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      <h1>Root -- the class of roots (or, more generally, elements of the root lattice)</h1>
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        <h2>Description</h2>
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          <p>a root is represented by the respective weight</p>
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        <h3>Menu</h3>
        <ul>
          <li><span><a title="adding roots" href="_add__Roots.html">addRoots</a> -- adding roots</span></li>
          <li><span><a title="the sum of two roots" href="_add__Roots_lp__Root__System_cm__Root_cm__Root_rp.html">addRoots(RootSystem,Root,Root)</a> -- the sum of two roots</span></li>
          <li><span><a title="multiplication of a root by an integer" href="___Z__Z_sp_st_sp__Root.html">ZZ * Root</a> -- multiplication of a root by an integer</span></li>
          <li><span><a title="the half-sum of positive roots" href="_half__Sum__Of__Roots.html">halfSumOfRoots</a> -- the half-sum of positive roots</span></li>
          <li><span><a title="a simple root" href="_simple__Root.html">simpleRoot</a> -- a simple root</span></li>
          <li><span><a title="the squared norm of a root" href="_norm_lp__Root__System_cm__Root_rp.html">norm(RootSystem,Root)</a> -- the squared norm of a root</span></li>
          <li><span><a title="coefficients at the simple roots" href="_root__Coefficients.html">rootCoefficients</a> -- coefficients at the simple roots</span></li>
          <li><span><a title="the set of all positive roots" href="_positive__Roots.html">positiveRoots</a> -- the set of all positive roots</span></li>
          <li><span><a title="the number of positive roots" href="_number__Of__Positive__Roots.html">numberOfPositiveRoots</a> -- the number of positive roots</span></li>
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          <h2>Methods that use an object of class Root:</h2>
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            <li><span><a title="the sum of two roots" href="_add__Roots_lp__Root__System_cm__Root_cm__Root_rp.html">addRoots(RootSystem,Root,Root)</a> -- the sum of two roots</span></li>
            <li><span><a title="evaluate the dual of a root at a Weight" href="_eval_lp__Root__System_cm__Weight_cm__Root_rp.html">eval(RootSystem,Weight,Root)</a> -- evaluate the dual of a root at a Weight</span></li>
            <li><span><a title="evaluate the dual of a root at a fundamental weight" href="_eval_lp__Root__System_cm__Z__Z_cm__Root_rp.html">eval(RootSystem,ZZ,Root)</a> -- evaluate the dual of a root at a fundamental weight</span></li>
            <li><span><a title="check whether a root is in the sub root system of the parabolic" href="_is__Root_lp__Root__System_cm__Parabolic_cm__Root_rp.html">isRoot(RootSystem,Parabolic,Root)</a> -- check whether a root is in the sub root system of the parabolic</span></li>
            <li><span><a title="the squared norm of a root" href="_norm_lp__Root__System_cm__Root_rp.html">norm(RootSystem,Root)</a> -- the squared norm of a root</span></li>
            <li><span><a title="apply to a root several reflections with respect to simple roots" href="_reflect_lp__Root__System_cm__Basic__List_cm__Root_rp.html">reflect(RootSystem,BasicList,Root)</a> -- apply to a root several reflections with respect to simple roots</span></li>
            <li><span><a title="apply to a root the reflection with respect to a simple root" href="_reflect_lp__Root__System_cm__Z__Z_cm__Root_rp.html">reflect(RootSystem,ZZ,Root)</a> -- apply to a root the reflection with respect to a simple root</span></li>
            <li><span><a title="the reflection with respect to a root" href="_reflection_lp__Root__System_cm__Root_rp.html">reflection(RootSystem,Root)</a> -- the reflection with respect to a root</span></li>
            <li><span><a title="the coefficients at the simple roots" href="_root__Coefficients_lp__Root__System_cm__Root_rp.html">rootCoefficients(RootSystem,Root)</a> -- the coefficients at the simple roots</span></li>
            <li><span><a title="apply an element of a Weyl group to a root" href="___Weyl__Group__Element_sp_st_sp__Root.html">WeylGroupElement * Root</a> -- apply an element of a Weyl group to a root</span></li>
            <li><span><a title="multiplication of a root by an integer" href="___Z__Z_sp_st_sp__Root.html">ZZ * Root</a> -- multiplication of a root by an integer</span></li>
          </ul>
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          <h2>For the programmer</h2>
          <p>The object <a title="the class of roots (or, more generally, elements of the root lattice)" href="___Root.html">Root</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of weights" href="___Weight.html">Weight</a> &lt; <a title="the class of all elements of modules that are handled by the engine" href="../../Macaulay2Doc/html/___Vector.html">Vector</a> &lt; <a title="the class of all basic lists" href="../../Macaulay2Doc/html/___Basic__List.html">BasicList</a> &lt; <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p>
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          <p>The source of this document is in <span class="tt">WeylGroups.m2:2059:0</span>.</p>
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