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DiffAlg :: projectivize

projectivize -- projectivize a differential form or vector field

Synopsis

Description

This returns the unique differential form that extends the given one from affine space to projective space.

i1 : w = newForm("2*x_0*dx_0+x_1^2*dx_1")

               2
o1 = 2x dx  + x dx
       0  0    1  1

o1 : DiffAlgForm
i2 : r = radial 2

o2 = x ax  + x ax  + x ax
      0  0    1  1    2  2

o2 : DiffAlgField
i3 : projectivize w

         2       2            3     2
o3 = 2x x dx  + x x dx  + (- x  - 2x x )dx
       0 2  0    1 2  1       1     0 2   2

o3 : DiffAlgForm
i4 : r_oo

o4 = 0

o4 : DiffAlgForm
i5 : projectivize newField ("ax_0+x_1*ax_2+a*ax_1")  

o5 = x ax  + a*x ax  + x ax
      3  0      3  1    1  2

o5 : DiffAlgField

Caveat

The projectivization process of a form increases the polynomial degree by one if the original element did not descend to projective space.

See also

Ways to use projectivize :