diff(DiffAlgForm) -- exterior differential

Function: diff
Usage:

diff w
Inputs:
- w, an instance of the type DiffAlgForm, a form
Outputs:
- an instance of the type DiffAlgForm, the exterior differential of w

Description

This function computes the exterior differential of a given differential form.

i1 : w = newForm(2,1,2,"a")

         2               2                          2           2           
o1 = (a x  + a x x  + a x  + a x x  + a  x x  + a  x )dx  + (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 )dx  + (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 )dx
      14 1 2    17 2   2

o1 : DiffAlgForm

i2 : diff w

o2 = ((2a  - a )x  + (a  - 2a )x  + (a  - a  )x )dx dx  + ((2a  - a )x  + (a 
         1    3  0     4     9  1     7    12  2   0  1       2    6  0     5
     ------------------------------------------------------------------------
     - a  )x  + (a  - 2a  )x )dx dx  + ((a  - a )x  + (2a   - a  )x  + (a   -
        12  1     8     15  2   0  2      5    7  0      11    13  1     14  
     ------------------------------------------------------------------------
     2a  )x )dx dx
       16  2   1  2

o2 : DiffAlgForm

Ways to use this method:

diff(DiffAlgForm) -- exterior differential

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/DiffAlg.m2:1189:0.