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    <title>monoid(...,Local=>...) -- specify local or global monomial order</title>
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o1 = QQ[x..y]

o1 : PolynomialRing</code></pre>
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              <pre><code class="language-macaulay2">i2 : 1 > x

o2 = true</code></pre>
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              <pre><code class="language-macaulay2">i3 : 1 &lt; y

o3 = true</code></pre>
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              <pre><code class="language-macaulay2">i4 : leadTerm matrix{{x+x^2, y+y^2}}

o4 = | x y2 |

1               2
o4 : Matrix (QQ[x..y])  &lt;-- (QQ[x..y])</code></pre>
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          <p>The optional argument <span class="tt">Local</span> specifies whether all variables are smaller than 1 in the monomial order. Providing <span class="tt">Local => true</span> induces a local monomial ordering and in particular implies <span class="tt">Global => false</span>. A shortcut for indicating a local monomial ordering is to use a <a title="the class of all lists -- {...}" href="___List.html">List</a> to provide the variables.</p>
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              <pre><code class="language-macaulay2">i5 : QQ[x,y, Local => true]

o5 = QQ {x..y}

o5 : PolynomialRing</code></pre>
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              <pre><code class="language-macaulay2">i6 : 1 > x

o6 = true</code></pre>
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              <pre><code class="language-macaulay2">i7 : 1 > y

o7 = true</code></pre>
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              <pre><code class="language-macaulay2">i8 : QQ{x,y}

o8 = QQ {x..y}

o8 : PolynomialRing</code></pre>
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              <pre><code class="language-macaulay2">i9 : leadTerm matrix{{x+x^2, y+y^2}}

o9 = | x y |

1                2
o9 : Matrix (QQ {x..y})  &lt;-- (QQ {x..y})</code></pre>
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          <p>This option may also be used when creating a new ring from an existing ring, creating a tensor product ring, or symmetric algebra.</p>
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        <h2>See also</h2>
        <ul>
          <li><span><a href="_heft_spvectors.html">heft vectors</a></span></li>
          <li><span><a href="_monomial_sporderings.html">monomial orderings</a></span></li>
          <li><span><a title="make or retrieve a monoid" href="_monoid.html">monoid</a> -- make or retrieve a monoid</span></li>
          <li><span><a title="make a copy of a ring, with some features changed" href="_new__Ring.html">newRing</a> -- make a copy of a ring, with some features changed</span></li>
          <li><span><a title="tensor product of monoids" href="_tensor_lp__Monoid_cm__Monoid_rp.html">tensor(Ring,Ring)</a> -- tensor product of monoids</span></li>
          <li><span><a title="the symmetric algebra of a module" href="_symmetric__Algebra.html">symmetricAlgebra</a> -- the symmetric algebra of a module</span></li>
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          <h2>Functions with optional argument named <span class="tt">Local</span>:</h2>
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            <li><span><a title="specify local or global monomial order" href="_monoid_lp..._cm__Local_eq_gt..._rp.html">monoid(...,Local=>...)</a> -- specify local or global monomial order</span></li>
            <li><span><kbd>newRing(...,Local=>...)</kbd> -- see <span><a title="make a copy of a ring, with some features changed" href="_new__Ring.html">newRing</a> -- make a copy of a ring, with some features changed</span></span></li>
            <li><span><kbd>symmetricAlgebra(...,Local=>...)</kbd> -- see <span><a title="the symmetric algebra of a module" href="_symmetric__Algebra.html">symmetricAlgebra</a> -- the symmetric algebra of a module</span></span></li>
            <li><span><kbd>tensor(Monoid,Monoid,Local=>...)</kbd> -- see <span><a title="tensor product of monoids" href="_tensor_lp__Monoid_cm__Monoid_rp.html">tensor(Monoid,Monoid)</a> -- tensor product of monoids</span></span></li>
            <li><span><kbd>tensor(Ring,Ring,Local=>...)</kbd> -- see <span><a title="tensor product of monoids" href="_tensor_lp__Monoid_cm__Monoid_rp.html">tensor(Monoid,Monoid)</a> -- tensor product of monoids</span></span></li>
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          <h2>Further information</h2>
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            <li><span>Default value: <a href="_false.html">false</a></span></li>
            <li><span>Function: <span><a title="make or retrieve a monoid" href="_monoid.html">monoid</a> -- make or retrieve a monoid</span></span></li>
            <li><span>Option key: <span><a title="an optional argument" href="___Local.html">Local</a> -- an optional argument</span></span></li>
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        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Macaulay2Doc/functions/monoid-doc.m2:563:0</span>.</p>
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