Questions tagged [quaternions]

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4
votes
1answer
93 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 ...
1
vote
1answer
127 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. ...
7
votes
2answers
508 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 ...
2
votes
1answer
60 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 ...
5
votes
1answer
186 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 ...
1
vote
1answer
214 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. ...
1
vote
0answers
41 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 ...
3
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0answers
100 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 ...
-7
votes
1answer
194 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....
9
votes
1answer
235 views

Bug in Mathematica 9 (Quaternion)

The code: << Quaternions`; Exp[Quaternion[1, 0, 0, 0]] produces an error: ...
1
vote
0answers
118 views

Quaternion calculation [closed]

Quaternion[0, Cos[Pi/20]/Sqrt[2], Sin[Pi/20]/Sqrt[2], 0] ** Quaternion[0, 1, 0, 0] ** Quaternion[0, -Cos[Pi/20]/Sqrt[2], -Sin[Pi/20]/Sqrt[2], 0] this should ...
0
votes
0answers
47 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}.
2
votes
0answers
162 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 ...
3
votes
1answer
322 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 ...
3
votes
2answers
164 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.
5
votes
1answer
232 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
-5
votes
2answers
559 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 ...
2
votes
1answer
1k 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? ...
5
votes
2answers
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 ...
5
votes
2answers
512 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. ...
3
votes
1answer
290 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 ...
8
votes
1answer
1k 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?
6
votes
1answer
605 views

command to expand quaternion multiplication

Is there are any command to expand quaternion multiplication as below STEP by STEP. Below is equation from my text. I'm self learner and for some reason I can't wrap my head around quaternion ...
19
votes
2answers
2k views

Fast Spherical Linear Interpolation of list of quaternions

An accurate way to interpolate between two quaternions is to use Spherical Linear Interpolation (Slerp) because it preserves the unit length, whereas straightforward linear interpolation does not, as ...