This function returns the degree of an homogeneous differential form or vector field.
In the following example we compute the degree of a differential form and a vector field.
i1 : w = newForm(2,1,3,"a")
3 2 2 3 2 2 2
o1 = (a x + a x x + a x x + a x + a x x + a x x x + a x x + a x x
0 0 3 0 1 9 0 1 18 1 6 0 2 12 0 1 2 21 1 2 15 0 2
------------------------------------------------------------------------
2 3 3 2 2 3 2
+ a x x + a x )dx + (a x + a x x + a x x + a x + a x x +
24 1 2 27 2 0 1 0 4 0 1 10 0 1 19 1 7 0 2
------------------------------------------------------------------------
2 2 2 3 3 2
a x x x + a x x + a x x + a x x + a x )dx + (a x + a x x +
13 0 1 2 22 1 2 16 0 2 25 1 2 28 2 1 2 0 5 0 1
------------------------------------------------------------------------
2 3 2 2 2 2
a x x + a x + a x x + a x x x + a x x + a x x + a x x +
11 0 1 20 1 8 0 2 14 0 1 2 23 1 2 17 0 2 26 1 2
------------------------------------------------------------------------
3
a x )dx
29 2 2
o1 : DiffAlgForm
|
i2 : degree(w)
o2 = {2, 1, 3}
o2 : List
|
i3 : X = newField(2,2,"b")
2 2 2 2
o3 = (b x + b x x + b x + b x x + b x x + b x )ax + (b x + b x x +
0 0 3 0 1 9 1 6 0 2 12 1 2 15 2 0 1 0 4 0 1
------------------------------------------------------------------------
2 2 2 2
b x + b x x + b x x + b x )ax + (b x + b x x + b x + b x x +
10 1 7 0 2 13 1 2 16 2 1 2 0 5 0 1 11 1 8 0 2
------------------------------------------------------------------------
2
b x x + b x )ax
14 1 2 17 2 2
o3 : DiffAlgField
|
i4 : degree X
o4 = {2, 2}
o4 : List
|
If the DiffAlgElement is non-homogeneous the function returns the highest degrees {n,r,d} of each homogeneous component in the given expression. For example, if the degree of w is {2,1,3}, then degree(w + (diff w)) returns, {2,2,3}