homog

homog

homogenize with respect to an indeterminate

Syntax

homog(V: RINGELEM, X: RINGELEM): RINGELEM
homog(V: MODULEELEM, X: RINGELEM): MODULEELEM
homog(L: LIST, X: RINGELEM): LIST
homog(I: IDEAL, X: RINGELEM): IDEAL
homog(M: MODULE, X: RINGELEM): MODULE

Description

This function returns the homogenization of the first arg with respect to the indeterminate X , which must have weight 1. The elements of the list L are homogenized separately.

NOTE: For an ideal/module the result is the ideal/module containing the homogenizations of all elements (and not simply the homogenizations of the specific generators).

Example

/**/  Use R ::= QQ[x,y,z,w];
/**/  homog(x^3-y, w);
x^3 -y*w^2

/**/  homog([x^3-y, x^4-z], w);
[x^3 -y*w^2, x^4 -z*w^3]

/**/  I := ideal(x^3-y, x^4-z);
/**/  homog(I, w);    -- don't just get the homogenizations of
                      -- the generators of I
ideal(x*y -z*w, x^2*z -y^2*w, x^3 -y*w^2, y^3 -x*z^2)

See Also

IsHomog