Questions tagged [quaternions]

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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. ...
1
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1answer
65 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 ...
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0answers
44 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. ...
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0answers
50 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 ...
4
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1answer
97 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
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1answer
261 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
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2answers
563 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
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1answer
66 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
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1answer
190 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 ...
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1answer
232 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. ...
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0answers
43 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 ...
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0answers
104 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 ...
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1answer
200 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
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1answer
245 views

Bug in Mathematica 9 (Quaternion)

The code: << Quaternions`; Exp[Quaternion[1, 0, 0, 0]] produces an error: ...
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0answers
123 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 ...
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0answers
50 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}.
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0answers
165 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
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1answer
381 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
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2answers
167 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
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1answer
237 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
-5
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2answers
637 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
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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? ...
6
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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
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2answers
553 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
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1answer
303 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
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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
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1answer
616 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
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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 ...