topsquark said: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
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]?
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.
f[x_, y_]=x^2 * ytopsquark 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.
Probably my counseling group. (Emo)I like Serena said:Now I wonder which non-abelian group cannot be represented by matrices... (Wondering)
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.