vector space</span></span></li>
<li><span><a href="_hilbert__Series_lp__Polynomial__Ring_rp.html" title="compute the Hilbert series of a ring">hilbertSeries(PolynomialRing)</a> -- compute the Hilbert series of a ring</span></li>
<li><span>isAffineRing(PolynomialRing), see <span><a href="_is__Affine__Ring.html" title="whether something is an affine ring">isAffineRing</a> -- whether something is an affine ring</span></span></li>
<li><span>isPolynomialRing(PolynomialRing), see <span><a href="_is__Polynomial__Ring.html" title="whether someting is a polynomial ring">isPolynomialRing</a> -- whether someting is a polynomial ring</span></span></li>
<li><span>isSkewCommutative(PolynomialRing), see <span><a href="_is__Skew__Commutative.html" title="whether a ring has skew commuting variables">isSkewCommutative</a> -- whether a ring has skew commuting variables</span></span></li>
<li><span>monoid(PolynomialRing), see <span><a href="_monoid.html" title="make or retrieve a monoid">monoid</a> -- make or retrieve a monoid</span></span></li>
<li><span>newCoordinateSystem(PolynomialRing,Matrix), see <span><a href="_new__Coordinate__System.html" title="change variables">newCoordinateSystem</a> -- change variables</span></span></li>
<li><span>newRing(PolynomialRing), see <span><a href="_new__Ring.html" title="make a copy of a ring, with some features changed">newRing</a> -- make a copy of a ring, with some features changed</span></span></li>
<li><span>numgens(PolynomialRing), see <span><a href="_numgens_lp__Ring_rp.html" title="number of generators of a polynomial ring">numgens(Ring)</a> -- number of generators of a polynomial ring</span></span></li>
<li><span>options(PolynomialRing), see <span><a href="_options_lp__Ring_rp.html" title="get values used for optional arguments">options(Ring)</a> -- get values used for optional arguments</span></span></li>
<li><span>precision(PolynomialRing), see <span><a href="_precision.html" title="">precision</a></span></span></li>
<li><span><a href="_presentation_lp__Polynomial__Ring_cm__Quotient__Ring_rp.html" title="presentation of a quotient ring">presentation(PolynomialRing,QuotientRing)</a> -- presentation of a quotient ring</span></li>
<li><span><a href="_select__Variables_lp__List_cm__Polynomial__Ring_rp.html" title="make a subring of a polynomial ring generated by selected variables">selectVariables(List,PolynomialRing)</a> -- make a subring of a polynomial ring generated by selected variables</span></li>
</ul>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Polynomial__Ring.html" title="the class of all ordered monoid rings">PolynomialRing</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Engine__Ring.html" title="the class of rings handled by the engine">EngineRing</a> < <a href="___Ring.html" title="the class of all rings">Ring</a> < <a href="___Type.html" title="the class of all types">Type</a> < <a href="___Mutable__Hash__Table.html" title="the class of all mutable hash tables">MutableHashTable</a> < <a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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