Having Maple be able to run on a Tesla personal supercomputer (with 4 teraflops) would be nice though. Mathematica runs on it.

Alec

Because the numbers of instruments are shifted by 1 in the table - they should be from 0 (piano) to 127 (gunshot), but for some unknown reason they are listed there from 1 (piano) to 128 (gunshot). The correct numbers are 1 less.

I tried to find a table listing correct numbers for the reference, but the top Google links gave the same shifted by 1 table. So one has to subtract 1 to use it.

Isn't that interesting - I mean midi?

Alec

Because the numbers of instruments are shifted by 1 in the table - they should be from 0 (piano) to 127 (gunshot), but for some unknown reason they are listed there from 1 (piano) to 128 (gunshot). The correct numbers are 1 less.

I tried to find a table listing correct numbers for the reference, but the top Google links gave the same shifted by 1 table. So one has to subtract 1 to use it.

Isn't that interesting - I mean midi?

Alec

The difference between 2 values is

0.87721779610207- 0.40325004753375;

                             0.4739677486

which equals

evalf(Pi*arctanh(1/2)^2/2);

                             0.4739677486

Note that

2*Pi*I*residue(arctan(z)^2/(1+4*z^2),z=I/2);
                                            2
                        -1/2 Pi arctanh(1/2)

In general,

2*Pi*I*residue(arctan(z)^2/(1+t^2*z^2),z=I/t);
                                           2
                            Pi arctanh(1/t)
                          - ----------------
                                   t

and numerical calculations and plotting suggest that the correct answer for t>0 is

W:=piecewise(t<1,V,t=1,Pi^3/24,V-Pi*arctanh(1/t)^2/t);

instead of V, using notations from Robert Israel's post above.

Alec

You could just print it to a file using either postscript, or pdf driver. You might need to install it first if you don't have it. For pdf, CutePDF can be used, for example. Or Adobe drivers - search Google.

If you want a better quality pdf, with links and bookmarks, then you can first export the worksheet to rtf, and then use something like Adobe Acrobat (full product, not just a reader).

Alec

You could just print it to a file using either postscript, or pdf driver. You might need to install it first if you don't have it. For pdf, CutePDF can be used, for example. Or Adobe drivers - search Google.

If you want a better quality pdf, with links and bookmarks, then you can first export the worksheet to rtf, and then use something like Adobe Acrobat (full product, not just a reader).

Alec

You can provide the complete path to the file - like "C:/temp/mymidi.mid" for example, in Windows. If the path is not provided, it is located in Maple's working directory, which can be found using curentdir(). The working directory can be also changed using currentdir.

To play it in Windows, one can just (double)-click the file in Windows Explorer, and it will play in Windows Media Player.

Alec

You can provide the complete path to the file - like "C:/temp/mymidi.mid" for example, in Windows. If the path is not provided, it is located in Maple's working directory, which can be found using curentdir(). The working directory can be also changed using currentdir.

To play it in Windows, one can just (double)-click the file in Windows Explorer, and it will play in Windows Media Player.

Alec

No.

Alec

Why do you ask your questions here?

It is a Maple related forum - there are no integer factorization professionals here. We might have some opinions, but you can't use them as a reference.

Deterministic and probabilistic are not good terms here - if a number is factored, it is factored - there are no doubts about that, except, maybe, that some of the factors can be further factored - but that is a different topic - of determining whether a number is prime or not - and deterministic or probabilistic methods are used for that, not for the original problem.

There is no a simple answer which method is faster. That depends on the numbers used - in particular, on their size, but also on their representation - say if they have a special form like, say, 2^n-1, then special methods are used. Also, different implementations (in particular, with parallelization, or without) have different speeds.

You could download them from the links given in wikipedia and try them yourself for various numbers - that would be a research. Asking what other people think is not a research.

Alec

Why do you ask your questions here?

It is a Maple related forum - there are no integer factorization professionals here. We might have some opinions, but you can't use them as a reference.

Deterministic and probabilistic are not good terms here - if a number is factored, it is factored - there are no doubts about that, except, maybe, that some of the factors can be further factored - but that is a different topic - of determining whether a number is prime or not - and deterministic or probabilistic methods are used for that, not for the original problem.

There is no a simple answer which method is faster. That depends on the numbers used - in particular, on their size, but also on their representation - say if they have a special form like, say, 2^n-1, then special methods are used. Also, different implementations (in particular, with parallelization, or without) have different speeds.

You could download them from the links given in wikipedia and try them yourself for various numbers - that would be a research. Asking what other people think is not a research.

Alec

Yes, that is what I thought, too. What does "widely" mean? For small numbers - something like Maple or Mathematica, probably. For larger numbers - something like FLINT, ECM, and custom NFS and quadratic sieve implementations. New versions of them appear quite often, and it is not exactly clear, whether a new implementation should count as a new algorithm, or not. Parallelization is a part of that problem, too.

Wikipedia provides many links, including links to pages with rather recent implementations, from which one can get to the very recent, including the development versions.

Alec

Yes, that is what I thought, too. What does "widely" mean? For small numbers - something like Maple or Mathematica, probably. For larger numbers - something like FLINT, ECM, and custom NFS and quadratic sieve implementations. New versions of them appear quite often, and it is not exactly clear, whether a new implementation should count as a new algorithm, or not. Parallelization is a part of that problem, too.

Wikipedia provides many links, including links to pages with rather recent implementations, from which one can get to the very recent, including the development versions.

Alec

One can see the library procedures code using showstat (with line numbering, but with a bad indentation), as it has been already shown in this thread, or Joe Riel's PrintProc (without line numbering and with indentation).

Try, for example, PrintProc(`convert/ratpoly`);

The code is usually practically unreadable though, because it is uncommented and written in an abominable programming style - that is one of the explanations why Maple has so many bugs.

Looking through `int/cook/IIntd3`, for example, brings a lot of fun. It is much easier (and faster) to write a short and clean version of it from scratch than to find a bug (or bugs?) in the logic there.

Alec

One can see the library procedures code using showstat (with line numbering, but with a bad indentation), as it has been already shown in this thread, or Joe Riel's PrintProc (without line numbering and with indentation).

Try, for example, PrintProc(`convert/ratpoly`);

The code is usually practically unreadable though, because it is uncommented and written in an abominable programming style - that is one of the explanations why Maple has so many bugs.

Looking through `int/cook/IIntd3`, for example, brings a lot of fun. It is much easier (and faster) to write a short and clean version of it from scratch than to find a bug (or bugs?) in the logic there.

Alec