Singular Manual: set

| #### D.14.8.1 set Procedure from library `sets.lib` (see sets_lib). Usage: set(l) or *=l (short form of * = set(l)); l list Return: Set, the set createt from the entered list Example:
    LIB "sets.lib";
    //example for set
    Set S0a = list(list(1,2,3),list(list(1,2)),list(10,11));
    Set S0b = list(list(10,11),list(list(1,2)));
    S0b<S0a;
    ==> 1
    S0a<S0b;
    ==> 0
    S0a==S0a;
    ==> 1
    S0a==S0b;
    ==> 0
    list L = 1,1,2,3;
    Set S1 = L;
    S1;
    ==> {3; 2; 1}
    ==> Set with 3 elements
    ==>
    ring R1;
    ring R2 = 0,(x,y),dp;
    Set S2 = list(R1,R1,R2);
    S2;
    ==> {(QQ),(x,y),(dp(2),C); (ZZ/32003),(x,y,z),(dp(3),C)}
    ==> Set with 2 elements
    ==>
    ideal I1 = x+y;
    ideal I2 = y^2;
    ideal I3 = x+y, (x+y)^3;
    Set S3 = list(I1,I2,I3);
    S3;
    ==> {y2; x+y}
    ==> Set with 2 elements
    ==>
    isEqual(I1,I3);
    ==> 1
    isEqual(I1,I2);
    ==> 0
    module M1 = x*gen(1), y*gen(1);
    module M2 = y^2*gen(2);
    module M3 = (x+y)*gen(1), (x-y)*gen(1);
    Set S4 = list(M1,M2,M3);
    S4;
    ==> {y2*gen(2); x*gen(1),y*gen(1)}
    ==> Set with 2 elements
    ==>
    intmat m1[2][3]= 1,2,3,4,5,6;
    intmat m2[2][3]= 1,2,3,4,5,7;
    Set S5 = list(m1,m2,m1);
    S5;
    ==> {1,2,3,4,5,7 ; 1,2,3,4,5,6 }
    ==> Set with 2 elements
    ==>
    bigintmat b1[2][3]= 1,2,3,4,5,6;
    bigintmat b2[2][3]= 1,2,3,4,5,7;
    Set S6 = list(b1,b2,b1);
    S6;
    ==> {[ [ 1, 2, 3 ], [ 4, 5, 7 ] ] ; [ [ 1, 2, 3 ], [ 4, 5, 6 ] ] }
    ==> Set with 2 elements
    ==>
    resolution r1 = res(maxideal(3),0);
    resolution r2 = res(maxideal(4),0);
    Set S7 = list(r1,r1,r2);
    size(S7);
    ==> 2

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