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DiffAlg :: moduliIdeal

moduliIdeal -- ideal generated by the coefficients of a differential form or vector field

Synopsis

Description

Given a differential form or vector field, this routine returns the ideal generated by the scalar coefficients of such element.


In this example we compute the equations that the scalar coefficients of a closed differential 1-form must satisfy.

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

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

o2 : DiffAlgForm
i3 : moduliIdeal(diff w)

o3 = ideal (2a  - a , a  - 2a , a  - a  , 2a  - a , a  - a  , a  - 2a  , a  - a , 2a   - a  , a   - 2a  )
              1    3   4     9   7    12    2    6   5    12   8     15   5    7    11    13   14     16

               QQ[i]
o3 : Ideal of ------[][a ..a  ]
               2        0   17
              i  + 1

See also

Ways to use moduliIdeal :

For the programmer

The object moduliIdeal is a method function.