# Maths - 3d multivector Code

## complete sfmulti3d class

This class can represent a 3D rotation. The class has 4 double numbers which represent the rotation as either quaternion, axis-angle or euler number depending on the cde int/enum

The class has methods to combine with other rotations. Also many other methods, including the ability to load and save to from VRML and x3d

There are 3 versions available depending on language:

The full source code is available on Sourceforge here:

## Axiom Program

There are a number of open source programs that can solve polynomial equations. I have used Axiom, how to install Axiom here.

As an example the following shows how to generate quaternions using Clifford algebra.

I have put user input in red:

 ```(1) -> )set mes auto off (1) -> K := Fraction Polynomial Integer ``` ``` (1) Fraction Polynomial Integer Type: Domain (2) -> qf := matrix[[1,0,0],[0,1,0],[0,0,1]]``` ``` +1 0 0+ | | (2) |0 1 0| | | +0 0 1+ Type: Matrix Integer (3) -> H := CliffordAlgebra(3, K, quadraticForm qf)``` ``` (3) CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) Type: Domain (4) -> bases : List H := [1,e(1),e(2),e(3),e(1)*e(2),e(2)*e(3),e(3)*e(1),e(1)*e(2)*e(3)]``` ``` (4) [1,e ,e ,e ,e e ,e e ,- e e ,e e e ] 1 2 3 1 2 2 3 1 3 1 2 3 Type: List CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) (5) -> matrix([[bases(i)*bases(j) for i in 1..8] for j in 1..8])``` ``` + 1 e e e e e e e - e e e e e + | 1 2 3 1 2 2 3 1 3 1 2 3| | | | e 1 - e e - e e - e e e e e e e | | 1 1 2 1 3 2 1 2 3 3 2 3 | | | | e e e 1 - e e e - e e e e - e e | | 2 1 2 2 3 1 3 1 2 3 1 3| | | | e e e e e 1 e e e e - e e e | | 3 1 3 2 3 1 2 3 2 1 1 2 | (5) | | | e e e - e e e e - 1 - e e - e e - e | | 1 2 2 1 1 2 3 1 3 2 3 3 | | | | e e e e e e - e e e - 1 e e - e | | 2 3 1 2 3 3 2 1 3 1 2 1 | | | |- e e - e e e e e e e - e e - 1 - e | | 1 3 3 1 2 3 1 2 3 1 2 2 | | | |e e e e e - e e e e - e - e - e - 1 | + 1 2 3 2 3 1 3 1 2 3 1 2 + Type: Matrix CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) ``` ` `

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.      Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics). This book is intended for mathematicians and physicists rather than programmers, it is very theoretical. It covers the algebra and calculus of multivectors of any dimension and is not specific to 3D modelling.