For example,

with(group):
transgroup(3,names);

                         [{"A(3)"}, {"S(3)"}]

gens:=transgroup([3,2],generators);

                     gens := {[[1, 3]], [[2, 3]]}

S_3:=permgroup(3,gens);

              S_3 := permgroup(3, {[[1, 3]], [[2, 3]]})

grouporder(S_3);

                                  6

ident := permgroup(3, {[]});

                     ident := permgroup(3, {[]})

cosets(S_3,ident);

     {[], [[1, 2]], [[1, 3]], [[2, 3]], [[1, 2, 3]], [[1, 3, 2]]}

y:=permgroup(3,{[[1,3]]});

                    y := permgroup(3, {[[1, 3]]})

c:=cosets(S_3,y);

                    c := {[], [[1, 2]], [[2, 3]]}

These are left coset representatives. The left cosets can be produced as

seq({seq(mulperms(i,j),i=elements(y))},j=c);

   {[], [[1, 3]]}, {[[1, 2]], [[1, 3, 2]]}, {[[2, 3]], [[1, 2, 3]]}

And the right cosets can be produced as

seq({seq(mulperms(j,i),i=elements(y))},j=c);

   {[], [[1, 3]]}, {[[1, 2]], [[1, 2, 3]]}, {[[2, 3]], [[1, 3, 2]]}

In Maple, the left cosets are called right cosets, and the right cosets are called left cosets - because the mulperms acts in the way opposite to usual.

Alec

int is different.

Alec

int is different.

Alec

May be, but with a cube root in the denominator, that doesn't seem very probable.

Unless you have some reasons to believe that it is possible.

Alec

May be, but with a cube root in the denominator, that doesn't seem very probable.

Unless you have some reasons to believe that it is possible.

Alec

not export to LaTeX - it is broken in Maple. Just regular LaTeX.

If you don't have it, then you definitely should install it - MiKTeX, for instance, or Tex Live.

Alec

not export to LaTeX - it is broken in Maple. Just regular LaTeX.

If you don't have it, then you definitely should install it - MiKTeX, for instance, or Tex Live.

Alec

Domains may be types in the CS sense, but they are very different from things called types in Maple. They include much more. I've just looked at the related manual - nothing like that exists in Maple. Some attempts in that direction were made (in particular, the ?Domains package), but they were not finished.

Alec

What I meant is that before using parallelization, especially with such an overhead as it currently has, with only using 3 or 4 processors giving approximately the same speed as without it, it has sense to try to find a way to make calculations faster without parallelization - as it is done in Python, say, which is also an interpreter, but works with linear algebra calculations in numpy with speed comparable to C, and in other cases not slower than 10 times compared to C.

100s processors currently mean 100s GPUs, and it would be nice if Maple worked with it. Both Python and Mathematica do.

Such things as chrem definitely should be written in C (as Mathematica does, by the way), with parallelization done in C.

In time the situation may change, but I was talking about the current situation.

Alec

I don't use Axiom that often, and I may be mistaken, but I got an impression that it uses domains rather than types, and the domains there seemed to be designed more carefully than Maple types, with more tight integration with other parts of the system, with coercion etc.

Simply saying, domains there seem to be more of use than types (or properties) in Maple.

Alec

Well, I posted that as a joke. With x^4 - probably, algsubs could be used instead of subs.

By the way, my original idea was even deeper - I planned to use Differentiate from the context menu. However, as usual, there was a bug there (or two.) First, it showed some abracadabra instead of x². Second, clicking on that abracadabra produced nothing - no actions were performed (in contrast with clicking on y, producing a derivative with respect to y.)

Alec

Well, I posted that as a joke. With x^4 - probably, algsubs could be used instead of subs.

By the way, my original idea was even deeper - I planned to use Differentiate from the context menu. However, as usual, there was a bug there (or two.) First, it showed some abracadabra instead of x². Second, clicking on that abracadabra produced nothing - no actions were performed (in contrast with clicking on y, producing a derivative with respect to y.)

Alec

Time told that already.

The idea was delirious, the implementation - deleterious.

As a result, Maplesoft was sold.

Alec

PS Unless that was the original plan - then it worked out brilliantly! -Alec

However, that doesn't work in more compicated cases, such as for x^4 or 1/x^2 instead of 5*x^2+y.

Alec

However, that doesn't work in more compicated cases, such as for x^4 or 1/x^2 instead of 5*x^2+y.

Alec