# 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);**

### See Also:

[CASA]
[homogeneousForm]
[leadingForm]
[numberOfTerms]