In this example we generate two random vector fields in three variables with polynomial coefficients of degree 2. Then we compute the rank of some distributions generated with them.
i1 : X = random newField(2,2,"a")
2 2 2 2
o1 = (2x - 2x x + 6x - 3x x + 6x x )ax + (- 7x + 5x x - x - 2x x -
0 0 1 1 0 2 1 2 0 0 0 1 1 0 2
------------------------------------------------------------------------
2 2 2 2
x x + x )ax + (- 3x - 4x x + 7x + 2x x - 7x x - 3x )ax
1 2 2 1 0 0 1 1 0 2 1 2 2 2
o1 : DiffAlgField
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i2 : Y = random newField(2,2,"a")
2 2 2 2 2
o2 = (x + 7x x + 3x + 2x x + x x + 8x )ax + (- x - 4x - 7x x - x x
0 0 1 1 0 2 1 2 2 0 0 1 0 2 1 2
------------------------------------------------------------------------
2 2 2 2
- x )ax + (3x - 4x x + 7x - 5x x + x )ax
2 1 0 0 1 1 0 2 2 2
o2 : DiffAlgField
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i3 : rank dist {X,Y}
o3 = 2
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i4 : rank dist {X,Y,X+Y,X-Y}
o4 = 2
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i5 : rank dist {X,Y,X|Y}
o5 = 3
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