Non-commutative multiplication in Mathematica

[topsquark]

Does anyone know if it's possible to tell Mathematica to do calculations with non-Abelian groups, such as the quaternions? For example, how do you tell it to do (3 + j)(4 - i)? I would like to extend this beyond quaternions so is there is a way to define arbitrary group definitions?

Thanks!

-Dan

 

[I like Serena]

Does anyone know if it's possible to tell Mathematica to do calculations with non-Abelian groups, such as the quaternions? For example, how do you tell it to do (3 + j)(4 - i)? I would like to extend this beyond quaternions so is there is a way to define arbitrary group definitions?

Thanks!

-Dan

Hey Dan!

How about: [M]Quaternion[3,0,1,0] * Quaternion[4,-1,0,0][/M]?

 

[Ackbach]

I don't know about arbitrary, but you can define any function you want, like I did with my LabVIEW quaternion library. You define the data structures you need, and the functions on those data structures.

 

[topsquark]

Hey Dan!

How about: [M]Quaternion[3,0,1,0] * Quaternion[4,-1,0,0][/M]?

Go figure. All I had to do was search Mathematica for quaternions. I suck at doing searches. (My ex-fiancee used to do all that for me.)

Thanks. Now if I could just get it to do [math]D_6[/math] or others. I haven't the foggiest idea how to follow up on Ackbach's suggestion. There's got to be a way to do the Mathematica thing but I have an old copy and I don't think I can get modules for that anymore.

-Dan

Addendum: You know, if I could find a matrix representation I could probably do it. Have to see about that.

 

[Ackbach]

Go figure. All I had to do was search Mathematica for quaternions. I suck at doing searches. (My ex-fiancee used to do all that for me.)

Thanks. Now if I could just get it to do [math]D_6[/math] or others. I haven't the foggiest idea how to follow up on Ackbach's suggestion. There's got to be a way to do the Mathematica thing but I have an old copy and I don't think I can get modules for that anymore.

-Dan

Addendum: You know, if I could find a matrix representation I could probably do it. Have to see about that.

Defining a function in Mathematica works like this:

f[x_, y_]=x^2 * y

That's obviously not all you need, but that's a fundamental piece.

 

[I like Serena]

Thanks. Now if I could just get it to do [math]D_6[/math] or others. I haven't the foggiest idea how to follow up on Ackbach's suggestion. There's got to be a way to do the Mathematica thing but I have an old copy and I don't think I can get modules for that anymore.

-Dan

Addendum: You know, if I could find a matrix representation I could probably do it. Have to see about that.

Indeed. We can represent $D_6$ with 2x2 rotation and reflection matrices.
And we can also represent the quaternions with 2x2 matrices, which is a bit more straight forward.
Now I wonder which non-abelian group cannot be represented by matrices... (Wondering)

 

[topsquark]

Now I wonder which non-abelian group cannot be represented by matrices... (Wondering)

Probably my counseling group. (Emo)

-Dan