University of Paderborn Department of Mathematics Diploma Thesis ...

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