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

## Synopsis

• 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