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<head><title>ring -- get the associated ring of an object</title>
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<div><h1>ring -- get the associated ring of an object</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>ring M</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, an object with a ring associated to it</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring.html">ring</a></span>, associated to the input object</span></li>
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<div class="single"><h2>Description</h2>
<div>For example, ring elements, matrices, ideals, modules, chain complexes, varieties, coherent sheaves, etc., all have a base ring naturally associated to them. <table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y,z];</pre>
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<tr><td><pre>i2 : ring x
o2 = R
o2 : PolynomialRing</pre>
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<tr><td><pre>i3 : M = matrix {{2*x, x+y},{y^3, z*y}};
2 2
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : ring M
o4 = R
o4 : PolynomialRing</pre>
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<tr><td><pre>i5 : S = QQ[x,y,z];</pre>
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<tr><td><pre>i6 : ring x
o6 = S
o6 : PolynomialRing</pre>
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<tr><td><pre>i7 : I = ideal (x*y, y*z);
o7 : Ideal of S</pre>
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<tr><td><pre>i8 : ring I
o8 = S
o8 : PolynomialRing</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_base__Rings.html" title="store the list of base rings of a ring">baseRings</a> -- store the list of base rings of a ring</span></li>
<li><span><a href="_coefficient__Ring.html" title="get the coefficient ring">coefficientRing</a> -- get the coefficient ring</span></li>
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<div class="waystouse"><h2>Ways to use <tt>ring</tt> :</h2>
<ul><li>ring(CC)</li>
<li>ring(ChainComplex)</li>
<li>ring(ChainComplexMap)</li>
<li>ring(CoherentSheaf)</li>
<li>ring(GradedModule)</li>
<li>ring(GradedModuleMap)</li>
<li>ring(GroebnerBasis)</li>
<li>ring(Ideal)</li>
<li>ring(Matrix)</li>
<li>ring(Module)</li>
<li>ring(MonomialIdeal)</li>
<li>ring(MutableMatrix)</li>
<li>ring(Number)</li>
<li>ring(Resolution)</li>
<li>ring(RingElement)</li>
<li>ring(RR)</li>
<li>ring(SheafOfRings)</li>
<li>ring(Variety)</li>
<li>ring(Vector)</li>
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