University of Paderborn Department of Mathematics Diploma Thesis ...
University of Paderborn Department of Mathematics Diploma Thesis ...
University of Paderborn Department of Mathematics Diploma Thesis ...
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108 CHAPTER 4. ALGORITHMS FOR STABLE IDEALS[0, 1, 0, 3, 0], [0, 0, 4, 0, 0]], [[1, 0, 0, 0, 0], [0, 2, 0, 0, 0],[0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 0, 3, 0, 0]],[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 6, 0, 0], [0, 0, 5, 1, 0],[0, 0, 4, 2, 0]], [[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0],[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]],[[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0],[0, 1, 0, 2, 0], [0, 0, 4, 0, 0]], [[1, 0, 0, 0, 0], [0, 2, 0, 0, 0],[0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 5, 0, 0], [0, 0, 4, 2, 0]],[[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 2, 0],[0, 0, 5, 0, 0], [0, 0, 4, 1, 0]], [[2, 0, 0, 0, 0], [1, 1, 0, 0, 0],[1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0],[0, 0, 3, 0, 0]], [[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0],[1, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 2, 0],[0, 0, 4, 0, 0]], [[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0],[1, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0],[0, 0, 5, 0, 0], [0, 0, 4, 1, 0]]}>> nops(%);Output12We have computed 12 saturated stable ideals with the given Hilbert polynomial. Again,as in Example 4.18, these ideals equal those, computed by Alyson Reeves in [16].In Example 4.18, we saw that there are 8 saturated stable ideals with the same Hilbertpolynomial and the same double saturation as the unique lexicographic ideal L p associatedto the Hilbert polynomial p(z) = 4z+1. The above lines show that there are four saturatedstable ideals with the given Hilbert polynomial but a double saturation, which differs fromthe double saturation <strong>of</strong> L p .