the wedge product - Maple Help

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liesymm[&^] - the wedge product

Calling Sequence

a &^ b

`&^`(a, b, c)

Parameters

a, b, c

-

expression involving differential forms relative to specific coordinates

Description

• 

This routine is part of the liesymm package and is loaded via with(liesymm) .

• 

It computes the wedge product of differential forms relative to the coordinates defined by setup().

• 

All 1-forms are generated by applying d() to the coordinates.

• 

All wedge products are automatically simplified to a wedge product of n 1-forms by extracting coefficients of wedge degree 0.

• 

All results of a wedge product are reported using an address ordering of the 1-forms to facilitate simplifications.  Thus dy &^ dx may simplify to dx &^ dy and if so will do so consistently within a given session.

• 

The ordering used for simplifications of the products of 1-forms is available as wedgeset1.

Examples

withliesymm:

setupx,y,z

x,y,z

(1)

dt &^ dx

0

(2)

dx &^ dy

dx &^ dy

(3)

5dx &^ dy &^ 3dz

15&^dx,dy,dz

(4)

`&^`adx,bdy,cdz

abc&^dx,dy,dz

(5)

See Also

liesymm, liesymm[hook], liesymm[Lie], liesymm[setup], liesymm[wedgeset], with


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