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# The power of duck typing and linear algrebra

## How linear algebra and python make a good fit

Algebraic operator are every where in python. + = * / Dict are every where in python.

What can we achieve by combining both of them?

Slides are here

## 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

Implementation as a trait here https://github.com/jul/archery

Basically it works BUT :

1. it is hard : with archery I stumbled on super
2. with VectorDict (obsolete) it lacks of genericity and the code is clumsy
3. 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...