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DiffAlg :: degree(DiffAlgElement)

degree(DiffAlgElement) -- degree of a differential form or a vector field

Synopsis

Description

This function returns the degree of a homogeneous differential form or vector field.


In the following example we compute the degree of a differential form and a vector field.

i1 : w = newForm(2,1,3,"a")

         3      2          2       3      2                     2           2
o1 = (a x  + a x x  + a x x  + a  x  + a x x  + a  x x x  + a  x x  + a  x x 
       0 0    3 0 1    9 0 1    18 1    6 0 2    12 0 1 2    21 1 2    15 0 2
     ------------------------------------------------------------------------
             2       3           3      2           2       3      2    
     + a  x x  + a  x )dx  + (a x  + a x x  + a  x x  + a  x  + a x x  +
        24 1 2    27 2   0     1 0    4 0 1    10 0 1    19 1    7 0 2  
     ------------------------------------------------------------------------
                     2           2         2       3           3      2    
     a  x x x  + a  x x  + a  x x  + a  x x  + a  x )dx  + (a x  + a x x  +
      13 0 1 2    22 1 2    16 0 2    25 1 2    28 2   1     2 0    5 0 1  
     ------------------------------------------------------------------------
           2       3      2                     2           2         2  
     a  x x  + a  x  + a x x  + a  x x x  + a  x x  + a  x x  + a  x x  +
      11 0 1    20 1    8 0 2    14 0 1 2    23 1 2    17 0 2    26 1 2  
     ------------------------------------------------------------------------
         3
     a  x )dx
      29 2   2

o1 : DiffAlgForm
i2 : degree(w)

o2 = {2, 1, 3}

o2 : List
i3 : X = newField(2,2,"b")

         2               2                          2           2           
o3 = (b x  + b x x  + b x  + b x x  + b  x x  + b  x )ax  + (b x  + b 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           
     b  x  + b x x  + b  x x  + b  x )ax  + (b x  + b x x  + b  x  + b x x  +
      10 1    7 0 2    13 1 2    16 2   1     2 0    5 0 1    11 1    8 0 2  
     ------------------------------------------------------------------------
                   2
     b  x x  + b  x )ax
      14 1 2    17 2   2

o3 : DiffAlgField
i4 : degree X

o4 = {2, 2}

o4 : List

Caveat

If the DiffAlgElement is non-homogeneous the function returns the highest degrees {n,r,d} of each homogeneous component in the given expression. For example, if the degree of w is {2,1,3}, then degree(w + (diff w)) returns, {2,2,3}