University of Paderborn Department of Mathematics Diploma Thesis ...

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96 CHAPTER 4. ALGORITHMS FOR STABLE IDEALSOutput of the procedure test contractible.◦ TRUE or FALSE — TRUE, if the monomial m is contractible in the ideal generated byM, and FALSE, otherwisetest_contractible:= proc(M, m, n)local LeftShift, mon, mon1, mon2, last, pos,contractible, cnt, i, j, k;begin/* If m is contained in M return FALSE(i.e. the monomial is not contractible) */if contains(M, m) > 0 thenreturn(FALSE);end_if;/* Compute the index of the last variable of mand the left-shift of m */for i from n+1 downto 0 doif m[i] 0 thenlast:= i;break;end_if;end_for;/* If m multiplied by its last variable is notcontained in M, then also return FALSE */mon:= m;mon[last]:= mon[last] + 1;pos:= contains(M, mon);if pos = 0 thenreturn(FALSE);end_if;/* Compute the left-shift of m and check whetherit is contained in the ideal */LeftShift:= {};for i from last downto 2 doif m[i] > 0 then
4.4. COMPUTING EXPANSIONS AND CONTRACTIONS 97mon:= m;mon[i]:= mon[i] - 1;mon[i-1]:= mon[i-1] + 1;LeftShift:= LeftShift union {mon};for j from i-1 downto 2 doif m[j] = 0 thenmon:= m;mon[i]:= mon[i] - 1;mon[j-1]:= mon[j-1] + 1;LeftShift:= LeftShift union {mon};elsebreak;end_if;end_for;end_if;end_for;/* Since the set M is ordered with respect to thelexicographic order, it suffices to check, whetherall elements of LeftShift are divisible by one ofthe monomials to the left of m.By ’pos’ we denote the position of this monomial(see above). */contractible:= FALSE;cnt:= nops(LeftShift);for i from 1 to nops(LeftShift) domon1:= LeftShift[i];for j from pos downto 1 domon2:= M[j];for k from n+1 downto 1 doif mon1[k] - mon2[k] >= 0 thencontractible:= TRUE;elsecontractible:= FALSE;break;end_if;end_for;if contractible = TRUE thencnt:= cnt - 1;break;end_if;
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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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University of Paderborn Department of Mathematics Diploma Thesis ...

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