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

Synopsis

• Function: homogenize

• Usage:

  homogenize e

• Inputs:
  • e, an instance of the type DiffAlgElement, a form or a vector field
• 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

See also

• projectivize -- projectivize a differential form or vector field
• isHomogeneous -- whether something is homogeneous (graded)