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

Synopsis

Usage:
homogenize e
Function: homogenize
Inputs:
- e, an object of class DiffAlgElement, a form or a vector field
Outputs:
- an object of class DiffAlgElement, the homogenization of e with respect to a new variable. The resulting form or vector field descent to projective space.

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 : r = radial 2

o2 = x ax  + x ax  + x ax
      0  0    1  1    2  2

o2 : DiffAlgField

i3 : homogenize w

         2       2            3     2
o3 = 2x x dx  + x x dx  + (- x  - 2x x )dx
       0 2  0    1 2  1       1     0 2   2

o3 : DiffAlgForm

i4 : r_oo

o4 = 0

o4 : DiffAlgForm

i5 : homogenize newField ("ax_0+x_1*ax_2+a*ax_1")  

o5 = x ax  + a*x ax  + x ax
      3  0      3  1    1  2

o5 : DiffAlgField

Caveat

The homogenization process of a form increases the polynomial degree by one.