This function defines homogeneous differential forms with generic scalar coefficients. By default, the affine coordinates will be x_0,...,x_n and the exterior differentials are denoted as dx_0,...,dx_n, respectively.
In this example we define an homogeneous differential 1-form 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 : w = newForm(2,1,1,"a")
o1 = (a x + a x + a x )dx + (a x + a x + a x )dx + (a x + a x +
0 0 3 1 6 2 0 1 0 4 1 7 2 1 2 0 5 1
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a x )dx
8 2 2
o1 : DiffAlgForm
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i2 : ring w
QQ[i]
o2 = ------[][a , a , a , a , a , a , a , a , a ][x , x , x ][dx , dx , dx ]
2 0 1 2 3 4 5 6 7 8 0 1 2 0 1 2
i + 1
o2 : PolynomialRing
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