Singular Manual: rcolon

| #### 7.10.5.2 rcolon Procedure from library `ncHilb.lib` (see ncHilb_lib). Usage: rcolon(list of relations, a monomial, an integer); L is a list of modules (each module represents a monomial), w is a monomail d is an integer for the degree bound (maximal total degree of monomials of the generating set of the input monomial ideal), Note : A two-sided monomial ideal and a monomial w for the input should be given in a special form. This form is a list of modules, where the generator of every module represents a monomial times a coefficient in the free associative algebra. The first entry, in each generator, represents a coefficient, that is 1, and every next entry is a variable. Ex: module p1=[1,y,z], represents the monomial y*z; module p2=[1,x,z,x], represents the monomial x*z*x for more details about the input, see examples. Example:
    LIB "ncHilb.lib";
    ring r=0,(X,Y,Z),dp;
    module w =[1,Y];
    module p1 =[1,Y,Z];
    module p2 =[1,Y,Z,X];
    module p3 =[1,Y,Z,Z,X,Z];
    module p4 =[1,Y,Z,Z,Z,X,Z];
    module p5 =[1,Y,Z,Z,Z,Z,X,Z];
    module p6 =[1,Y,Z,Z,Z,Z,Z,X,Z];
    module p7 =[1,Y,Z,Z,Z,Z,Z,Z,X,Z];
    module p8 =[1,Y,Z,Z,Z,Z,Z,Z,Z,X,Z];
    list l1=list(p1,p2,p3,p4,p5,p6,p7,p8);
    rcolon(l1,w,10);
    ==> J[1]=Z
    ==> + generators of the given ideal;

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