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<head><title>Monoid -- the class of all monoids</title>
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<div><h1>Monoid -- the class of all monoids</h1>
<div class="single"><h2>Description</h2>
<div>A monoid is a set with a multiplicative operation on it and an identity element. A typical monoid is the set of monomials in a polynomial ring, which we consider to be created before the polynomial ring is created.</div>
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<div class="waystouse"><h2>Types of monoid :</h2>
<ul><li><span><a href="___Ordered__Monoid.html" title="the class of all ordered monoids">OrderedMonoid</a> -- the class of all ordered monoids</span></li>
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<h2>Functions and methods returning a monoid :</h2>
<ul><li><span>degreesMonoid(GeneralOrderedMonoid), 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>degreesRing(GeneralOrderedMonoid), see <span><a href="_degrees__Ring_lp__Ring_rp.html" title="the ring of degrees">degreesRing(Ring)</a> -- the ring of degrees</span></span></li>
<li><span><a href="___Monoid_sp_st_st_sp__Monoid.html" title="tensor product of monoids">Monoid ** Monoid</a> -- tensor product of monoids</span></li>
<li><span>tensor(Monoid,Monoid), see <span><a href="_tensor_lp__Ring_cm__Ring_rp.html" title="tensor product">tensor(Ring,Ring)</a> -- tensor product</span></span></li>
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<h2>Methods that use a monoid :</h2>
<ul><li><span><a href="_options_lp__Monoid_rp.html" title="get values used for optional arguments">options(Monoid)</a> -- get values used for optional arguments</span></li>
<li><span>use(Monoid), see <span><a href="_use_lp__Ring_rp.html" title="install ring variables and ring operations">use(Ring)</a> -- install ring variables and ring operations</span></span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Monoid.html" title="the class of all monoids">Monoid</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <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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