pyoctonion 3.9

Octonion Number System

pyoctonion

Octonion in Python

Authors: Charith Atapattu & Kalpa Thudewaththage

In this project, we introduce Python Library for octonions. There is a Python Library for facilitating algebra in quaternions called "pyquaternion". However, no python Library for doing algebraic operations in octonions. We introduce this "pyoctonion" library for researchers who need calculations in octonions. Due to lack of commutativity and Associativity, manual simpliflication is always time consuming and might go wrong. This package will certainly help to check octonionic identities and work with wide range of problems in octonions.

Installation

Install from PyPI Please visit the pyoctonion homepage for full information and the latest documentation. Designed for Python 2.7+ and 3.0+

$ pip install pyoctonion

Quick Start

Run the following for a basic overview. A copy of this example can be found in demo.ipynb.

Basic Usage

In your code, simply import the Octonion object from the pyoctonion module:

from pyoctonion import Octonion

Octonion Features

Define Octonion objects

Define a,b,c Octonions.

a = Octonion(1,2,3,4,5,6,7,8)
b = Octonion(1,3,5,7,9,2,4,6)
c = Octonion(8,7,6,5,4,3,2,1)

#printing octonion objects values
print(a)
print(b)
print(c)

output

+1.0000 +2.0000i +3.0000j +4.0000k +5.0000l +6.0000il +7.0000jl +8.0000kl
+1.0000 +3.0000i +5.0000j +7.0000k +9.0000l +2.0000il +4.0000jl +6.0000kl
+8.0000 +7.0000i +6.0000j +5.0000k +4.0000l +3.0000il +2.0000jl +1.0000kl

Addition

a + b

output

+2.0000 +5.0000i +8.0000j +11.0000k +14.0000l +8.0000il +11.0000jl +14.0000kl

Subtraction

a - b

output

+0.0000 -1.0000i -2.0000j -3.0000k -4.0000l +4.0000il +3.0000jl +2.0000kl

Multiplication

a * b

output

-181.0000 -48.0000i -17.0000j -40.0000k +83.0000l +0.0000il +35.0000jl +4.0000kl

Division

a / b

output

+0.8281 +0.2353i +0.1041j +0.2172k -0.3303l +0.0543il -0.0950jl +0.0543kl

Norm

a.norm

output

14.2828568570857

Conjugation

a.conjugate

output

+1.0000 -2.0000i -3.0000j -4.0000k -5.0000l -6.0000il -7.0000jl -8.0000kl

Inverse

a.inverse

output

+0.0049 -0.0098i -0.0147j -0.0196k -0.0245l -0.0294il -0.0343jl -0.0392kl

Power

a ** 3

output

-608.0000 -400.0000i -600.0000j -800.0000k -1000.0000l -1200.0000il -1400.0000jl -1600.0000kl

Real Part

a.x_0

output

1

Similary, we can obtain coeficient of imaginary units

Example 1:

a.x_1

output

2

Example 2:

a.x_7

output

8