Singular Manual: linReduceIdeal

| ##### 7.5.2.0. linReduceIdeal Procedure from library `bfun.lib` (see bfun_lib). Usage: linReduceIdeal(I [,s,t,u]); I an ideal, s,t,u optional ints Return: ideal or list, linear reductum (over field) of I by its elements Purpose: reduces a list of polys only by linear reductions (no monomial multiplications) Note: If s<>0, a list consisting of the reduced ideal and the coefficient vectors of the used reductions given as module is returned. Otherwise (and by default), only the reduced ideal is returned. If t<>0 (and by default) all monomials are reduced (if possible), otherwise, only leading monomials are reduced. If u<>0 (and by default), the ideal is first sorted in increasing order. If u is set to 0 and the given ideal is not sorted in the way described, the result might not be as expected. Display: If `printlevel`=1, progress debug messages will be printed, if printlevel>=2, all the debug messages will be printed. Example:
    LIB "bfun.lib";
    ring r = 0,(x,y),dp;
    ideal I = 3,x+9,y4+5x,2y4+7x+2;
    linReduceIdeal(I);     // reduces tails
    ==> _[1]=0
    ==> _[2]=3
    ==> _[3]=x
    ==> _[4]=y4
    linReduceIdeal(I,0,0); // no reductions of tails
    ==> _[1]=0
    ==> _[2]=3
    ==> _[3]=x+9
    ==> _[4]=y4+5x
    list l = linReduceIdeal(I,1); // reduces tails and shows reductions used
    l;
    ==> [1]:
    ==>    _[1]=0
    ==>    _[2]=3
    ==>    _[3]=x
    ==>    _[4]=y4
    ==> [2]:
    ==>    _[1]=gen(4)-2*gen(3)+3*gen(2)-29/3*gen(1)
    ==>    _[2]=gen(1)
    ==>    _[3]=gen(2)-3*gen(1)
    ==>    _[4]=gen(3)-5*gen(2)+15*gen(1)
    module M = I;
    matrix(l[1]) - matrix(M)*matrix(l[2]);
    ==> _[1,1]=0
    ==> _[1,2]=0
    ==> _[1,3]=0
    ==> _[1,4]=0

User manual for Singular version 4.4.1, 2025, generated by texi2html.