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<div><h1>component example</h1>
<div>The following simple example illustrates the use of <a href="_remove__Lowest__Dimension.html" title="remove components of lowest dimension">removeLowestDimension</a>,<a href="_top__Components.html" title="compute top dimensional component">topComponents</a>,<a href="_radical.html" title="the radical of an ideal">radical</a>, and <a href="_minimal__Primes.html" title="minimal associated primes of an ideal">minimalPrimes</a>.<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[a..d];</pre>
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<tr><td><pre>i2 : I = monomialCurveIdeal(R,{1,3,4})
3 2 2 2 3 2
o2 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : J = ideal(a^3,b^3,c^3-d^3)
3 3 3 3
o3 = ideal (a , b , c - d )
o3 : Ideal of R</pre>
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<tr><td><pre>i4 : I = intersect(I,J)
4 3 3 3 4 3 3 4 6 3 2
o4 = ideal (b - a d, a*b - a c, b*c - a*c d - b*c*d + a*d , c - b*c d -
------------------------------------------------------------------------
3 3 5 5 2 3 2 3 2 4 2 4 3 3 3 3 2 3
c d + b*d , a*c - b c d - a*c d + b d , a c - a d + b d - a c*d ,
------------------------------------------------------------------------
3 3 3 3 2 3 3 2 3 2 2 3 2 3 3 2 3 2
b c - a d , a*b c - a c*d + b c*d - a*b d , a b*c - a c d + b c d -
------------------------------------------------------------------------
2 3 3 3 3 2 4 2 3 2
a b*d , a c - a b*d , a c - a b d)
o4 : Ideal of R</pre>
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<tr><td><pre>i5 : removeLowestDimension I
3 2 2 2 3 2
o5 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o5 : Ideal of R</pre>
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<tr><td><pre>i6 : topComponents I
3 2 2 2 3 2
o6 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o6 : Ideal of R</pre>
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<tr><td><pre>i7 : radical I
2 2 3 2 6 3 3 2 4 5
o7 = ideal (b*c - a*d, a*c - b d, b - a c, c - c d - b d + b*d )
o7 : Ideal of R</pre>
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<tr><td><pre>i8 : minimalPrimes I
3 2 2 2 3 2
o8 = {ideal (- b*c + a*d, - c + b*d , a*c - b d, - b + a c), ideal (- c +
------------------------------------------------------------------------
2 2
d, b, a), ideal (c + c*d + d , b, a)}
o8 : List</pre>
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