- #1

- 2,018

- 808

Thanks!

-Dan

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Mathematica
- Thread starter topsquark
- Start date

In summary, Dan is looking for a way to do calculations with non-Abelian groups, specifically quaternions, in Mathematica. He also wants to know if it's possible to define arbitrary group definitions. Ackbach suggests defining a function and finding a matrix representation for these groups, but Dan is unsure how to proceed with this. He then jokes about his difficulty with searching and mentions his ex-fiancee doing it for him. Ackbach suggests using 2x2 matrices to represent $D_6$ and quaternions, but Dan wonders if there are non-abelian groups that cannot be represented by matrices. He jokes about his counseling group not being able to be represented by matrices.

- #1

- 2,018

- 808

Thanks!

-Dan

Physics news on Phys.org

- #2

I like Serena

Homework Helper

MHB

- 16,336

- 258

topsquark said:

Thanks!

-Dan

Hey Dan!

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

- #3

Ackbach

Gold Member

MHB

- 4,155

- 91

- #4

- 2,018

- 808

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.)I like Serena said:Hey Dan!

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

Thanks. Now if I could just get it to do \(\displaystyle D_6\) 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.

- #5

Ackbach

Gold Member

MHB

- 4,155

- 91

topsquark said: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 \(\displaystyle D_6\) 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:

Code:

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

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

- #6

I like Serena

Homework Helper

MHB

- 16,336

- 258

topsquark said:Thanks. Now if I could just get it to do \(\displaystyle D_6\) 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)

- #7

- 2,018

- 808

Probably my counseling group. (Emo)I like Serena said:Now I wonder which non-abelian group cannot be represented by matrices... (Wondering)

-Dan

Non-commutative multiplication in Mathematica is a type of multiplication operation where the order of the factors affects the result. In other words, the product of two expressions is not the same if the order of the factors is reversed. This type of multiplication is commonly used in algebra and physics, where the order of operations is important.

In regular multiplication, the order of the factors does not affect the result. For example, in regular multiplication, 2 x 3 and 3 x 2 both equal 6. However, in non-commutative multiplication, these expressions would result in different values. In Mathematica, non-commutative multiplication is denoted by the symbol ** or by using the NonCommutativeMultiply function.

Non-commutative multiplication is often used in mathematical and scientific fields, such as algebra, quantum mechanics, and group theory. It is also commonly used in computer programming languages like Mathematica to perform calculations involving non-commutative operations.

To perform non-commutative multiplication in Mathematica, you can use the ** symbol or the NonCommutativeMultiply function. For example, to multiply the expressions a and b in non-commutative order, you can use a ** b or NonCommutativeMultiply[a, b].

Yes, non-commutative multiplication can be applied to any number of factors in Mathematica. For example, you can use a ** b ** c to multiply the expressions a, b, and c in non-commutative order. The order in which the factors are written will affect the result.

- Replies
- 2

- Views
- 2K

- Replies
- 4

- Views
- 1K

Mathematica
Running simultaneous computation in mathematica

- Replies
- 5

- Views
- 4K

- Replies
- 2

- Views
- 2K

- Replies
- 1

- Views
- 2K

Mathematica
Solving Systems with Iteration in Mathematica

- Replies
- 4

- Views
- 3K

- Replies
- 5

- Views
- 5K

Mathematica
Multi scale analysis using mathematica

- Replies
- 1

- Views
- 2K

Mathematica
NIntegrate w/ MaxErrorIncreases in Mathematica 8

- Replies
- 5

- Views
- 2K

- Replies
- 2

- Views
- 3K

Share: