LyX also. It is not a pure LaTeX, but it is derived from it and is close to it. There are plugins for both Maple and Sage in TeXmacs and they also can be accessed from LyX (but not that easily.)

I would like both of them more if they used pure LaTeX. Lyx is closer to that. Originally, it started as WySiWym front-end for LaTeX, but then it started to go further and further from that. Still, it is much closer to LaTeX than TeXmacs.

Also, TexMacs's second part of the name which came from emacs, shows how it uses keyboard - a lot of commands need to push 3 keys simultaneously, as in emacs. There are people who like that, but I am not one of them.

Alec

I think that Sage made the same mistake as Maple with the name choice. Searching (say Google) for Mathematica shows pages related to Mathematica, and searching for Maple or Sage points to a lot of other things.

Alec

Fantastic!

And it also has a link to Acer Active near the bottom!

Alec

Acer and Alejandro,

Congratulations! As usual (with only one or two exceptions in the past), both monthly and quarterly awards were well deserved. I learned a lot during last few months from both of you, as well as from Jacques Carette, Robert Israel, Joe Riel, Axel Vogt (the alphabetical order coincides with the points order), and other active participants in this forum.

Alec

Clifford package written by Rafal Ablamowicz with later collaboration with Bertfried Fauser is very good.

The first link didn't work for me. I think, this one should work.

Generally speaking, most of the packages that I know, written outside of Maplesoft and not included in Maple distribution, are good, in sharp contrast with packages written by Maplesoft people and included in Maple distribution.

That just confirms that all good things in this life are free.

Alec

Differential forms in differential geometry is one of the standard constructions of Grassmann algebra. Anyway, even restricting only to homogeneous forms with &plus and &mult instead of + and *, such operations as (dx &wedge dy) &wedge (dx &wedge dy) should be defined.

Alec

PS I am trying to not to say a word about Lie algebras, because it is even larger part of my specialty (representation theory) than tensors, Grassmann algebra, and differential forms. -Alec

I don't know about Physics, but in Mathematics Grassman Algebra ΛV is the direct sum of Λ⁰V, Λ¹V, ..., Λ^{nV, with an operation ∧ defined for any 2 elements (including, say sums of scalars, 1-forms and 2-forms). Such operations as in my post above are completely normal, with + or with +. Now, it appears that they can't be done in the DifferentialGeometry package?! Alec}

I tried to find an example where that could be useful, but I couldn't. Addition seems to be working OK.

with(DifferentialGeometry):
DGsetup([x,y],M):
a:=dx &wedge dy: 

b:=a+0;
                             b := dx ^ dy
evalb(a=b);
                                 true

So there shouldn't be any difference for transformations (including translations.)

Anyway, one of these 2 things should be fixed for consistency. Either 0 dx and 0 dx &wedge dy should simplify to 0, or a multiplication of a form to 0 should give the sum of such 0's.

By the way, just found another thing that is definitely wrong,

evalDG(a &wedge a);

Error, (in DifferentialGeometry:-Tools:-DGzero)
  given degree, 4, exceeds that of frame dimension, 2.

Obviously, that should be 0. Now, the question is, what kind of 0? If zeros were simplified to 0, such a problem wouldn't arise.

Another thing, not related to that (but related to the DifferentialGeometry package),

c:=1+dx + dy;
                           c := 1 + dx + dy

evalDG(c &wedge c);

                                         2
                            (1 + dx + dy)

What is this?

Alec

That's interesting.

Alec

That's interesting.

Alec

Thank you.

Looking for piecewise on that page I used Ctrl+F, and noticed that it had a replace field. I tried to replace piecewise to piecewis, and it worked!

It looked as a simple solution for typos in the help pages. It wasn't saved though.

Alec

Thank you.

Looking for piecewise on that page I used Ctrl+F, and noticed that it had a replace field. I tried to replace piecewise to piecewis, and it worked!

It looked as a simple solution for typos in the help pages. It wasn't saved though.

Alec

I'm not sure that it would be better. I don't know about the current situation, but in the past Maple's distribution included some additional Java packages which were not a part of the newest Java distribution, and using the newest distribution instead of Maple's created some problems because of that.

Alec

I'm not sure that it would be better. I don't know about the current situation, but in the past Maple's distribution included some additional Java packages which were not a part of the newest Java distribution, and using the newest distribution instead of Maple's created some problems because of that.

Alec

Now, after thinking about that for some time, I think that Axel Vogt is right and there is no need for such things as 0 dx or 0 dx &wedge dy .  They could be simplified to 0. In this case, giving 0 as a result of multiplication by 0 would be fine.

Alec