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DiffAlg :: List * DiffAlgForm

List * DiffAlgForm -- pull-back of a differential form by a rational map

Synopsis

Description

Given a list of polynomials F = (F_0,...,F_n) and a differential form w on n+1 variables, the pull-back F*w is defined as the composition w(F).


In this example we compute the pull-back of the 1-differential form w with respect to the mapping F = (F_0,F_1,F_2).

i1 : F_0 = random newForm(1,0,1,"a");
i2 : F_1 = random newForm(1,0,2,"a");
i3 : F_2 = random newForm(1,0,1,"a");
i4 : w = random newForm(2,2,1,"a")

o4 = (- 5x  - 3x  + 6x )dx dx  + (- 3x  + 4x  + 7x )dx dx  + (- 3x  + 2x  -
          0     1     2   0  1        0     1     2   0  2        0     1  
     ------------------------------------------------------------------------
     3x )dx dx
       2   1  2

o4 : DiffAlgForm
i5 : {F_0,F_1,F_2}*w

         3      2           2       3       2                   2
o5 = (17x  + 75x x  - 885x x  - 800x  + 593x  + 3162x x  - 3680x  + 288x  -
         0      0 1       0 1       1       0        0 1        1       0  
     ------------------------------------------------------------------------
     256x )dx dx
         1   0  1

o5 : DiffAlgForm