This function defines homogeneous vector fields with generic scalar coefficients. By default, the affine coordinates will be x_0,...,x_n and the partial derivatives are denoted as ax_0,...,ax_n, respectively.
In this example we define an homogeneous vector field with linear polynomial coefficients in 3 variables. The scalar coefficients are chosen to be defined with the variable a. The index of the scalar coefficients will always start in 0.
i1 : X = newField(2,2,"a")
2 2 2 2
o1 = (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
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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
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2
a x x + a x )ax
14 1 2 17 2 2
o1 : DiffAlgField
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i2 : ring X
QQ[i]
o2 = ------[][a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a , a ][x , x , x ][ax , ax , ax ]
2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0 1 2 0 1 2
i + 1
o2 : PolynomialRing
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