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<head><title>monomials -- matrix of monomials in a ring element or matrix</title>
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<div><h1>monomials -- matrix of monomials in a ring element or matrix</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>monomials f</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, either a <a href="___Matrix.html" title="the class of all matrices">Matrix</a> or a <a href="___Ring__Element.html" title="the class of all ring elements handled by the engine">RingElement</a></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, a one row matrix in the same ring with all of the monomials that appear in <tt>f</tt></span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_monomials_lp..._cm_sp__Variables_sp_eq_gt_sp..._rp.html">Variables => ...</a>, -- specify variables</span></li>
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<div class="single"><h2>Description</h2>
<div>Each monomial only appears once, and the monomials are sorted in what order?<table class="examples"><tr><td><pre>i1 : R = ZZ[a..d,x,y];</pre>
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<tr><td><pre>i2 : m = matrix{{a*x^2+b*x*y+c*y^2, a*x^3+b*x^2*y+c*x*y^2+d*y^3+a*x^2}}
o2 = | ax2+bxy+cy2 ax3+bx2y+cxy2+dy3+ax2 |
1 2
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : monomials m
o3 = | ax3 bx2y cxy2 dy3 ax2 bxy cy2 |
1 7
o3 : Matrix R <--- R</pre>
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If the monomials in only some of the variables are desired, use the optional argument <a href="_monomials_lp..._cm_sp__Variables_sp_eq_gt_sp..._rp.html" title="specify variables">monomials(..., Variables => ...)</a>.<table class="examples"><tr><td><pre>i4 : monomials(m, Variables=>{x,y})
o4 = | x3 x2y xy2 y3 x2 xy y2 |
1 7
o4 : Matrix R <--- R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_coefficients.html" title="monomials and their coefficients">coefficients</a> -- monomials and their coefficients</span></li>
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<div class="waystouse"><h2>Ways to use <tt>monomials</tt> :</h2>
<ul><li>monomials(Matrix)</li>
<li>monomials(RingElement)</li>
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