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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_ideals.html" title="">ideals</a> > <a href="_minimal_spprimes_spof_span_spideal.html" title="">minimal primes of an ideal</a></div>
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<div><h1>minimal primes of an ideal</h1>
<div><h2>using minimalPrimes</h2>
To obtain a list of the minimal associated primes for an ideal <tt>I</tt> (i.e. the smallest primes containing <tt>I</tt>), use the function <a href="_minimal__Primes.html" title="minimal associated primes of an ideal">minimalPrimes</a>.<table class="examples"><tr><td><pre>i1 : R = QQ[w,x,y,z];</pre>
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<tr><td><pre>i2 : I = ideal(w*x^2-42*y*z, x^6+12*w*y+x^3*z, w^2-47*x^4*z-47*x*z^2)
2 6 3 4 2 2
o2 = ideal (w*x - 42y*z, x + x z + 12w*y, - 47x z - 47x*z + w )
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : minimalPrimes I
3
o3 = {ideal (x + z, w, y), ideal (x, w, y), ideal (x, z, w)}
o3 : List</pre>
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If the ideal given is a prime ideal then <tt>minimalPrimes</tt> will return the ideal given.<table class="examples"><tr><td><pre>i4 : R = ZZ/101[w..z];</pre>
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<tr><td><pre>i5 : I = ideal(w*x^2-42*y*z, x^6+12*w*y+x^3*z, w^2-47*x^4*z-47*x*z^2);
o5 : Ideal of R</pre>
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<tr><td><pre>i6 : minimalPrimes I
2 4 2 2 2 2 2 3
o6 = {ideal (12w*x + y*z, - 47x z - 47x*z + w , x y*z - 12w*x*z + 11w ,
------------------------------------------------------------------------
2 2 2 3 4 6 3
43w x*z + y z - 31w , - 42x - 42x z + w*y)}
o6 : List</pre>
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<h2>warning</h2>
Warning (15 May 2001): If you stop a function mid process and then run <tt>minimalPrimes</tt> an error is given. Restarting Macaulay2 and then running <tt>minimalPrimes</tt> works around this.<p/>
See <a href="_associated_spprimes_spof_span_spideal.html" title="">associated primes of an ideal</a> for information on finding associated prime ideals and <a href="_primary_spdecomposition.html" title="">primary decomposition</a> for more information about finding the full primary decomposition of an ideal.</div>
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