Question: Dual numbers, dual quaternions, attempting to define basic algebra

Hello,

I would like to write some functions and algebra that work with dual numbers.

http://en.wikipedia.org/wiki/Dual_number 

http://en.wikipedia.org/wiki/Dual_quaternion 

I have not found a library that supports this.

The basis of dual numbers it is epsilon^2=0, similar to i,j,k in complex algebra where i^2=-1,i*j=-1 etc.

I never made a module in Maple yet, I believe and hope I can define this algebra in a worksheet.

So I tried dabbling with statements such as ( 'ep' below is the greek '&epsilon' letter ):

assume(ep*ep=0)

assume(ep^2=0)

f:=1+ep*4

g:=1-ep

But, I did not get far because even up to this stage, I do not know how to get maple to assume e^2=0 and simplify my expressions accordingly.

For example

expand(d*f)

just gives me

1+5*ep+4*ep^2

but I want the 4*ep^2 to disappear because I am assuming ep^2=0.

Not happening, so what else do I have to do ?

Is there another way I can define special constants such as i,j,k for complex numbers for my own algebra ?

Is there a way I can tell assume function that ep,'&epsilon' is pure symbolic ?

Any suggestions on writing a module if that is the only way ?

Thanks.