Int is certainly continuous and more than that, compact in standard cases. But Diff is usually not, I think, because otherwise it would be a continuous operator inverse to a compact operator Int, and compact operators usually can't have continuous inverse operators in infinite dimensional spaces.

Linearity, in general, doesn't imply continuity.

Alec

That is certainly true. But it might be faster, and it may be worth to try. Who knows -maybe it can be factorized, simplified, or reduced to some special form,such as λ⁴-a, for example. If a problem is related to some nice structure (as it happens often in physics), that may be the case.

Also, in some cases the printing of the output is very slow, much slower than the calculations themselves, and even can crash Maple. One should make sure that the output is not printed.

Alec

That is certainly true. But it might be faster, and it may be worth to try. Who knows -maybe it can be factorized, simplified, or reduced to some special form,such as λ⁴-a, for example. If a problem is related to some nice structure (as it happens often in physics), that may be the case.

Also, in some cases the printing of the output is very slow, much slower than the calculations themselves, and even can crash Maple. One should make sure that the output is not printed.

Alec

I am usually trying to avoid using wrappers. One way of doing that is using an Array (or Arrays) in the arguments for return instead of using the returned value. The Arrays are passed by reference (i.e. as a pointer to their beginning), so problems with returned value type don't arise. Also, it seems as if complex arguments may be also passed by reference and not by value, in such case they could also be used for return.

Alec

I am usually trying to avoid using wrappers. One way of doing that is using an Array (or Arrays) in the arguments for return instead of using the returned value. The Arrays are passed by reference (i.e. as a pointer to their beginning), so problems with returned value type don't arise. Also, it seems as if complex arguments may be also passed by reference and not by value, in such case they could also be used for return.

Alec

I had several times Maple running for several days. Usually it was for computing of the next term of a sequence in the OEIS. In such situations, computing few previous terms first, I could estimate the time needed for the next term.

Alec

I had several times Maple running for several days. Usually it was for computing of the next term of a sequence in the OEIS. In such situations, computing few previous terms first, I could estimate the time needed for the next term.

Alec

You could try to find the Characteristic Polynomial first - that should be fast. And then try to find its roots.

Alec

You could try to find the Characteristic Polynomial first - that should be fast. And then try to find its roots.

Alec

1. Who developed Calculus routines in Maple, I don't know. They certainly don't work the way it should.

2. A (pure) mathematician is a person with a PhD in pure mathematics, continuing doing research or teaching after getting his or her PhD. A masters is not OK. Degree in physics, engineering, or computer science also don't qualify, as well as a degree in applied mathematics, or computational mathematics. You can be a (pure) mathematician in those cases if you get a PhD in pure mathematics in addition to other degree, and continue doing research and/or teaching after that. Every rule has exceptions, and I know a few exceptions to that, but that is, I think, the usual meaning of the term.

3. The current situation with Calculus in SAGE, if I understand is correctly, is following. It uses wrappers (written in SAGE, or Python) for Maxima and some other packages. During this Summer many of them were replaced (or planned to be replaced) with SAGE and Cython code. Currently, it is a project in development. Being mathemathicians, and teaching Calculus, in particular, provides some warranties that the things are done right, i.e. usable for teaching Calculus.

Alec

David,

I am saying that many things in Maple are done in a way that contradicts usual practise in both research mathematics and teaching mathematics. Nobody doing research or teaching himself or herself would do it that way. Whether Maple developers got a proper mathematical education, I don't know, and I didn't imply that they did or did not.

Alec

I understand that very well. If it had Mathematics package, it would be very cool.

Alec

I understand that very well. If it had Mathematics package, it would be very cool.

Alec

I would do that as

with(Statistics):
X:=RandomVariable(Uniform(1,100)):
S:=Sample(X,5000):
Histogram(S);

Alec

In the form it stated in Wikipedia, it sounds as if Gaston Gonnet said that Maple lost market share due to the interface, and now, with new interface, it got (or is going to get) the share back. I don't think that he meant that.

Unfortunately, what I think about the reasons of losing market share, is unpublishable (and nobody cares anyway :).

Alec