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<head><title>ideal(MonomialIdeal) -- converts a monomial ideal to an ideal</title>
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<div><h1>ideal(MonomialIdeal) -- converts a monomial ideal to an ideal</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>ideal I</tt></div>
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<li><span>Function: <a href="_ideal.html" title="make an ideal">ideal</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>a <a href="___Monomial__Ideal.html">monomial ideal</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Ideal.html">ideal</a></span>, which is generated by the monomials in <tt>I</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : I = monomialIdeal(x*y^2, x^2*z, y^2*z)
2 2 2
o2 = monomialIdeal (x*y , x z, y z)
o2 : MonomialIdeal of R</pre>
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<tr><td><pre>i3 : ideal I
2 2 2
o3 = ideal (x*y , x z, y z)
o3 : Ideal of R</pre>
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Most operations between <a href="___Ideal.html">ideals</a> and <a href="___Monomial__Ideal.html">monomial ideals</a> automatically perform the necessary conversions, so one rarely needs to apply the function <tt>ideal</tt> to a <a href="___Monomial__Ideal.html">monomial ideal</a>.<table class="examples"><tr><td><pre>i4 : I * ideal I
2 4 3 2 4 3 2 4 2 2 2 2 4 2 2 2 4 2
o4 = ideal (x y , x y z, x*y z, x y z, x z , x y z , x*y z, x y z , y z )
o4 : Ideal of R</pre>
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<tr><td><pre>i5 : I + ideal(x*y+y*z)
2 2 2
o5 = ideal (x*y , x z, y z, x*y + y*z)
o5 : Ideal of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_monomial__Ideal.html" title="make a monomial ideal">monomialIdeal</a> -- make a monomial ideal</span></li>
<li><span><a href="_generators_lp__Ideal_rp.html" title="the generator matrix of an ideal">generators(Ideal)</a> -- the generator matrix of an ideal</span></li>
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