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<head><title>associatedPrimes(..., Strategy => ...)</title>
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<div><h1>associatedPrimes(..., Strategy => ...)</h1>
<div class="single"><h2>Description</h2>
<div>The strategy option value is currently not considered while computing associated primes<p/>
There are three methods for computing associated primes in Macaulay2: If the ideal is a monomial ideal, use code that Greg Smith and Serkan Hosten wrote. If a primary decomposition has already been found, use the stashed associated primes found. If neither of these is the case, then use Ext modules to find the associated primes (this is <tt>Strategy=>1</tt>)<p/>
In order to use the monomial ideal algorithm, it is necessary to make <tt>I</tt> into a monomial ideal.<table class="examples"><tr><td><pre>i1 : S = QQ[a,b,c,d,e];</pre>
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<tr><td><pre>i2 : I1 = ideal(a,b,c);
o2 : Ideal of S</pre>
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<tr><td><pre>i3 : I2 = ideal(a,b,d);
o3 : Ideal of S</pre>
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<tr><td><pre>i4 : I3 = ideal(a,e);
o4 : Ideal of S</pre>
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<tr><td><pre>i5 : P = I1*I2*I3
3 2 2 2 2 2 2
o5 = ideal (a , a e, a b, a*b*e, a d, a*d*e, a b, a*b*e, a*b , b e, a*b*d,
------------------------------------------------------------------------
2
b*d*e, a c, a*c*e, a*b*c, b*c*e, a*c*d, c*d*e)
o5 : Ideal of S</pre>
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<tr><td><pre>i6 : L1 = associatedPrimes P
o6 = {ideal (e, a), ideal (d, b, a), ideal (c, b, a), ideal (d, c, b, a),
------------------------------------------------------------------------
ideal (e, c, b, a), ideal (e, d, b, a), ideal (e, d, c, b, a)}
o6 : List</pre>
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<tr><td><pre>i7 : L2 = apply(associatedPrimes monomialIdeal P, J -> ideal J)
o7 = {ideal (a, e), ideal (a, b, c), ideal (a, b, d), ideal (a, b, c, d),
------------------------------------------------------------------------
ideal (a, b, c, e), ideal (a, b, d, e), ideal (a, b, c, d, e)}
o7 : List</pre>
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<tr><td><pre>i8 : M1 = set apply(L1, I -> sort flatten entries gens I)
o8 = set {{c, b, a}, {d, b, a}, {d, c, b, a}, {e, a}, {e, c, b, a}, {e, d, b,
------------------------------------------------------------------------
a}, {e, d, c, b, a}}
o8 : Set</pre>
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<tr><td><pre>i9 : M2 = set apply(L2, I -> sort flatten entries gens I)
o9 = set {{c, b, a}, {d, b, a}, {d, c, b, a}, {e, a}, {e, c, b, a}, {e, d, b,
------------------------------------------------------------------------
a}, {e, d, c, b, a}}
o9 : Set</pre>
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<tr><td><pre>i10 : assert(M1 === M2)</pre>
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The method using Ext modules comes from Eisenbud-Huneke-Vasconcelos, Invent. Math 110 (1992) 207-235.</div>
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<h2>Further information</h2>
<ul><li><span>Default value: <tt>1</tt></span></li>
<li><span>Function: <span><a href="_associated__Primes.html" title="find the associated primes of an ideal">associatedPrimes</a> -- find the associated primes of an ideal</span></span></li>
<li><span>Option name: <span><a href="___Strategy.html" title="name for an optional argument">Strategy</a> -- name for an optional argument</span></span></li>
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