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| * [[/PowerSeries]] -- separate precision from arithmetic, come up with applications that it will be used for: power series that converge in a particular p-adic disc. Modules over these rings. * [[/Factoring]] -- work on factoring of polynomials over local fields. * [[/Templates]] -- templates for elements of p-adic fields. * [[/SymbolicIntegration]] -- symbolic integration over p-adics. p-adic Igusa zeta functions. Get rational functions in a symbolic p. Look at Denef's webpage. * [[/LogarithmsForExt]] -- logarithms and exponentials for p-adic extension fields. * [[/FunctionFields]] -- Hess' automorphism algorithm for finding isomorphisms between function fields. |
* [[/PowerSeries|Power Series]] -- separate precision from arithmetic, come up with applications that it will be used for: power series that converge in a particular p-adic disc. Modules over these rings. * [[/Factoring|Factoring]] -- work on factoring of polynomials over local fields. * [[/Templates|Templates]] -- templates for elements of p-adic fields. * [[/SymbolicIntegration|Symbolic Integration]] -- symbolic integration over p-adics. p-adic Igusa zeta functions. Get rational functions in a symbolic p. Look at Denef's webpage. * [[/LogarithmsForExt|Logarithms and Exponentials]] -- logarithms and exponentials for p-adic extension fields. * [[/FunctionFields|]] -- Hess' automorphism algorithm for finding isomorphisms between function fields. |
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| * [[http://trac.sagemath.org/sage_trac/ticket/12545|Trac 12545: create highly optimized p-adic L-series implementation for various special cases]] (William Stein, Jennifer Balakrishnan, Mirella Cipierini) |
We'll be drawing our projects from the following sources.
The wiki page for enhancements to p-adics in Sage.
The list of open p-adic tickets on Trac.
- Computational projects proposed by participants on Sunday afternoon.
Sunday Project Proposals
Power Series -- separate precision from arithmetic, come up with applications that it will be used for: power series that converge in a particular p-adic disc. Modules over these rings.
Factoring -- work on factoring of polynomials over local fields.
Templates -- templates for elements of p-adic fields.
Symbolic Integration -- symbolic integration over p-adics. p-adic Igusa zeta functions. Get rational functions in a symbolic p. Look at Denef's webpage.
Logarithms and Exponentials -- logarithms and exponentials for p-adic extension fields.
/FunctionFields -- Hess' automorphism algorithm for finding isomorphisms between function fields.
/WittVectors -- Witt vectors over general rings.
/HilbertSymbols -- General Hilbert symbols for p-adic fields.
/Completions -- Completions of number fields.
/LinearAlgebra -- think. then implement.
Inversion -- Speed up inversion.
/PadicRootAlgorithm -- Implement Panayi's p-adic root finding algorithm.
Trac 12545: create highly optimized p-adic L-series implementation for various special cases (William Stein, Jennifer Balakrishnan, Mirella Cipierini)