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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_ideals.html" title="">ideals</a> > <a href="_creating_span_spideal.html" title="">creating an ideal</a></div>
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<div><h1>creating an ideal</h1>
<div><h2>ideal</h2>
An ideal <tt>I</tt> is represented by its generators. We use the function <a href="_ideal.html" title="make an ideal">ideal</a> to construct an ideal.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : I = ideal (a^2*b-c^2, a*b^2-d^3, c^5-d)
2 2 2 3 5
o2 = ideal (a b - c , a*b - d , c - d)
o2 : Ideal of R</pre>
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<h2>monomial ideals</h2>
For a monomial ideal you can use the function <a href="_monomial__Ideal.html" title="make a monomial ideal">monomialIdeal</a>.<table class="examples"><tr><td><pre>i3 : J = monomialIdeal (a^2*b, b*c*d, c^5)
2 5
o3 = monomialIdeal (a b, c , b*c*d)
o3 : MonomialIdeal of R</pre>
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The distinction is small since a monomial ideal can be constructed using <tt>ideal</tt> . However, there are a few functions, like <a href="../../PrimaryDecomposition/html/_primary__Decomposition.html" title="irredundant primary decomposition of an ideal">primaryDecomposition</a> that run faster if you define a monomial ideal using <tt>monomialIdeal</tt>.<h2>monomialCurveIdeal</h2>
An interesting class of ideals can be obtained as the defining ideals in projective space of monomial curves. For example the twisted cubic is the closure of the set of points <tt>(1,t^1,t^2,t^3)</tt> in projective space. We use a list of the exponents and <a href="_monomial__Curve__Ideal.html" title="make the ideal of a monomial curve">monomialCurveIdeal</a> to get the ideal.<table class="examples"><tr><td><pre>i4 : monomialCurveIdeal(R,{1,2,3})
2 2
o4 = ideal (c - b*d, b*c - a*d, b - a*c)
o4 : Ideal of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_ideal.html" title="make an ideal">ideal</a> -- make an ideal</span></li>
<li><span><a href="_monomial__Ideal.html" title="make a monomial ideal">monomialIdeal</a> -- make a monomial ideal</span></li>
<li><span><a href="_monomial__Curve__Ideal.html" title="make the ideal of a monomial curve">monomialCurveIdeal</a> -- make the ideal of a monomial curve</span></li>
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