OT Proposal for project Database of Irrational Constants

[Georgi Guninski]

Happy 2*1013 new year!

I propose a project for database of irrational constants.
As the name suggests, it will have irrational constants.
Probably both online and offline version should be available,
the offline version will be for custom queries.
Don't have estimate what time will it take to implement.

Related existing projects OEIS [1] The L-functions and modular
forms database (LMFDB) [2]

[1] https://oeis.org/
[2] https://www.lmfdb.org/

[Vincent Delecroix]

This has already been done (but not available online anymore)

https://en.wikipedia.org/wiki/Inverse_Symbolic_Calculator

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[David Roe]

There is also numberdb.org.  For a list of database projects of this type, see mathbases.org.

David

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[TB]

Their GitHub page is https://github.com/numberdb

A similar program to the Inverse Symbolic Calculator, that is available
to download, is RIES [1]. It also have an online interface [2]. There
are also tools for guessing sequences which seem to be relevant, e.g.
CFiniteSequences.guess() in Sage [3] or more in FriCAS.

Regards,
TB

[1] https://mrob.com/pub/ries/index.html
[2] https://thomasahle.com/ries/
[3]
https://doc.sagemath.org/html/en/reference/combinat/sage/rings/cfinite_sequence.html

On 04/01/2026 19:29, David Roe wrote:
> There is also numberdb.org <http://numberdb.org/>.  For a list of
> database projects of this type, see mathbases.org <https://mathbases.org/>.

> David
>
> On Sun, Jan 4, 2026 at 9:18 AM Vincent Delecroix

> <20100.d...@gmail.com <mailto:20100.d...@gmail.com>> wrote:
>
> This has already been done (but not available online anymore)
>

> https://en.wikipedia.org/wiki/Inverse_Symbolic_Calculator <https://
> en.wikipedia.org/wiki/Inverse_Symbolic_Calculator>

>
> On Sat, 3 Jan 2026 at 09:58, Georgi Guninski <ggun...@gmail.com
> <mailto:ggun...@gmail.com>> wrote:
> >
> > Happy 2*1013 new year!
> >
> > I propose a project for database of irrational constants.
> > As the name suggests, it will have irrational constants.
> > Probably both online and offline version should be available,
> > the offline version will be for custom queries.
> > Don't have estimate what time will it take to implement.
> >
> > Related existing projects OEIS [1] The L-functions and modular
> > forms database (LMFDB) [2]
> >

> > [1] https://oeis.org/ <https://oeis.org/>
> > [2] https://www.lmfdb.org/ <https://www.lmfdb.org/>

> >
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> sage-devel/CAGUWgD94aUuN0JoDAOSPPRGrpRswPODC-

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[Doris Behrendt]

Hi all,

> On 5. Jan 2026, at 16:47, TB <math...@gmail.com> wrote:
>
> Their GitHub page is https://github.com/numberdb
>
> A similar program to the Inverse Symbolic Calculator, that is available to download, is RIES [1]. It also have an online interface [2]. There are also tools for guessing sequences which seem to be relevant, e.g. CFiniteSequences.guess() in Sage [3] or more in FriCAS.
>

I never heard of FriCAS. I just had a look at https://fricas.sourceforge.net/history.html and some other webpages. I never heard of it tbh.

Would anyone on this list be so kind and give me an overview of what the main differences in comparison to SageMath are?

I could ask some AI, but I prefer the knowledge of the experts here ;-)

-- Doris

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[Ralf Hemmecke]

On 1/6/26 10:51, 'Doris Behrendt' via sage-devel wrote:

> I never heard of FriCAS. I just had a look at https://
> fricas.sourceforge.net/history.html and some other webpages. I never
> heard of it tbh.

The official website is eigther https://fricas.github.io or
https://fricas.org.

Since you seem to be interested in guessing, look at
https://fricas.github.io/api/Guess.html and the respective article
https://arxiv.org/abs/math/0702086.

A general comparison is hard to make. Since FriCAS grew out of AXIOM, it
it is a compact system that is strong in many areas, in particular
integration. A main ingredient of FriCAS is that it comes with a
strongly typed programming language that may detect wrong code already
at compile time. SAGE probably covers more areas by incorporating lots
of other open-source packages into a whole system. It's programming
language is Python (or Cython). In fact, SAGE also has an interface to
FriCAS and allows to use the FriCAS integration routines from within SAGE.

Maybe other people can add.

Ralf

[Dima Pasechnik]

On Tuesday, January 6, 2026 at 6:04:05 AM UTC-6 Ralf Hemmecke wrote:

On 1/6/26 10:51, 'Doris Behrendt' via sage-devel wrote:

> I never heard of FriCAS. I just had a look at https://
> fricas.sourceforge.net/history.html and some other webpages. I never
> heard of it tbh.

The official website is eigther https://fricas.github.io or
https://fricas.org.

Since you seem to be interested in guessing, look at
https://fricas.github.io/api/Guess.html and the respective article
https://arxiv.org/abs/math/0702086.

A general comparison is hard to make. Since FriCAS grew out of AXIOM, it
it is a compact system that is strong in many areas, in particular
integration. A main ingredient of FriCAS is that it comes with a
strongly typed programming language that may detect wrong code already
at compile time. SAGE probably covers more areas by incorporating lots
of other open-source packages into a whole system. It's programming
language is Python (or Cython).

Sage certainly covers more maths areas than Axiom/FriCAS, and usually with efficient implementations.

E.g. doing number theory or graph theory, or group theory, or coding theory in Axiom/FriCAS isn't going to take you very far.

OTOH Sage never had its own symbolic integration, it merely provides interfaces, whereas in Axiom/FriCAS it's

one of the areas where it excels. 

[Vishwas Bajaj]

Hi all,

Just to add a small perspective building on what Ralf mentioned.

One aspect I’ve found particularly interesting is how Sage positions itself more as an integration layer rather than a single tightly-coupled CAS. While this means Sage historically didn’t implement symbolic integration natively, the design choice pays off by allowing Sage to leverage mature systems like FriCAS for areas where they are strongest.

In contrast, FriCAS/Axiom’s tightly integrated, strongly typed language enables very robust symbolic workflows (especially for integration), but this same design makes it harder to organically expand into broader areas like number theory, graph theory, or coding theory at scale.

From this angle, Sage’s interface-driven approach seems less like a limitation and more like a deliberate architectural trade-off: breadth and extensibility over specialization. The fact that Sage can expose FriCAS integration routines when needed makes the two systems feel more complementary than competitive.

Happy to hear if others have seen this trade-off play out differently in practice.

Best regards,

Vishwas

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