University of Paderborn Department of Mathematics Diploma Thesis ...

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84 CHAPTER 4. ALGORITHMS FOR STABLE IDEALSOutput. Set of minimal generators of the ideal L p .Proof. (Correctness) By Remark 1.11 and Theorem 2.25, the algorithm is correct.MuPAD Source Code 4.7. A possible implementation of Algorithm 4.6 is the following,where we use lists to represent monomials as in 4.1 and 4.3. The procedure expects aHilbert polynomial p and the index of the last variable of R and outputs the set of generatorsof the unique lexicographic ideal L p .Input for the procedure compute L p.◦ p — the Hilbert polynomial of R/I◦ n — the index of the last variable of the polynomial ring ROutput of the procedure compute L p.◦ L p — a list of lists encoding the set of minimal generators of the lexicographic idealL p associated to pcompute_L_p:= proc(p, n)local indet, coeff, deg, m, a, L_p, monom, cnt, i;beginindet:= op(p)[2][1];deg:= degree(p);m:= [0 $ deg + 1];a:= m;/* Compute the m_i’s */for i from deg downto 1 docoeff:= lcoeff(p);m[i+1]:= i! * coeff;p:= p - poly(expand(binomial(indet + i, i+1)),[indet])+ poly(expand(binomial(indet + i - m[i+1], i+1)),[indet]);end_for;m[1]:= op(p)[1];/* Compute the a_i’s */a[deg + 1]:= m[deg + 1];for i from deg - 1 downto 0 do
4.3. COMPUTING THE LEXICOGRAPHIC IDEAL L P 85a[i+1]:= m[i+1] - m[i+2];end_for;/* Construction of the set of minimal generators of L_p */L_p:= [];for i from 0 to n-deg-2 domonom:= [0 $ i, 1, 0 $ n-i];L_p:= append(L_p, monom);end_for;cnt:= 0;if n-deg-1
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University of PaderbornDepartment o
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”Im großen Garten der Geometriek
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AbstractThe main result of this the
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Glossary of MuPAD procedures 129Bib
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This thesis is organized in four ch
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6described in Chapter 4.Additionall
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8 CHAPTER 1. NOTATIONS AND PREREQUI
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20 CHAPTER 2. STABLE IDEALSExample
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22 CHAPTER 2. STABLE IDEALSset, whe
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26 CHAPTER 2. STABLE IDEALSRemark a
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28 CHAPTER 2. STABLE IDEALSby Lemma
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30 CHAPTER 2. STABLE IDEALSwith Hil
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32 CHAPTER 2. STABLE IDEALSfor all
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