Macaulay2 » Documentation
Packages » DiffAlg :: List * DiffAlgForm
next | previous | forward | backward | up | index | toc

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

- Operator: *
- Usage:
    `L * w`
- Inputs:
  - L, a list, the rational map represented by a list of polynomials as 0-forms, see DiffAlgForm
  - w, an instance of the type DiffAlgForm, a differential form
- Outputs:
  - an instance of the type DiffAlgForm, the pull-back of w via L

## 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

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/DiffAlg.m2:1024:0.