Singular Manual: pairset

| #### D.12.4.11 pairset Procedure from library `teachstd.lib` (see teachstd_lib). Usage: pairset(G); G ideal or module Return: list L, L[1] = the pairset of G as list (not containing pairs for which the product or the chain criterion applies), L[2] = intvec v, v[1]= # product criterion, v[2]= # chain criterion Example:
    LIB "teachstd.lib";
    ring r=0,(x,y,z),dp;
    ideal G = x2y+x2,y3+xyz,xyz2+z4;
    pairset(G);"";
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=x2y+x2
    ==>       _[2]=y3+xyz
    ==>    [2]:
    ==>       _[1]=x2y+x2
    ==>       _[2]=xyz2+z4
    ==>    [3]:
    ==>       _[1]=y3+xyz
    ==>       _[2]=xyz2+z4
    ==> [2]:
    ==>    0,0
    ==>
    module T = [x2y3-z2,x2y],[x2y2+z2,x2-y2],[x2y4+z3,x2+y2];
    pairset(T);
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=x2y3*gen(1)+x2y*gen(2)-z2*gen(1)
    ==>       _[2]=x2y2*gen(1)+x2*gen(2)-y2*gen(2)+z2*gen(1)
    ==>    [2]:
    ==>       _[1]=x2y3*gen(1)+x2y*gen(2)-z2*gen(1)
    ==>       _[2]=x2y4*gen(1)+z3*gen(1)+x2*gen(2)+y2*gen(2)
    ==> [2]:
    ==>    0,1

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