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<div><h1>QuotientRing -- the class of all quotient rings</h1>
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<div class="waystouse"><h2>Functions and methods returning a quotient ring :</h2>
<ul><li><span>coimage(RingMap), see <span><a href="_coimage.html" title="coimage of a map">coimage</a> -- coimage of a map</span></span></li>
<li><span><a href="_graph__Ring_lp__Ring__Map_rp.html" title="the coordinate ring of the graph of the regular map corresponding to a ring map">graphRing(RingMap)</a> -- the coordinate ring of the graph of the regular map corresponding to a ring map</span></li>
<li><span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></li>
<li><span>Ring / List, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>Ring / Module, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>Ring / RingElement, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>Ring / Sequence, see <span><a href="___Ring_sp_sl_sp__Ideal.html" title="make a quotient ring">Ring / Ideal</a> -- make a quotient ring</span></span></li>
<li><span>singularLocus(Ideal), see <span><a href="_singular__Locus.html" title="singular locus">singularLocus</a> -- singular locus</span></span></li>
<li><span>singularLocus(Ring), see <span><a href="_singular__Locus.html" title="singular locus">singularLocus</a> -- singular locus</span></span></li>
</ul>
<h2>Methods that use a quotient ring :</h2>
<ul><li><span>ambient(QuotientRing), see <span><a href="_ambient_lp__Ring_rp.html" title="ambient polynomial ring">ambient(Ring)</a> -- ambient polynomial ring</span></span></li>
<li><span><a href="_codim_lp__Quotient__Ring_rp.html" title="compute the codimension">codim(QuotientRing)</a> -- compute the codimension</span></li>
<li><span>degreesMonoid(QuotientRing), 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>describe(QuotientRing), see <span><a href="_describe.html" title="real description">describe</a> -- real description</span></span></li>
<li><span>dim(QuotientRing), 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>hilbertSeries(QuotientRing), see <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></span></li>
<li><span>ideal(QuotientRing), see <span><a href="_ideal_lp__Ring_rp.html" title="returns the defining ideal">ideal(Ring)</a> -- returns the defining ideal</span></span></li>
<li><span>isAffineRing(QuotientRing), 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>isQuotientOf(Ring,QuotientRing), see <span><a href="_is__Quotient__Of_lp__Ring_cm__Ring_rp.html" title="whether one ring is a quotient of another">isQuotientOf(Ring,Ring)</a> -- whether one ring is a quotient of another</span></span></li>
<li><span>isQuotientOf(Type,QuotientRing), see <span><a href="_is__Quotient__Of_lp__Type_cm__Ring_rp.html" title="whether one ring is a quotient of a ring of a given type">isQuotientOf(Type,Ring)</a> -- whether one ring is a quotient of a ring of a given type</span></span></li>
<li><span>isQuotientRing(QuotientRing), see <span><a href="_is__Quotient__Ring.html" title="whether something is a quotient ring">isQuotientRing</a> -- whether something is a quotient ring</span></span></li>
<li><span>isSkewCommutative(QuotientRing), 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(QuotientRing), see <span><a href="_monoid.html" title="make or retrieve a monoid">monoid</a> -- make or retrieve a monoid</span></span></li>
<li><span>newRing(QuotientRing), 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(QuotientRing), 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(QuotientRing), 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(QuotientRing), 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>presentation(QuotientRing), see <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></span></li>
<li><span>random(QuotientRing), see <span><a href="_random_lp__Type_rp.html" title="random element of a type">random(Type)</a> -- random element of a type</span></span></li>
<li><span><a href="_trim_lp__Quotient__Ring_rp.html" title="">trim(QuotientRing)</a></span></li>
</ul>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Quotient__Ring.html" title="the class of all quotient rings">QuotientRing</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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