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<div><h1>generators -- provide matrix or list of generators</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>generators x</tt><br/><tt>gens x</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>x</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span>provides the generators of <tt>x</tt> in a convenient form, as a list or a matrix, depending on the type</span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>CoefficientRing => </tt><span><span>default value null</span>, only used if <tt>x</tt> is a ring</span></span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
Produces the generators of a Gröbner basis, a polynomial ring, an ideal, a free module, a free group, a submodule given by means of generators (or for which generators have been computed), or a free monoid.<p/>
Usually the result is a list of generators, but the generators of a module or Gröbner basis are provided as the columns in a matrix. The matrix is stored in a module M under M.generators, unless the matrix is the identity matrix.<p/>
The symbol <tt>gens</tt> is a synonym for <tt>generators</tt>.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_numgens.html" title="the number of generators">numgens</a> -- the number of generators</span></li>
<li><span><a href="___Monoid.html" title="the class of all monoids">Monoid</a> -- the class of all monoids</span></li>
<li><span><a href="___Groebner__Basis.html" title="the class of all Gröbner bases">GroebnerBasis</a> -- the class of all Gröbner bases</span></li>
<li><span><a href="___Module.html" title="the class of all modules">Module</a> -- the class of all modules</span></li>
<li><span><a href="_relations.html" title="the defining relations">relations</a> -- the defining relations</span></li>
<li><span><a href="_subquotient.html" title="make a subquotient module">subquotient</a> -- make a subquotient module</span></li>
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<div class="waystouse"><h2>Ways to use <tt>generators</tt> :</h2>
<ul><li><span><a href="_generators_lp__General__Ordered__Monoid_rp.html" title="list of generators">generators(GeneralOrderedMonoid)</a> -- list of generators</span></li>
<li><span><a href="_generators_lp__Groebner__Basis_rp.html" title="the generator matrix of a Gröbner basis">generators(GroebnerBasis)</a> -- the generator matrix of a Gröbner basis</span></li>
<li><span><a href="_generators_lp__Ideal_rp.html" title="the generator matrix of an ideal">generators(Ideal)</a> -- the generator matrix of an ideal</span></li>
<li><span>generators(MonomialIdeal), see <span><a href="_generators_lp__Ideal_rp.html" title="the generator matrix of an ideal">generators(Ideal)</a> -- the generator matrix of an ideal</span></span></li>
<li><span><a href="_generators_lp__Module_rp.html" title="the generator matrix of a module">generators(Module)</a> -- the generator matrix of a module</span></li>
<li><span><a href="_generators_lp__Ring_rp.html" title="the list of generators of a ring">generators(Ring)</a> -- the list of generators of a ring</span></li>
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