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<head><title>monomialIdeal(Matrix) -- monomial ideal of lead monomials</title>
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<div><h1>monomialIdeal(Matrix) -- monomial ideal of lead monomials</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>monomialIdeal L</tt></div>
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<li><span>Function: <a href="_monomial__Ideal.html" title="make a monomial ideal">monomialIdeal</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>L</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, <span>a <a href="___Ring__Element.html">ring element</a></span>, <span>a <a href="___List.html">list</a></span>, or <span>a <a href="___Sequence.html">sequence</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Monomial__Ideal.html">monomial ideal</a></span>, the monomial ideal of lead monomials of the elements of L</span></li>
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<div class="single"><h2>Description</h2>
<div>If L is a matrix, then it must have only one row. For all of these types, the result is generated by only the lead monomials given: no Gröbner bases are computed. See <a href="_monomial__Ideal_lp__Ideal_rp.html" title="monomial ideal of lead monomials of a Gröbner basis">monomialIdeal(Ideal)</a> if the lead monomials of a Gröbner basis is desired.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b,c];</pre>
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<tr><td><pre>i2 : I = monomialIdeal(a^3,b^3,c^3, a^2-b^2)
2 3 3
o2 = monomialIdeal (a , b , c )
o2 : MonomialIdeal of R</pre>
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<tr><td><pre>i3 : M = monomialIdeal vars R
o3 = monomialIdeal (a, b, c)
o3 : MonomialIdeal of R</pre>
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<tr><td><pre>i4 : J = monomialIdeal 0_R
o4 = 0
o4 : MonomialIdeal of R</pre>
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If the coefficient ring is ZZ, lead coefficients of the monomials are ignored.<table class="examples"><tr><td><pre>i5 : R = ZZ[x,y]
o5 = R
o5 : PolynomialRing</pre>
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<tr><td><pre>i6 : monomialIdeal(2*x,3*y)
o6 = monomialIdeal (x, y)
o6 : MonomialIdeal of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Monomial__Ideal.html" title="the class of all monomial ideals handled by the engine">MonomialIdeal</a> -- the class of all monomial ideals handled by the engine</span></li>
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