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DiffAlg :: newForm

newForm -- constructor of a differential form

Synopsis

Description

This function defines homogeneous differential forms with generic scalar coefficients. By default, the affine coordinates will be x_0,...,x_n and their exterior derivatives are denoted as dx_0,...,dx_n, respectively.


In this example we define a 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 with 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  
     ------------------------------------------------------------------------
     a x )dx
      8 2   2

o1 : DiffAlgForm
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, 3 skew commutative variables

Caveat

The coefficient i is the imaginary unit.

See also

Ways to use newForm :