New inverter, new format, 2.459 billion math constants.

20 views
Skip to first unread message

plouffe

unread,
Jul 3, 2008, 2:22:57 PM7/3/08
to

Hello,

I am downloading it now, the new version of my inverter.
I changed the format to 64 digits and normalized.

Well, there are 2.459 billion mathematical constants in it.
This time I used Maple and Mathematica and in
some occasion Pari-Gp to generate the numbers.

The data is presently <dumped> into a work directory
here : http://www.lacim.uqam.ca/~plouffe/ip/
the files are gziped, to take a look at one just
click on the file and normaly the firefox browser
will uncompress it on the fly. If you do not use
firefox you may save it on your computer and
uncompress it with winrar of gunzip (unix).

The pc (actualy it is a mac) where the database
will reside is currently being organized in Montréal,
there are 90000 files for a total of 297 gigabytes.
The disk is a 300 gigabytes, so I think it is time
I stop generating constants!

In the database there are something like 25 million
constants that were generated by the OEIS database.

For the moment, I intend to at least organize the
data so that anybody interested in it may download
(yes download) the database. This summer I intend
to re-work the lookup script to take into account
that new format.

The database it of course what I think is an
interesting constant. The base table has about
186 known constants
http://www.lacim.uqam.ca/~plouffe/b000.txt
and the rest are entries
similar to the first and second versions
of this project (the inverse symbolic calculator 1995-now)
the plouffe inverter (1998-now).

If you have any suggestions, of course they are welcome.

note : the current plouffe_inverter program to analyze
math constants will be compatible with the new format
of course. It is still in Maple syntax, I should change
it to mathematica, mathematica is faster, much faster
than maple for many computations...

For the nostalgic, the current inverter with 200 million
constants is all here :
http://www.lacim.uqam.ca/~plouffe/plouffe_inverter_tables/


Simon Plouffe


amzoti

unread,
Jul 3, 2008, 3:10:47 PM7/3/08
to
> 186 known constantshttp://www.lacim.uqam.ca/~plouffe/b000.txt

> and the rest are entries
> similar to the first and second versions
> of this project (the inverse symbolic calculator 1995-now)
> the plouffe inverter (1998-now).
>
> If you have any suggestions, of course they are welcome.
>
> note : the current plouffe_inverter program to analyze
> math constants will be compatible with the new format
> of course. It is still in Maple syntax, I should change
> it to mathematica, mathematica is faster, much faster
> than maple for many computations...
>
> For the nostalgic, the current inverter with 200 million
> constants is all here :http://www.lacim.uqam.ca/~plouffe/plouffe_inverter_tables/
>
> Simon Plouffe

Hello Mr, Plouffe,

first, I'd like to thank you for providing such a wonderful resource
to all of us.

I know it gets used as witnessed by many posting on sci.math.

Anyway - I was wondering if you had anything written up as to how you
go about creating such a large database?

Where do you get all of the data?

How do you go about choosing what goes in and what doesn't - as it is
conceivable that there could be an infinity (never ending) number of
constants which one could add.

Anyway - thanks for doing this.

~A

plouffe

unread,
Jul 3, 2008, 3:41:56 PM7/3/08
to simon....@gmail.com

The data is computed from programs I wrote in Maple
mainly and mathematica, I am collecting numbers like
this since 1986. At the time they were in BASIC!.
The main inspiration is the classic Abramowitz & Stegun
(available on my home page), another source of
data is the OEIS database that I helped to create
on the web with Neil Sloane, now Neil is the main
architect of that project, I just helped in the beginning
with Maple from 1991 just before the widely available internet.

The rest is my own inspiration and experience I guess.
I always computed numbers and sometimes I stumble on
some examples like arctan(1/2)/Pi, that number was discovered
experimentally with an HP calculator. I had found a simple
rational construction to get the binary digits of that
number one by one. I found this example in 1983.

I studied number theory for a long time (hardy and wright)
and I was always surprised on how easy it is to
construct a real number with certain properties without
any mean to find what it is! This is where I realized that
a computer could store a lot of those constants and
use special programs to try to find an expression
given the number. This is why I created the ISC
in 1995, one calculator with 1 button, you type
a number and it gives the question.

That problem of identifying constants is a hard one,
to say a pun , it is a hard disk one, it all comes
back to our capacity to store and compute numbers
to a certain precision and the speed at which we
can <guess> what a number is like 0.422784335..
if you do not have any clue it is hard to find
that it is 1-gamma and there are a lot of
these examples.

I had a project of doing a ph d with that
idea in 1993, but when I submitted my idea
to my thesis director at that time he
considered this idea of having tables and
programs for real numbers as foolish, I think
he was wrong. I used my inverter in 1995 to
find the formula for pi in base 2, but not
only the inverter, I used Pari-GP to find
the integer relation, curiously, Pari-GP
is the program that my director created...
funny isn't ?

The choice of having a certain math
constant in or out of the database is
the capacity for us to have 1 line
of description, the simplest we can find
to describe what the number is. The same
criteria of originality and simplicity
is used now by Neil sloane and all the
collaborators in the OEIS database.

Simon Plouffe

Axel Vogt

unread,
Jul 19, 2008, 3:17:12 PM7/19/08
to
plouffe wrote:
>
> Hello,
>
> I am downloading it now, the new version of my inverter.
> I changed the format to 64 digits and normalized.
>
> Well, there are 2.459 billion mathematical constants in it.
> This time I used Maple and Mathematica and in
> some occasion Pari-Gp to generate the numbers.

...

> If you have any suggestions, of course they are welcome.
>
> note : the current plouffe_inverter program to analyze
> math constants will be compatible with the new format
> of course. It is still in Maple syntax, I should change
> it to mathematica, mathematica is faster, much faster
> than maple for many computations...
>
> For the nostalgic, the current inverter with 200 million
> constants is all here :
> http://www.lacim.uqam.ca/~plouffe/plouffe_inverter_tables/
>
>
> Simon Plouffe


I have a question about the web version when browsing:

Do have a list or overview for the definition of those
functions used there?

For example: what does 'sr' mean in 7601734505331404 =
sr(Pi)/exp(1/2)/sr(2) ?

clicl...@freenet.de

unread,
Jul 19, 2008, 5:30:58 PM7/19/08
to

Axel Vogt schrieb:

> plouffe wrote:
> >
> > I am downloading it now, the new version of my inverter.
> > I changed the format to 64 digits and normalized.
> >
> > Well, there are 2.459 billion mathematical constants in it.
> > This time I used Maple and Mathematica and in
> > some occasion Pari-Gp to generate the numbers.
>
> ...
>
> > If you have any suggestions, of course they are welcome.
> >
> > note : the current plouffe_inverter program to analyze
> > math constants will be compatible with the new format
> > of course. It is still in Maple syntax, I should change
> > it to mathematica, mathematica is faster, much faster
> > than maple for many computations...
> >
> > For the nostalgic, the current inverter with 200 million
> > constants is all here :
> > http://www.lacim.uqam.ca/~plouffe/plouffe_inverter_tables/
> >
>
> I have a question about the web version when browsing:
>
> Do have a list or overview for the definition of those
> functions used there?
>
> For example: what does 'sr' mean in 7601734505331404 =
> sr(Pi)/exp(1/2)/sr(2) ?

sr() = sqrt(), no doubt:

[PrecisionDigits:=20, NotationDigits:=16]
SQRT(pi)/EXP(1/2)/SQRT(2)
0.7601734505331404

Martin.

Reply all
Reply to author
Forward
0 new messages