Frobby: Software for computations on monomial ideals

[Bjake Hammersholt Roune]

I am the author of the program Frobby, which does computations on
monomial ideals. I think Sage is a great project, and I would like to
contribute by making it possible to use Frobby as a part of Sage. My
question is whether Frobby is an appropriate thing to add to Sage, and
if so how I might begin to make that happen. Here is some information
on Frobby to make it possible to answer that question:

The most interesting computation that Frobby currently does is to
compute the Alexander dual/socle/irreducible decomposition (these are
almost equivalent) of any monomial ideal. It often does so 100 to 1000
times faster than the best alternative programs, due to careful
implementation and the use of a new algorithm (the Slice Algorithm),
while also often consuming less memory (as evidenced by other programs
running out of memory). A preprint description of the algorithm and
detailed benchmarks are available at http://www.broune.com/papers/slice.ps
. I am continually improving the program.

Frobby is written in C++ and is licensed as GPL v. 2.0 or later. It
depends only on GMP, and is available at www.broune.com/frobby/ . It
builds using a makefile with no user interaction, and there is a
makefile target for creating a statically linked library. It is
developed on Cygwin and has so far been tested on a few Linux systems
and two macs (the latter in a development version). It includes a
large automated test suite available as a makefile target. The
functionality is exposed as a command-line program, and as a C++
header file that references no internal data structures and is
intended to remain as source-level compatible in future versions as
possible.

Cheers
Bjarke Hammersholt Roune
www.broune.com

[David Joyner]

On Sun, Mar 30, 2008 at 5:26 PM, Bjake Hammersholt Roune
<bjarke...@gmail.com> wrote:
>
> I am the author of the program Frobby, which does computations on
> monomial ideals. I think Sage is a great project, and I would like to
> contribute by making it possible to use Frobby as a part of Sage. My
> question is whether Frobby is an appropriate thing to add to Sage, and
> if so how I might begin to make that happen. Here is some information

Just a few ideas. Hopefully someone who is more of an expert on
commutative algebra computations will weigh in.

The usual procedure is to
(1) make an optional SAGE package (spkg file - see the programming
manual, maybe use the
macaulay interface as a model)
(2) announce it to sage-devel and file a ticket for it on trac, asking
for comments.

SAGE already has gfan. I haven't used it but my understanding is that it is
also a package for commutive algebra computations for monomial ideals.
Maybe you could compare them? Are there Grobner bases computations which both
frobby and gfan can do? Does it do any toric variety computations?

I skimmed quickly over your paper. Looks like good work on first glance.

[Bjake Hammersholt Roune]

On 30 Mar., 19:15, "David Joyner" <wdjoy...@gmail.com> wrote:
> Just a few ideas. Hopefully someone who is more of an expert on
> commutative algebra computations will weigh in.
>
> The usual procedure is to
> (1) make an optional SAGE package (spkg file - see the programming
> manual, maybe use the
> macaulay interface as a model)
> (2) announce it to sage-devel and file a ticket for it on trac, asking
> for comments.
>

This seems like a good way to go about it. Thank you for the advice.

> SAGE already has gfan. I haven't used it but my understanding is that it is
> also a package for commutive algebra computations for monomial ideals.
> Maybe you could compare them? Are there Grobner bases computations which both
> frobby and gfan can do? Does it do any toric variety computations?
>

Frobby performs computations on monomial ideals that you have already
obtained somehow - it does not do things like compute initial ideals.
Thus Frobby and Gfan complement each other, since Gfan does not do
computations on monomial ideals (except that it can draw them in three
dimensions). Gfan does output monomial ideals, which Frobby can then
process further.

It's funny - I had not explicitly thought about the fact that these
programs compliment each other well, despite my good friend Anders N.
Jensen (who is the author of Gfan) having been my office mate for a
year. It must be because most non-random ideals that I've been dealing
with have been produced by the program 4ti2.

Cheers
Bjarke

[William Stein]

I just want to point out quickly that we (=Sage devel community) also
have an interest in including 4ti2 in Sage at some point, if somebody were
to come along and do the integration work (hint, hint).

William