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| These are project ideas for [[days15|Sage Days 15]]. | These are project ideas for [[days15|Sage Days 15]] == MSVC 2008 port of PARI-2.4.2.alpha0 == Do a port of PARI-2.4.2.alpha0 to MSVC 2008, including MPIR support. == Low Level Simplicial Sets, CW Complexes, and Morphisms for Simplicial Complexes and Chain Complexes == PEOPLE: S. Ault, B. Antieau * S. Ault has a CW Complex class up and running (including the chain_complex() method). The next step is to work on a homology_with_generators method within the ChainComplex (See trac #5882). * B. Antieau has simplicial complex morphisms, and has the functor to morphisms of chain complexes. * There are simplicial complex morphism and chain complex morphism classes, and there is a method on the former to produce and instance of the latter, including base rings, augmentation, chain v. cochain. * Working on various associated complexes of a map, like graph, mapping_{cone,cylinder,path_space}. * Working on fiber products. * Prepping for induced maps on homology, cohomology, ring structure on cohomology. |
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| PEOPLE: Fredrik Johansson | PEOPLE: Fredrik Johansson, William Stein, Robert Bradshaw |
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| PEOPLE: Christian, John Palmieri, S. Ault, Bob Bruner | |
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Stuff for the final report: * Installation problems on Mac OS X fixed * Defined SAGE framework for modules over the Steenrod algebra and created a first proof-of-concept implementation of some modules. == MinRes - Mininmal resolutions over the Steenrod algebra == PEOPLE: Bob Bruner, Christian Nassau, John Palmieri, David Roe * Create SAGE interface to Bruner's minimal resolutions package * * Package is general for mod 2 connected algebras, but currently only has support for mod 2 Steenrod algebra and the subalgebra <$Sq^1$, $Sq^2$, $Sq^4$> * Focus is on multiplicative structure: $Ext_A(M,M)$ as an algebra w.r.t. Yoneda product, and $Ext_A(M,N)$ and $Ext_A(N,M)$ modules over it. Accomplished this week: * Crude Steenrod algebra as vector space datatype and interface to module creation and minimal resolution calculation * Results integrated into Yacop's GUI and database manager. Still to do: * Integrate crude datatype into better Steenrod module datatype * Implement MinRes's FP module datatype * Implement chain maps (MinRes can lift an arbitrary cocycle - from this the multiplicative structure is evident, including Toda brackets) * Create spectral sequence datatype to accept Ext algebras and modules as inputs, and differentials (calculated using Bruner's thesis in case of H_\infty ring spectra) (lazy evaluation essential here) and use algebra structure to extend and explore consequences. == Quaternion Algebras (implement odd power of p dividing level case) == PEOPLE: Alia Hamieh, Jerome Lefebvre, William Stein. * working on it. == Sage/Magma Comparison Audit == PEOPLE: William Stein, Bill Hart, Robert Bradshaw, Alia Hamieh, Jerome Lefebvre. * See [[sagebeatsmagma]] and [[magma]] * Alia compared all of the functionality in both quadratic forms package and algebraic geometry package. She also has implemented an algorithm to be included in the binary quadratic form package. * Jerome has done so for representation theory and is working on improving the group algebra in sage. And we are both done with comparing. And we have both submitted the changes we wanted to make on this. == CANCELLED (already in Sage!) Generalized Bernoulli Numbers == PEOPLE: William Stein * There is a simple 2 or 3 line formula for generalized Bernoulli numbers in terms of non-generalized ones, which could be used to speed up the chi.bernoulli_number(k) command (for a Dirichlet character chi) by a factor of thousands. * [[:/bern:|more details]] == Cylindrical Algebraic Decomposition == PEOPLE: Carl Witty == Pynac Integration == PEOPLE: Mike Hansen, William Stein, Robert Bradshaw, Carl Witty == Sparse Linear Algebra == PEOPLE: Bill Hart, S. Ault == Javascript Graph Editor == PEOPLE: Rob Beezer, Mike Hansen, David Roe, Nicolas Thiery == eMPIRe Projects == PEOPLE: Bill Hart == Category Patches == PEOPLE: Nicolas Thiery, Robert Bradshaw, Mike Hansen, Craig Citro, Carl Witty == Notebook Work == PEOPLE: Mike Hansen, (William Stein), Tom Boothby == Latex for (Combinatorial) Graphs == PEOPLE: Rob Beezer, Fidel Barrera, John Palmieri, Emily Kirkman [[attachment:view-graphs.png|Screenshot]] [[http://trac.sagemath.org/sage_trac/ticket/5975|Details at #5975]] == Wrap mpmath == PEOPLE: Fredrik Johansson == p-adic Integration == PEOPLE: Robert Bradshaw, Kiran Kedlaya * Prepared patches to address bugs in tickets 5947, 5948; see [[http://trac.sagemath.org/sage_trac/ticket/5948|trac 5948]]. These have been reviewed by Jen Balakrishnan. * Prepared patch to address ticket 5430; see [[http://trac.sagemath.org/sage_trac/ticket/5430|trac 5430]]. == p-adic Polynomials == PEOPLE: Kiran Kedlaya, David Roe * David is preparing a large patch at [[http://trac.sagemath.org/sage_trac/ticket/6048|trac 6048]] to restructure p-adic polynomials. Besides adding new functionality, this should fix several previously reported bugs; once this is in, we should check [[http://trac.sagemath.org/sage_trac/ticket/1210|1210]], [[http://trac.sagemath.org/sage_trac/ticket/2943|2943]], [[http://trac.sagemath.org/sage_trac/ticket/4656|4656]], [[http://trac.sagemath.org/sage_trac/ticket/5075|5075]], and maybe some others. |
Sage Days 15 Project Ideas
These are project ideas for Sage Days 15
MSVC 2008 port of PARI-2.4.2.alpha0
- Do a port of PARI-2.4.2.alpha0 to MSVC 2008, including MPIR support.
