Jason Merrill wrote:
> I have some ideas and questions I'd like to share about how to make a
> nice interface for derivatives of objects with several variables and/
> or dimensions.  Right now, Sage has diff for partial derivatives, and
> gradient for gradients, but I think there's room for extending Sage's
> capabilities.
> 
> I'm hesitant to spend a chunk of time writing these ideas down,
> though, because my last two efforts[1,2] didn't earn much interest.
> Am I doing it wrong?  Is this just not a great time in the project's
> life cycle for this kind of discussion?  I'd like to contribute to
> making Sage a joy for me and people like me to use, but some of my
> ideas are too big for me to unilaterally implement as a newcomer to
> the project without others' input.  Reply off list if it seems more
> appropriate, though others might benefit from hearing how to most
> usefully share ideas.
> 
> [1]
> Symbolic/Numeric interface thoughts:
> http://groups.google.com/group/sage-devel/browse_thread/thread/dd03e6efb0b991d3/19c2c432ab056aea?lnk=gst&q=jwmerrill#19c2c432ab056aea
> 
> [2]
> syntax could be more consistent:
> http://groups.google.com/group/sage-devel/browse_thread/thread/953447e501ec30d3/95291cca41657015?lnk=gst&q=syntax+consistent#95291cca41657015

Jason,

I really like your careful, well-thought out posts.  I've hit a busy 
time, though, so I can't do much about it, so that explains my personal 
lack of response, maybe.

I agree with the ideas of your first post; things should work much more 
consistently like you said.  I would absolutely love to see some of 
those things implemented.  I really like your second post too; I've 
spent at least some time partially tearing apart the plotting interfaces 
to try to get more consistent syntax, but ran out of the time I had 
allotted before coming up with something good.

For both of these ideas, I think the next step would be to implement 
some code so that people can actually try it out.  I would be excited 
about a patch.  Unfortunately, I'm already backlogged on my own 
"consistency and niceness" projects related to the linear algebra 
interface and backend.  One thing that I've learned in trying to do the 
sort of thing that you are suggesting is that you ought to piecemeal it 
out and do it a little at a time.  That gives people more manageable 
chunks to comment on and also makes it so that you don't have a month of 
work and a 1 megabyte patch to merge in all at once.

As for differentiation, I agree that things could be extended quite a 
bit.  There was a start of an effort to do some build some differential 
geometry structure into Sage a while ago, but I think that it stagnated. 
  I also wrote a small function to thread diff over lists so that we 
could do matrix derivatives.  It's up on trac at #3941.

Thanks,

Jason


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