# homogenize(DiffAlgElement) -- homogenize a differential form or vector field

## Synopsis

• Function: homogenize
• Usage:
homogenize e
• Inputs:
• Outputs:
• an instance of the type DiffAlgElement, the homogenization of e with respect to a new variable. The resulting form or vector field is homogeneous.

## Description

 i1 : w = newForm("2*x_0*dx_0+x_1^2*dx_1") 2 o1 = 2x dx + x dx 0 0 1 1 o1 : DiffAlgForm i2 : homogenize w 2 o2 = 2x x dx + x dx 0 2 0 1 1 o2 : DiffAlgForm
 i3 : homogenize newField ("ax_0+x_1*ax_2+a*ax_1") o3 = x ax + a*x ax + x ax 3 0 3 1 1 2 o3 : DiffAlgField

## Caveat

The homogenization process of a form adds one variable to the given element.