Second Singular GAP developers meeting (Kaiserslautern)

The second Singular-GAP developers meeting, 14-18.11.2011, Kaiserslautern

Welcome to the second Singular-GAP developers meeting in Kaiserslautern.

Starting from Tuesday we will meet in room number 419, building 48.

Sponsored by:

SPP-1489: Algorithmic and experimental methods in algebra, geometry and number theory

Participants:

• Mohamed Barakat (University of Kaiserslautern) -- Customer #1
• Reimer Behrends (University of St Andrews)
• Christian Eder (University of Kaiserslautern)
• Max Horn (Braunschweig University)
• Olexandr Konovalov (University of St Andrews)
• Martin Lee (University of Kaiserslautern)
• Frank Lübeck (RWTH Aachen University)
• Oleksandr Motsak (University of Kaiserslautern)
• Max Neunhöffer (University of St Andrews)
• Hans Schönemann (University of Kaiserslautern)
• Andreas Steenpaß (University of Kaiserslautern)

Development

This is to describe the current state of affairs of the GAP package libsingular.

What works?

• Compile libsingular and the GAP package, run GAP, load the package.
• The two memory management schemes coexist peacefully within the same process.
• Call the Singular interpreter from GAP giving it a string to evaluate. (Singular output is collected in a string).
• Read variables in the Singular interpreter and return their values to GAP. (For the moment, integers, intvecs, intmats and strings are supported).
• Define a singular polynomial ring from GAP, access its indeterminates. (The ring is represented by a GAP object which references the Singular object.)
• Define monomials in that ring. (Polynomials are represented by GAP objects which reference the Singular object.)
• Add and multiply polynomials, multiply polynomials with scalars.
• Transform a singular polynomial to a string.

What does not yet work?

• Handling of errors occurring in the Singular interpreter
• Writing to Singular variables from GAP
• Polynomial rings with monomial ordering (no fundamental problem visible, just not yet implemented)
• Other Singular data types represented by GAP objects
• More arithmetic operations for polynomials
• There are not yet nice methods installed in GAP using + and * for polynomials.
• Lots more...

Questions (to be discussed next week):

• How to handle errors occurring in the Singular interpreter?
• What Singular data types are to be represented in GAP, for example, do we need "number" or do we use GAP's numbers instead?
• Is the "current ring" issue in Singular addressed properly?
• Does the memory management actually work when stressed?
• Are there possible memory leaks?
• Do we have any performance issues?

Future directions:

• Provide everything Mohamed needs for homalg using the integrated libsingular (update: as external rings -- works!).
• Implement access to more of Singular's features.
• Make sure that it is viable to implement higher level algorithms in the GAP language using libsingular objects.
• Integration of the Singular objects in GAP's object zoo.

What to do this week?

• Discuss the above questions and possibly others.
• Discuss the future directions.
• Solve technical problems.
• Move on with the implementation.
• Discuss libsingular with a view to the upcoming parallelized GAP (HPCGAP).

Program for the week:

• Plan the future development
  • give an overview of what already works (Max N.)
  • discuss error handling in Singular (Max N. + Hans)
  • homalg's external wish list (short) (Mohamed) -> works!
  • homalg's internal wish list (long) (Mohamed)
  • which Singular objects make sense in GAP, all?
  • stress tests
  • integration of Singular objects
  • interpret Singular libraries in GAP (example: groebner)
• Parallelization!!!
  • Reimer gave a wonderful talk. Thanks Reimer.

Sources

• hg clone ssh://[email protected]/libsingular
  For this to work please send Max N. your ssh-public key: Max Neunhöffer [email protected]

• ftp://ftp.gap-system.org/pub/gap/gap45/beta/gap4r5p2_2011_11_06-15_33.zip

Further Github wikis

Singular: How to contribute