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<div><h1>GroebnerBasis -- the class of all Gröbner bases</h1>
<div class="single"><h2>Description</h2>
<div>A Gröbner basis in Macaulay2 consists of a Gröbner basis computation, and several associated matrices. Normally you don't need to refer to these objects directly, as many operations on matrices and modules create them, and refer to them. For more information, see <a href="___Gröbner_spbases.html" title="">Gröbner bases</a>.</div>
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<div class="waystouse"><h2>Functions and methods returning a Groebner basis :</h2>
<ul><li><span><a href="_force__G__B.html" title="declare that the columns of a matrix are a Gröbner basis">forceGB</a> -- declare that the columns of a matrix are a Gröbner basis</span></li>
<li><span>forceGB(Matrix), see <span><a href="_force__G__B.html" title="declare that the columns of a matrix are a Gröbner basis">forceGB</a> -- declare that the columns of a matrix are a Gröbner basis</span></span></li>
<li><span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></li>
<li><span>gb(Ideal), see <span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></span></li>
<li><span>gb(Matrix), see <span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></span></li>
<li><span>gb(Module), see <span><a href="_gb.html" title="compute a Gröbner basis">gb</a> -- compute a Gröbner basis</span></span></li>
<li><span>markedGB, see <span><a href="_marked__G__B_lp__Matrix_cm__Matrix_rp.html" title="make a marked Gröbner basis">markedGB(Matrix,Matrix)</a> -- make a marked Gröbner basis</span></span></li>
<li><span><a href="_marked__G__B_lp__Matrix_cm__Matrix_rp.html" title="make a marked Gröbner basis">markedGB(Matrix,Matrix)</a> -- make a marked Gröbner basis</span></li>
</ul>
<h2>Methods that use a Groebner basis :</h2>
<ul><li><span>ZZ % GroebnerBasis, see <span><a href="__pc.html" title="a binary operator, usually used for remainder and reduction">%</a> -- a binary operator, usually used for remainder and reduction</span></span></li>
<li><span><a href="_betti_lp__Groebner__Basis_rp.html" title="diagram of the degrees of a groebner basis">betti(GroebnerBasis)</a> -- diagram of the degrees of a groebner basis</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>getChangeMatrix(GroebnerBasis), see <span><a href="_get__Change__Matrix.html" title="get the change of basis matrix">getChangeMatrix</a> -- get the change of basis matrix</span></span></li>
<li><span>leadTerm(GroebnerBasis), see <span><a href="_lead__Term_lp__Matrix_rp.html" title="get the greatest term of each column">leadTerm(Matrix)</a> -- get the greatest term of each column</span></span></li>
<li><span><a href="___Matrix_sp_pc_sp__Groebner__Basis.html" title="calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis">Matrix % GroebnerBasis</a> -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis</span></li>
<li><span>RingElement % GroebnerBasis, see <span><a href="___Matrix_sp_pc_sp__Groebner__Basis.html" title="calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis">Matrix % GroebnerBasis</a> -- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis</span></span></li>
<li><span>Matrix // GroebnerBasis, see <span><a href="___Matrix_sp_sl_sl_sp__Matrix.html" title="factor a map through another">Matrix // Matrix</a> -- factor a map through another</span></span></li>
<li><span>RingElement // GroebnerBasis, see <span><a href="___Matrix_sp_sl_sl_sp__Matrix.html" title="factor a map through another">Matrix // Matrix</a> -- factor a map through another</span></span></li>
<li><span><a href="_mingens_lp__Groebner__Basis_rp.html" title="(partially constructed) minimal generator matrix">mingens(GroebnerBasis)</a> -- (partially constructed) minimal generator matrix</span></li>
<li><span><a href="_quotient_lp__Matrix_cm__Groebner__Basis_rp.html" title="matrix quotient">quotient(Matrix,GroebnerBasis)</a> -- matrix quotient</span></li>
<li><span>quotientRemainder(Matrix,GroebnerBasis), see <span><a href="_quotient__Remainder.html" title="matrix quotient and remainder">quotientRemainder</a> -- matrix quotient and remainder</span></span></li>
<li><span>remainder(Matrix,GroebnerBasis), see <span><a href="_remainder.html" title="matrix remainder">remainder</a> -- matrix remainder</span></span></li>
<li><span>ring(GroebnerBasis), see <span><a href="_ring.html" title="get the associated ring of an object">ring</a> -- get the associated ring of an object</span></span></li>
<li><span>status(GroebnerBasis), see <span><a href="_status.html" title="status of a resolution computation">status</a> -- status of a resolution computation</span></span></li>
<li><span><a href="_syz_lp__Groebner__Basis_rp.html" title="retrieve the syzygy matrix">syz(GroebnerBasis)</a> -- retrieve the syzygy matrix</span></li>
<li><span><a href="_target_lp__Groebner__Basis_rp.html" title="find target of a Gröbner basis">target(GroebnerBasis)</a> -- find target of a Gröbner basis</span></li>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Groebner__Basis.html" title="the class of all Gröbner bases">GroebnerBasis</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <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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