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DiffAlg :: DiffAlgForm ^ DiffAlgForm

DiffAlgForm ^ DiffAlgForm -- exterior product

Synopsis

Description

This function computes the exterior product of two differential forms.

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 : h = newForm(2,1,1,"b")

o2 = (b x  + b x  + b x )dx  + (b x  + b x  + b x )dx  + (b x  + b x  +
       0 0    3 1    6 2   0     1 0    4 1    7 2   1     2 0    5 1  
     ------------------------------------------------------------------------
     b x )dx
      8 2   2

o2 : DiffAlgForm
i3 : w ^ h

                      3                                 2                    
o3 = ((- a b  + a b )x  + (- a b  + a b  - a b  + a b )x x  + (- a  b  + a b 
          1 0    0 1  0       4 0    3 1    1 3    0 4  0 1       10 0    9 1
     ------------------------------------------------------------------------
                      2                    3                          
     - a b  + a b )x x  + (- a  b  + a b )x  + (- a b  + a b  - a b  +
        4 3    3 4  0 1       10 3    9 4  1       7 0    6 1    1 6  
     ------------------------------------------------------------------------
           2                                                             
     a b )x x  + (- a  b  + a  b  - a b  + a b  - a b  + a b )x x x  + (-
      0 7  0 2       13 0    12 1    7 3    6 4    4 6    3 7  0 1 2     
     ------------------------------------------------------------------------
                                   2                                       2
     a  b  + a  b  - a  b  + a b )x x  + (- a  b  + a  b  - a b  + a b )x x 
      13 3    12 4    10 6    9 7  1 2       16 0    15 1    7 6    6 7  0 2
     ------------------------------------------------------------------------
                                           2                     3         
     + (- a  b  + a  b  - a  b  + a  b )x x  + (- a  b  + a  b )x )dx dx  +
           16 3    15 4    13 6    12 7  1 2       16 6    15 7  2   0  1  
     ------------------------------------------------------------------------
                      3                                 2                    
     ((- a b  + a b )x  + (- a b  + a b  - a b  + a b )x x  + (- a  b  + a b 
          2 0    0 2  0       5 0    3 2    2 3    0 5  0 1       11 0    9 2
     ------------------------------------------------------------------------
                      2                    3                          
     - a b  + a b )x x  + (- a  b  + a b )x  + (- a b  + a b  - a b  +
        5 3    3 5  0 1       11 3    9 5  1       8 0    6 2    2 6  
     ------------------------------------------------------------------------
           2                                                             
     a b )x x  + (- a  b  + a  b  - a b  + a b  - a b  + a b )x x x  + (-
      0 8  0 2       14 0    12 2    8 3    6 5    5 6    3 8  0 1 2     
     ------------------------------------------------------------------------
                                   2                                       2
     a  b  + a  b  - a  b  + a b )x x  + (- a  b  + a  b  - a b  + a b )x x 
      14 3    12 5    11 6    9 8  1 2       17 0    15 2    8 6    6 8  0 2
     ------------------------------------------------------------------------
                                           2                     3         
     + (- a  b  + a  b  - a  b  + a  b )x x  + (- a  b  + a  b )x )dx dx  +
           17 3    15 5    14 6    12 8  1 2       17 6    15 8  2   0  2  
     ------------------------------------------------------------------------
                      3                                 2               
     ((- a b  + a b )x  + (- a b  + a b  - a b  + a b )x x  + (- a  b  +
          2 1    1 2  0       5 1    4 2    2 4    1 5  0 1       11 1  
     ------------------------------------------------------------------------
                            2                     3                          
     a  b  - a b  + a b )x x  + (- a  b  + a  b )x  + (- a b  + a b  - a b  +
      10 2    5 4    4 5  0 1       11 4    10 5  1       8 1    7 2    2 7  
     ------------------------------------------------------------------------
           2                                                             
     a b )x x  + (- a  b  + a  b  - a b  + a b  - a b  + a b )x x x  + (-
      1 8  0 2       14 1    13 2    8 4    7 5    5 7    4 8  0 1 2     
     ------------------------------------------------------------------------
                                    2                                       2
     a  b  + a  b  - a  b  + a  b )x x  + (- a  b  + a  b  - a b  + a b )x x 
      14 4    13 5    11 7    10 8  1 2       17 1    16 2    8 7    7 8  0 2
     ------------------------------------------------------------------------
                                           2                     3
     + (- a  b  + a  b  - a  b  + a  b )x x  + (- a  b  + a  b )x )dx dx
           17 4    16 5    14 7    13 8  1 2       17 7    16 8  2   1  2

o3 : DiffAlgForm