# DiffAlgForm ^ DiffAlgForm -- exterior product

## Synopsis

• Usage:
w ^ h
• Operator: ^
• Inputs:
• w, an instance of the type DiffAlgForm, a differential form
• h, an instance of the type DiffAlgForm, a differential form
• Outputs:
• an instance of the type DiffAlgForm, the exterior product of w and h

## Description

This function computes the exterior product of two differential forms.

 ```i1 : w = newForm(2,1,2,"a") 2 2 2 2 o1 = (a x + a x x + a x + a x x + a x x + a x )dx + (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 )dx + (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 )dx 14 1 2 17 2 2 o1 : DiffAlgForm``` ```i2 : h = newForm(2,1,1,"b") o2 = (b x + b x + b x )dx + (b x + b x + b x )dx + (b x + b x + 0 0 3 1 6 2 0 1 0 4 1 7 2 1 2 0 5 1 ------------------------------------------------------------------------ b x )dx 8 2 2 o2 : DiffAlgForm``` ```i3 : w ^ h 3 2 o3 = ((- a b + a b )x + (- a b + a b - a b + a b )x x + (- a b + a b 1 0 0 1 0 4 0 3 1 1 3 0 4 0 1 10 0 9 1 ------------------------------------------------------------------------ 2 3 - a b + a b )x x + (- a b + a b )x + (- a b + a b - a b + 4 3 3 4 0 1 10 3 9 4 1 7 0 6 1 1 6 ------------------------------------------------------------------------ 2 a b )x x + (- a b + a b - a b + a b - a b + a b )x x x + (- 0 7 0 2 13 0 12 1 7 3 6 4 4 6 3 7 0 1 2 ------------------------------------------------------------------------ 2 2 a b + a b - a b + a b )x x + (- a b + a b - a b + a b )x x 13 3 12 4 10 6 9 7 1 2 16 0 15 1 7 6 6 7 0 2 ------------------------------------------------------------------------ 2 3 + (- a b + a b - a b + a b )x x + (- a b + a b )x )dx dx + 16 3 15 4 13 6 12 7 1 2 16 6 15 7 2 0 1 ------------------------------------------------------------------------ 3 2 ((- a b + a b )x + (- a b + a b - a b + a b )x x + (- a b + a b 2 0 0 2 0 5 0 3 2 2 3 0 5 0 1 11 0 9 2 ------------------------------------------------------------------------ 2 3 - a b + a b )x x + (- a b + a b )x + (- a b + a b - a b + 5 3 3 5 0 1 11 3 9 5 1 8 0 6 2 2 6 ------------------------------------------------------------------------ 2 a b )x x + (- a b + a b - a b + a b - a b + a b )x x x + (- 0 8 0 2 14 0 12 2 8 3 6 5 5 6 3 8 0 1 2 ------------------------------------------------------------------------ 2 2 a b + a b - a b + a b )x x + (- a b + a b - a b + a b )x x 14 3 12 5 11 6 9 8 1 2 17 0 15 2 8 6 6 8 0 2 ------------------------------------------------------------------------ 2 3 + (- a b + a b - a b + a b )x x + (- a b + a b )x )dx dx + 17 3 15 5 14 6 12 8 1 2 17 6 15 8 2 0 2 ------------------------------------------------------------------------ 3 2 ((- a b + a b )x + (- a b + a b - a b + a b )x x + (- a b + 2 1 1 2 0 5 1 4 2 2 4 1 5 0 1 11 1 ------------------------------------------------------------------------ 2 3 a b - a b + a b )x x + (- a b + a b )x + (- a b + a b - a b + 10 2 5 4 4 5 0 1 11 4 10 5 1 8 1 7 2 2 7 ------------------------------------------------------------------------ 2 a b )x x + (- a b + a b - a b + a b - a b + a b )x x x + (- 1 8 0 2 14 1 13 2 8 4 7 5 5 7 4 8 0 1 2 ------------------------------------------------------------------------ 2 2 a b + a b - a b + a b )x x + (- a b + a b - a b + a b )x x 14 4 13 5 11 7 10 8 1 2 17 1 16 2 8 7 7 8 0 2 ------------------------------------------------------------------------ 2 3 + (- a b + a b - a b + a b )x x + (- a b + a b )x )dx dx 17 4 16 5 14 7 13 8 1 2 17 7 16 8 2 1 2 o3 : DiffAlgForm```