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<head><title>Singular Book 1.8.15 -- saturation</title>
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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_basic_spcommutative_spalgebra.html" title="">basic commutative algebra</a> > <a href="___M2__Singular__Book.html" title="Macaulay2 examples for the Singular book">M2SingularBook</a> > <a href="___Singular_sp__Book_sp1.8.15.html" title="saturation">Singular Book 1.8.15</a></div>
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<div><h1>Singular Book 1.8.15 -- saturation</h1>
<div><table class="examples"><tr><td><pre>i1 : A = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : I1 = ideal(x^5*z^3, x*y*z, y*z^4);
o2 : Ideal of A</pre>
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<tr><td><pre>i3 : saturate(I1,z)
5
o3 = ideal (y, x )
o3 : Ideal of A</pre>
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Now we compute the saturation using a loop.<table class="examples"><tr><td><pre>i4 : J = I1:z
3 5 2
o4 = ideal (x*y, y*z , x z )
o4 : Ideal of A</pre>
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<tr><td><pre>i5 : k = 0;</pre>
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<tr><td><pre>i6 : while not isSubset(J,I1) do (
k = k+1;
I1 = J;
J = I1 : z;
);</pre>
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<tr><td><pre>i7 : J
5
o7 = ideal (y, x )
o7 : Ideal of A</pre>
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<tr><td><pre>i8 : k
o8 = 4</pre>
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We needed to use quotient four times.</div>
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