University of Paderborn Department of Mathematics Diploma Thesis ...

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94 CHAPTER 4. ALGORITHMS FOR STABLE IDEALSMuPAD Source Code 4.13. As in 4.9 and 4.11, let M denote a set of minimal generatorsof a saturated stable ideal (ordered with respect to the lexicographic order), m amonomial and n the index of the last variable of R. The procedure below checks for theexpandability of the monomial m in the ideal generated by M and returns “TRUE” if mis expandable and “FALSE”, otherwise.Input for the procedure test expandable.◦ M — a list of lists encoding the set of generators of some stable ideal in lexicographicorder◦ m — a list encoding a monomial◦ n — the index of the last variable of the polynomial ring ROutput of the procedure test expandable.◦ TRUE or FALSE — TRUE, if the monomial m is expandable in the ideal generated byM, and FALSE, otherwisetest_expandable:= proc(M, m, n)local RightShift, mon, last, i, j;begin/* If m is not contained in M, then returnFALSE (i.e. m is not expandable) */if contains(M, m) = 0 thenreturn(FALSE);end_if;/* Compute the right-shift of the monomial m.Therefore, first compute the index of thethe last variable in m */for i from n+1 downto 1 doif m[i] 0 thenlast:= i;break;end_if;end_for;RightShift:= {};for i from 1 to last do
4.4. COMPUTING EXPANSIONS AND CONTRACTIONS 95if m[i] > 0 thenmon:= m;mon[i]:= mon[i] - 1;mon[i+1]:= mon[i+1] + 1;RightShift:= RightShift union {mon};for j from i+1 to last doif m[j] = 0 thenmon:= m;mon[i]:= mon[i] - 1;mon[j+1]:= mon[j+1] + 1;RightShift:= RightShift union {mon};elsebreak;end_if;end_for;end_if;end_for;/* If any element of the right-shift is contained inthe set of minimal generators M of the idealconsidered, return FALSE (i.e. the monomial is notexpandable), otherwise return TRUE (i.e. the monomialis expandable). */for i from 1 to nops(RightShift) doif contains(M, RightShift[i]) > 0 thenreturn(FALSE);end_if;end_for;return(TRUE);end_proc:MuPAD Source Code 4.14. With the same notation as in 4.13, the following procedurechecks whether the monomial m is contractible in the ideal generated by the set M. Itreturns “TRUE” if m is contractible and “FALSE” if this is not the case.Input for the procedure test contractible.◦ M — a list of lists encoding the set of generators of some stable ideal in lexicographicorder◦ m — a list encoding a monomial◦ n — the index of the last variable of the polynomial ring R
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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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