# Questions tagged [quaternions]

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37 views

### Define quaternions by properties instead of coordinates

I'd like to manipulate an expression of quaternions and only use the following properties ...
46 views

### How implement Dual Quaternion algebra in Mathematica?

How can we manipulate and operate with dual quaternionic variables in Mathematica? Since a dual quaternion can be expressed like this $\hat q = a + \epsilon b$ where $a,b \in \mathbb{H}$, or ...
111 views

### How to calculate Gamma functions values for Quaternions using Mathematica?

How can we calculate the values for the Gamma function using Quaternions on Mathematica? For example: ...
30 views

### Errors in NDSolve for complex matrices

This is the problem. It is quite simple, and looks unwieldy only because I had to rewrite quaternions as complex matrices. ...
103 views

### Cryptic NDSolve::nlnum when working with matrices

This problem was initially formulated in quaternions, but I had to rewrite them to complex matrices (as they seem to be supported better). Possibly introducing some errors along the way. So the ...
49 views

### NDSolve and quaternions

I have tried to solve a set of equations of motion in Mathematica and got an error. Then, I simplified it as much as possible, and the following example gives the same error. ...
53 views

### Find vectors describing two interconnected pyramids in Euclidean space

I need the help of competent linear algebra specialists in Mathematica. In the Euclidean space, two tetrahedrons are turned at different angles. Their vertices coincide with the beginning of the base ...
101 views

### Wrong Output in self defined Quaternionic Multiplication

I tried to define quaternionic multiplication in terms of pairs of complex numbers where I identify $\mathbb{C}^2$ with $\mathbb{H}$ via $(z,w)\mapsto z+jw$. Consequently, I used the multiplication ...
337 views

### Converting quaternion to Euler Angles

I am using quaternions to describe 3D rotations which parametrized by Euler angles, and as a preliminary task I am trying to implement conversion routines that go between Euler angles and quaternions. ...
613 views

### Symbolic Quaternion Multiplication

It is possible to do the symbolic multiplication $qq^*$ of a quaternion $q=a+bi+cj+dk$ by its conjugate $q^*=a-bi-cj-dk$ using Mathematica? It seems that Quaternion package only works with numeric ...
70 views

### Select elements in a list of tuples of quaternions that satisfy a condition

I defined 24 quaternions using the Quaternions package and i create the list of all possible 4-tuples using ListQuad = Tuples[ListQuaternions, 4] where ...
195 views

### Feature of quaternion Cos, Cot etc

I am new to SE Mathematica, and search gives no answer; so here is my problem: During the testing of my numerical library for quaternions with Mathematica (package Quaternions) I observed the ...
249 views

### Convert, using the Pauli matrices, an $n \times m$ matrix of quaternions into a $2 n \times 2 m$ matrix with complex entries, and vice versa

I'd like to go between $n \times m$ matrices with quaternionic entries to (using, it would seem, the Pauli matrix conversion scheme) to $2 n \times 2 m$ matrices with complex entries, and vice versa. ...
45 views

### Compute component of a Quaternion with an assumption [closed]

I am really new to mathematica and the syntax sometimes is a bit hard for me. I come from Matlab environment. I think this question is really easy for the most of you. I am trying to use quaternions ...
115 views

### How can one best implement the multiplication of octonions using the Quaternions package?

I excerpt from p. 4 of the recent paper of P. J. Forrester (https://arxiv.org/pdf/1610.08081.pdf): "Let $p_1$ and $p_2$ be quaternions. The octonion algebra consists of elements of the form \$p_1+p_2 ...
207 views

### Can one use the new random matrices features of Version 11 in addressing a certain octonionic-based question?

I have cross-posted the question https://math.stackexchange.com/questions/2012301/can-one-test-an-octonionic-interpretation-for-a-conjecture-apparently-valid-in and https://physics.stackexchange....
246 views

### Bug in Mathematica 9 (Quaternion)

The code: << Quaternions; Exp[Quaternion[1, 0, 0, 0]] produces an error: ...
127 views

### Quaternion calculation [closed]

Quaternion[0, Cos[Pi/20]/Sqrt, Sin[Pi/20]/Sqrt, 0] ** Quaternion[0, 1, 0, 0] ** Quaternion[0, -Cos[Pi/20]/Sqrt, -Sin[Pi/20]/Sqrt, 0] this should ...
51 views

### How can I get a list of the “coefficients” of Quaternion[1, 2, 3, 4]? [duplicate]

I want to input: Quaternion[1, 2, 3, 4] to get a list: {1,2,3,4}.
167 views

### Animate FromQuarternionTo3DRotation nb file with 4 quarternion values [closed]

I have a csv file. Inside the csv file, there are few rows of 4 quartenion values. I would like to animate the quarternion nb in http://demonstrations.wolfram.com/FromQuaternionTo3DRotation/ I ...
432 views

### Program to demonstrate rotation according to quaternion values [duplicate]

On the Wolfram|Alpha website, I type quaternion(1,1,1,1) into the search field. Wolfram|Alpha shows a 3D transformation of the quaternion values representing the orientation of an object. I have 9 ...
179 views

### I need to make and manipulate a group ( the quaternion)

I am trying to define a group and use it to defined its classes, its character table, and irreducible representations. I am having trouble finding code to define a group and use it.
250 views

### Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
695 views

### Output of mathematica. Quaternion to Matrix [closed]

If I have the following instructions: How will it be the output/how will it appears in Mathematica? something like this: I can't recognize the output in mathematica... How can I do to appear the ...
2k views

### How to work with quarternions in Wolfram Mathematica? [closed]

How can I write the insructions from this link http://blog.wolframalpha.com/2011/08/25/quaternion-properties-and-interactive-rotations-with-wolframalpha/ in Mathematica to obtain the same result? ...
2k views

### Converting a rotation matrix to a quaternion

I found a very good link about quaternions in Mathematica , but I don't know how to create a quaternion from a rotation matrix. Can anyone help me, please? Update I need this: A rotation may be ...
580 views

### Getting Values From Quaternions

I'm using the Quaternion package: << Quaternions Very simply, I would like to be able to get the individual components of the quaternions by themselves. ...
318 views

### FromQuaternion and QuaternionQ not working symbolically?

How can I get Mathematica to work with quaternions symbolically? I want to do some quaternion math without defining the actual coefficients, and then extract the coefficients from the resulting ...
2k views

### Octonions in Mathematica

Is there a package or Notebook for Mathematica that can enable me to do some numerical calculations with octonions? Maybe a way to plug-in the octonion multiplication table?