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DiffAlg :: newField

newField -- constructor of a vector field

Synopsis

Description

This function defines homogeneous vector fields with generic scalar coefficients. By default, the affine coordinates will be x_0,...,x_n and the partial derivatives are denoted as ax_0,...,ax_n, respectively.


In this example we define a homogeneous vector field with linear polynomial coefficients in 3 variables. The scalar coefficients are chosen to be defined with the variable a. The index of the scalar coefficients will always start with 0.

i1 : X = newField(2,2,"a")

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

o1 : DiffAlgField
i2 : ring X

      QQ[i]
o2 = ------[][a , a , a , a , a , a , a , a , a , a , a  , a  , a  , a  , a  , a  , a  , a  ][x , x , x ][ax , ax , ax ]
      2        0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   0   1   2    0    1    2
     i  + 1

o2 : PolynomialRing

Caveat

The coefficient i is the imaginary unit.

See also

Ways to use newField :