# CASA Function: homogeneousForm

Collects the terms of a polynomial of a certain degree.

### Calling Sequence:

- f := homogeneousForm(poly,vars,degree)

### Parameters:

- poly : polynom(anything,vars)
- A polynomial in the variables vars over some coefficient domain.

- vars : list(name)
- A list of variable names.

- degree : integer
- The degree of the terms that should be collected from the polynomial

### Result:

- p : homogeneousPolynom(vars)
- A homogeneous polynom over the same coefficient domain as poly in the variables vars of degree degree.

### Description:

- homogeneousForm(poly,vars,degree) collects the terms of degree degree and returns the form (a homogeneous polynomial) that is built from that terms
- The sum over all homogeneous forms from degree 0 to the degree of poly in vars, should give poly.

### Examples:

`> ` **f := x^2+3*x*y+y;**

`> ` **f2:=homogeneousForm(f,[x,y],2);**

`> ` **f1:=homogeneousForm(f,[x,y],1);**

`> ` **f0:=homogeneousForm(f,[x,y],0);**

`> ` **evalb(f = f2+f1+f0);**

### See Also:

[CASA]
[type/homogeneousPolynomial]
[leadingForm]
[homogenize]