Promoting SAGE at Mapleprimes
Alec Mihailovs
to
http://www.mapleprimes.com/forum/a110375
where Mike Hansen posted a comment at the end of the thread, there is a
question from Alejandro Jakubi in
http://www.mapleprimes.com/forum/clairautsyoungstheorem
He asked whether SAGE is using Maxima or Axiom for calculus.
I am not a SAGE developer (just a happy user), and I could say something
wrong about that. Could somebody post there explaining that, please?
Also, it would be nice to see another response in A110375 thread to keep in
on the top of Recent posts list (that's what many people use - in the menu
from the left hand side.)
Thank you,
Alec Mihailovs
William Stein
>
> I am trying to promote SAGE at Mapleprimes (in various threads).
Thank you!
> In addition to
>
> http://www.mapleprimes.com/forum/a110375
>
> where Mike Hansen posted a comment at the end of the thread, there is a
> question from Alejandro Jakubi in
>
> http://www.mapleprimes.com/forum/clairautsyoungstheorem
>
> He asked whether SAGE is using Maxima or Axiom for calculus.
Sage does not use Axiom for anything. Sage uses Maxima as
a backend for a lot of Calculus right now. In the long run it
will likely use Maxima less and new faster more modern code
that it is in the pipeline (this is work being funded by Google,
but not as part of Google Summer of Code). It will be interesting
to see how all of these physics/mathematicians/etc. assumptions
will play out in Sage as compared to how they played out in
Maple.
It is likely in Sage that we'll have for calculus
a global proof=True and proof=False
mode, like we have with number fields, linear algebra, etc.
With proof=False, assumptions about partial commuting,
functions being continuous, etc., like maple makes, would
be in force. The default unless explicitly changed would be
proof=True. One could see everywhere in the source where
the proof flag is used, hence see precisely what assumptions
are being made in a computation...
> I am not a SAGE developer (just a happy user), and I could say something
> wrong about that. Could somebody post there explaining that, please?
Please feel free to post my remark there. I don't have account.
> Also, it would be nice to see another response in A110375 thread to keep in
> on the top of Recent posts list (that's what many people use - in the menu
> from the left hand side.)
I'm not sure what to say except I agree with all the posts in that thread.
Somebody could post a precise table of timings comparing Sage,
Mathematica, Maple, and Pari, say, all on a common architecture.
That would fit in the thread.
>
> Thank you,
> Alec Mihailovs
I enjoyed reading this story that you posted in one of the threads:
"That reminded me something that V.I. Arnold said in one of his books.
He noticed in one of physical books that it was said about the
derivative that it is a mathematical approximation to the slope of the
tangent line. When he talked with the author of that book and told him
that it _is_ the slope - not an approimation to it, he said - only
from mathematician's point of view. In real life (f(x+t)-f(x))/t has
sense only for t not less than, if I recall correctly, 10^(-16), and
for that value it gives the real slope, and smaller values don't make
physical sense because Newtonian physics doesn't work on such small
distances and quantum mechanics should be used there instead (with
completely different formulas). So the limit that mathematician's use
is only approximation to the real slope. Also, he said, you
mathematicians write a lot of other wrong things - for example, that
the graph of y=exp(-x^2) doesn't intersect the x-axis while everybody
can see that they intersect and not that far from 0, and for x=10
nobody can insert even an atom between them."