If L is a list of vector fields, this routine tests the involutivity of L.
In this example we test the involutivity of two vector fields.
i1 : X = newField("3*x_0*ax_0+x_1*ax_1")
o1 = 3x ax + x ax
0 0 1 1
o1 : DiffAlgField
|
i2 : Y = radial 3
o2 = x ax + x ax + x ax + x ax
0 0 1 1 2 2 3 3
o2 : DiffAlgField
|
i3 : isInvolutive dist {X,Y}
o3 = true
|
In this example we compute a basis of the annihilator of a random projective logarithmic differential 1-form. Then we verify that it is an involutive distribution.
i4 : w = random logarithmicForm(2,{1,2},"a",Projective => true)
2 2 2
o4 = (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
o4 : DiffAlgForm
|
i5 : X = newField(2,2,"a")
2 2 2 2
o5 = (a x + a x x + a x + a x x + a x x + a x )ax + (a x + a 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
a x + a x x + a x x + a x )ax + (a x + a x x + a x + a x x +
10 1 7 0 2 13 1 2 16 2 1 2 0 5 0 1 11 1 8 0 2
------------------------------------------------------------------------
2
a x x + a x )ax
14 1 2 17 2 2
o5 : DiffAlgField
|
i6 : D = genKer(X_w,X); |
i7 : #D o7 = 6 |
i8 : isInvolutive dist D o8 = true |