# CASA Function: homogenize

Homogenizes a polynomial.

### Calling Sequence:

• p := homogenize(poly,vars,x)

### Parameters:

poly : polynom(anything.vars)
• A polynomial in the variables vars over some coefficient domain.
vars : list(name)
• A list of variable names.
x : name
• The name of a variable, the homogenizing variable.

### Result:

p : polynom
• A polynom over the same coefficient domain as poly in the variables vars and x.

### Description:

• homogenize(poly,vars,x) homogenizes a polynomial in vars with respect to the homogenizing variable x.
• It is not checked whether the homogenizing variable already appears in the variables vars or in the coeeficient domain. In such a case the result is the same as homogenizing with a variable not appearing in vars or the coefficient domain and then replacing that variable with x. In this case the result might not be homogeneous.

### Examples:

> homogenize(x^2+3*x^2*y+y,[x,y],z); > homogenize(x*y*z+5*y+11*z,[x,y],w); > homogenize(x*y*z+5*y+11*z,[x,y],x); > homogenize(x*y*z+5*y+11*z,[x,y],y); > homogenize(x*y*z+5*y+11*z,[x,y],z); 