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    <title>GroebnerWalk -- Compute Groebner bases via the Groebner walk</title>
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o2 : Ideal of R1</code></pre>
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          <p>If we want a Groebner basis of I with respect to the monomial order given by using a different weight vector and then graded reverse lexicographic we could substitute and compute directly,</p>
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              <pre><code class="language-macaulay2">i3 : R2 = QQ[x,y,z,u,v, MonomialOrder=>Weights=>{0,0,0,1,1}];</code></pre>
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              <pre><code class="language-macaulay2">i4 : I2 = sub(I1, R2);

o4 : Ideal of R2</code></pre>
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              <pre><code class="language-macaulay2">i5 : elapsedTime gb I2
 -- 2.62691s elapsed

o5 = GroebnerBasis[status: done; S-pairs encountered up to degree 16]

o5 : GroebnerBasis</code></pre>
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          <p>but it is faster to compute directly in the first order and then use the Groebner walk.</p>
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              <pre><code class="language-macaulay2">i6 : elapsedTime groebnerWalk(gb I1, R2)
 -- 2.15622s elapsed

o6 = GroebnerBasis[status: done; S-pairs encountered up to degree 0]

o6 : GroebnerBasis</code></pre>
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        <h2>Caveat</h2>
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          <p>The target ring must be the same ring as the ring of the starting ideal, except with different monomial order. The ring must be a polynomial ring over a field.</p>
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        <h2>See also</h2>
        <ul>
          <li><span><a title="Gröbner basis, as a matrix" href="../../Macaulay2Doc/html/_groebner__Basis.html">groebnerBasis</a> -- Gröbner basis, as a matrix</span></li>
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            <h2>Author</h2>
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              <li><a href="https://www.math.cornell.edu/~djp282">Dylan Peifer</a><span> &lt;<a href="mailto:djp282%40cornell.edu">djp282@cornell.edu</a>></span></li>
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            <h2>Version</h2>
            <p>This documentation describes version <b>1.0.0</b> of GroebnerWalk, released <b>November 17, 2017</b>.</p>
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            <h2>Citation</h2>
            <p>If you have used this package in your research, please cite it as follows:</p>
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                  <pre><code class="language-bib">@misc{GroebnerWalkSource,
  title = {{GroebnerWalk: Groebner bases via the Groebner walk. Version~1.0.0}},
  author = {Dylan Peifer},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}
</code></pre>
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            <h2>Exports</h2>
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                <li>Functions and commands                  <ul>
                    <li><span><a title="get current value of walkTrace" href="_get__Walk__Trace.html">getWalkTrace</a> -- get current value of walkTrace</span></li>
                    <li><span><a title="convert a Groebner basis" href="_groebner__Walk.html">groebnerWalk</a> -- convert a Groebner basis</span></li>
                    <li><span><a title="set value of walkTrace" href="_set__Walk__Trace.html">setWalkTrace</a> -- set value of walkTrace</span></li>
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                <li>Methods                  <ul>
                    <li><span><kbd>groebnerWalk(GroebnerBasis,Ring)</kbd> -- see <span><a title="convert a Groebner basis" href="_groebner__Walk.html">groebnerWalk</a> -- convert a Groebner basis</span></span></li>
                    <li><span><kbd>groebnerWalk(Ideal,Ring)</kbd> -- see <span><a title="convert a Groebner basis" href="_groebner__Walk.html">groebnerWalk</a> -- convert a Groebner basis</span></span></li>
                    <li><span><kbd>setWalkTrace(ZZ)</kbd> -- see <span><a title="set value of walkTrace" href="_set__Walk__Trace.html">setWalkTrace</a> -- set value of walkTrace</span></span></li>
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          <h2>For the programmer</h2>
          <p>The object <a title="Compute Groebner bases via the Groebner walk" href="index.html">GroebnerWalk</a> is <span>a <a title="the class of all packages" href="../../Macaulay2Doc/html/___Package.html">package</a></span>, defined in <span class="tt">GroebnerWalk.m2</span>.</p>
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          <p>The source of this document is in <span class="tt">GroebnerWalk.m2:435:0</span>.</p>
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