improved notation for octonian numbers

Let it all hang out

improved notation for octonian numbers

PostPosted by drab » Tue Jan 17, 2017 7:56 am

Currently, the 4 parts of an quaternian can be specified by

1i2j3k4

and the 8 parts of an octonian can be specified by

1i2j3k4l5ij6jk7kl8

I find this discommoding, because all of the complex parts of a quaternion are specified by 1 letter (i j k), and only 1 extra part of an octonion is specified by 1 letter (l), and the other 3 are specified by 2 letters (ij jk kl).

I would prefer that ALL of the 4 extra parts of an octonion be specifed by 2 letters.
That would much more clearly distinguish the quaternions and and octonions.

Furthermore, the 1-letter and 2-letter codes could be more parallel and meaningful.

The extra 4 octonion codes could all start with 1st letter o, and the second letter could be the same as the corresponding quaternion code.

So, it would look like this

1i2j3k4ou5oi6oj7ok8
drab
 
Posts: 315
Joined: Thu Oct 09, 2014 6:23 am

Re: improved notation for octonian numbers

PostPosted by forummaster » Thu Jan 26, 2017 11:11 am

I'm not quite ready to implement this idea, but when I do would you mind if "ou" -> "os" as to be parallel with suffix notation (from Jacob Brickman) who suggested that octonions use a suffix format such as

1s2i3j4k5l6ij7jk8kl

or in your notation

1s2i3j4k5os6oi7oj8ok

and correspondingly in infix notation

1i2j3k4os5oi6oj7ok8

For more details see my paper "Hypercomplex Notation in APL" to which I'll be adding your Unit Normalized Radian notation.
forummaster
 
Posts: 567
Joined: Wed Jan 23, 2013 1:00 pm

Re: improved notation for octonian numbers

PostPosted by drab » Fri Jan 27, 2017 12:15 pm

That would be great.
drab
 
Posts: 315
Joined: Thu Oct 09, 2014 6:23 am

Re: improved notation for octonian numbers

PostPosted by drab » Mon Jan 30, 2017 6:18 am

This is certainly not critical, but the input syntax could be a little more flexible ...

1i2j3
1i2j3k0
1j3i2
SYNTAX ERROR
drab
 
Posts: 315
Joined: Thu Oct 09, 2014 6:23 am

Re: improved notation for octonian numbers

PostPosted by forummaster » Mon Jan 30, 2017 11:38 am

drab wrote:This is certainly not critical, but the input syntax could be a little more flexible ...

1i2j3
1i2j3k0
1j3i2
SYNTAX ERROR
Yes, that's possible, but it looks more like a typo. Why would anyone want to enter the coordinates in other than the normal order? I would rather keep the error message so as to catch this transposition.
forummaster
 
Posts: 567
Joined: Wed Jan 23, 2013 1:00 pm


Return to Open Discussion

Who is online

Users browsing this forum: No registered users and 1 guest

cron