isHomogeneous(DiffAlgElement) -- tests if a form (or field) is homogeneous

Synopsis

Function: isHomogeneous
Usage:

isHomogeneous(e)
Inputs:
- e, an instance of the type DiffAlgElement, representing a form or a field
Outputs:
- a Boolean value, true if the form (or field) is homogeneous

Description

In this example we test if a vector field is homogeneous,

i1 : X = newField("3*ax_0+x_1*ax_1")

o1 = 3ax  + x ax
        0    1  1

o1 : DiffAlgField

i2 : isHomogeneous X

o2 = false

In this example we test if a projective logarithmic differential 1-form is homogeneous,

i3 : w = random logarithmicForm(2,{1,2},"a",Projective => true)

                    2                           2              2            
o3 = (120x x  + 144x  + 306x x  + 108x x  + 108x )dx  + (- 120x  - 144x x  -
          0 1       1       0 2       1 2       2   0          0       0 1  
     ------------------------------------------------------------------------
                            2              2       2
     108x x  - 264x x  - 72x )dx  + (- 306x  + 264x  - 108x x  + 72x x )dx
         0 2       1 2      2   1          0       1       0 2      1 2   2

o3 : DiffAlgForm

i4 : isHomogeneous w

o4 = true

Ways to use this method: