Introduction
Algebra is a wonderful abstraction that make the infamous 2D point example of a class or nameddict useless when you have complex data type (that is HW accelerated on Intel CPU).
I Algebra 101 : it is all about consistency between symbol and behaviour
Simple: Is something consistent with linear algebra?
it requires 17 simple unit tests suffice to say so
So just let makes a test this rules are followed, and then a class that applies these behaviours and we have implemented it.
II I have linear algebra behaviour. How useful can it be?
Well, you have basic data type like { x: 1, y :2, z :3 } that is actually behaving like an euclidean vector.
If an object is a MutableMapping thus we can create a universal operator for saying how much an object «looks like» another one.
Practical use :
- finding doublons in database;
- text matching (after a pass of ntlk + word counters);
- pattern fitting;
...
That is the basis of Textual indexation and profiling (it is not only for evil purpose)
https://github.com/jul/ADictAddiction/blob/master/example/cosdemo.py
III State of the art of 2 working POC how to use MutableMapping (dict) and super
Most of the operation tested here
https://github.com/jul/ADictAdd_iction/
Implementation as a trait here
https://github.com/jul/archery
Basically it works BUT :
- it is hard : with archery I stumbled on super
- with VectorDict (obsolete) it lacks of genericity and the code is clumsy
- python 2 div behaviour was screwing this (and since these library were relying on base operator, I got biten)
Prepare to throw 2 away
IV the future
A chain is as strong as its weakest link : if a lib is based on composing the python based operator, the algebra will be as consistent as the CORE behaviour of the operator in the language.
Conclusion
Algebra is a powerful abstraction that is still underused.
Possible development :
- Rieman/Hermitian algebra: using the power of the math used in Quantum Mechanics/relativity and python in the same fashion
- Using Quaternion to have quirkless rotation in euclidean 3D...