Low Level Simplicial Sets, CW Complexes, and Morphisms for Simplicial Complexes and Chain Complexes
PEOPLE: S. Ault, B. Antieau
S. Ault has a CW Complex class up and running (including the chain_complex() method). The next step is to work on a homology_with_generators method within the ChainComplex (See trac #5882).
- B. Antieau has simplicial complex morphisms, and has the functor to morphisms of chain complexes.
- There are simplicial complex morphism and chain complex morphism classes, and there is a method on the former to produce and instance of the latter, including base rings, augmentation, chain v. cochain.
- Working on various associated complexes of a map, like graph, mapping_{cone,cylinder,path_space}.
- Working on fiber products.
- Prepping for induced maps on homology, cohomology, ring structure on cohomology.
Prime Pi
PEOPLE: Fredrik Johansson, William Stein, Robert Bradshaw
- Investigate implementing the Meissel, Lehmer, Lagarias, Miller, Odlyzko for computing the number of primes up to x.
Steenrod Algebra cohomology (Yacop integration)
PEOPLE: Christian, John Palmieri, S. Ault, Bob Bruner
A first version is already available. Here's a page with installation instructions: Yacop
Stuff for the final report:
- Installation problems on Mac OS X fixed
- Defined SAGE framework for modules over the Steenrod algebra and created a first proof-of-concept implementation of some modules.
MinRes - Mininmal resolutions over the Steenrod algebra
PEOPLE: Bob Bruner, Christian Nassau, John Palmieri, David Roe
- Create SAGE interface to Bruner's minimal resolutions package *
- Package is general for mod 2 connected algebras, but currently only has
support for mod 2 Steenrod algebra and the subalgebra <Sq^1, Sq^2, Sq^4>
Focus is on multiplicative structure: Ext_A(M,M) as an algebra w.r.t. Yoneda
product, and Ext_A(M,N) and Ext_A(N,M) modules over it.
Accomplished this week:
- Crude Steenrod algebra as vector space datatype and interface to module creation and
- minimal resolution calculation
- Results integrated into Yacop's GUI and database manager.
Still to do:
- Integrate crude datatype into better Steenrod module datatype
Implement MinRes's FP module datatype
Implement chain maps (MinRes can lift an arbitrary cocycle - from this the multiplicative
- structure is evident, including Toda brackets)
- Create spectral sequence datatype to accept Ext algebras and modules as inputs, and
- differentials (calculated using Bruner's thesis in case of H_\infty ring spectra) (lazy evaluation essential here) and use algebra structure to extend and explore consequences.
Quaternion Algebras (implement odd power of p dividing level case)
PEOPLE: Alia Hamieh, Jerome Lefebvre, William Stein.
- working on it.
Sage/Magma Comparison Audit
PEOPLE: William Stein, Bill Hart, Robert Bradshaw, Alia Hamieh, Jerome Lefebvre.
See sagebeatsmagma and magma
- Alia compared all of the functionality in both quadratic forms package and algebraic geometry package. She also has implemented an algorithm to be included in the binary quadratic form package.
- Jerome has done so for representation theory and is working on improving the group algebra in sage.
And we are both done with comparing. And we have both submitted the changes we wanted to make on this.
CANCELLED (already in Sage!) Generalized Bernoulli Numbers
PEOPLE: William Stein
- There is a simple 2 or 3 line formula for generalized Bernoulli numbers in terms of non-generalized ones, which could be used to speed up the chi.bernoulli_number(k) command (for a Dirichlet character chi) by a factor of thousands.
Cylindrical Algebraic Decomposition
PEOPLE: Carl Witty
Pynac Integration
PEOPLE: Mike Hansen, William Stein, Robert Bradshaw, Carl Witty
Sparse Linear Algebra
PEOPLE: Bill Hart, S. Ault
Javascript Graph Editor
PEOPLE: Rob Beezer, Mike Hansen, David Roe, Nicolas Thiery
eMPIRe Projects
PEOPLE: Bill Hart
Category Patches
PEOPLE: Nicolas Thiery, Robert Bradshaw, Mike Hansen, Craig Citro, Carl Witty
Notebook Work
PEOPLE: Mike Hansen, (William Stein), Tom Boothby
Latex for (Combinatorial) Graphs
PEOPLE: Rob Beezer, Fidel Barrera, John Palmieri, Emily Kirkman
Wrap mpmath
PEOPLE: Fredrik Johansson
p-adic Integration
PEOPLE: Robert Bradshaw, Kiran Kedlaya
Prepared patches to address bugs in tickets 5947, 5948; see trac 5948. These have been reviewed by Jen Balakrishnan.
Prepared patch to address ticket 5430; see trac 5430.
p-adic Polynomials
PEOPLE: Kiran Kedlaya, David Roe