Re: [Axiom-developer] Raising the bar (again)

[Martin Baker]

On 06/03/15 11:32, address@hidden wrote:
> Have you seen "Visual Complex Analysis" by Tristan Needham?

Yes, I agree that there are a lot of examples in there which show how 
visualisation helps people get a better understanding of the 
mathematics. Also I think this type of mathematics may be better suited 
to Axiom than discreet algebras such as finite groups.

I still think this is more useful to end users of Axiom than developers 
(it gives an intuitive understanding of the mathematics not the code), I 
think this is a good thing as end users may turn into developers but I'm 
not sure its part of the documentation. I suppose you could link 
graphics to small chunks of code as in David Mimno talk but not sure how 
that would explain the code?

> There is a technology called d3.js that looks especially interesting:
> https://github.com/mbostock/d3/wiki/Gallery
> and I have spent a little time looking at it. It is data driven
> so Axiom can feed it data just like it does for the current graphics.
> A websocket connection would allow two-way interaction with Axiom.

Yes, these new javascript graphics libraries look interesting but things 
are changing fast and I've not had a chance to really try them. A few 
years ago, before the javascript stuff took off, I tried writing an 
alternative graphics library in SPAD (in FriCAS) but SPAD seems limited 
for writing interfaces. However I do think it needs a tight coupling 
between the maths and the graphics and the ideal would be if it were all 
written in the same language.

For example, in the Needham book, say the user wanted to experiment with 
hyperbolic space. They might want to change the mathematical parameters, 
apply transforms, set boundaries, overlay a grid to see how it gets 
distorted, view it from different angles, change the colour or 
appearance. All these things interactively. Do you think a websocket 
connection will allow this and will it require special javascript to be 
written for each domain, or could the code that is specific to say 
hyperbolic space be written in SPAD and exported to js which then does 
all the interactive stuff?

> If the next generation cannot understand the code then Axiom will die.
> Why write code that will die?

I'm not disputing that, but I would like something like this to help 
people (including myself) understand the mathematics.

Martin