# Singular

#### 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; ```