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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. * [[/WittVectors]] -- Witt vectors over general rings. * [[/HilbertSymbols]] -- General Hilbert symbols for p-adic fields. * [[/Completions]] -- Completions of number fields. * [[/LinearAlgebra]] -- think. then implement. |
* [[/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|Function Fields]] -- Hess' automorphism algorithm for finding isomorphisms between function fields. * [[/WittVectors|Witt Vectors]] -- Witt vectors over general rings. * [[/HilbertSymbols|Hilbert symbols]] -- General Hilbert symbols for p-adic fields. * [[/Completions|Completions]] -- Completions of number fields. * [[/LinearAlgebra|Linear Algebra]] -- think. then implement. * [[/Inversion|Inversion]] -- Speed up inversion. * [[/PadicRootAlgorithm|Panayi's root finding algorithm]] -- Implement Panayi's p-adic root finding algorithm. * [[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) * [[http://trac.sagemath.org/sage_trac/ticket/812|Trac 812: p-adic L-series via overconvergent modular symbols]] (William Stein, Jennifer Balakrishnan) * [[/BugSquash|Report and fix bugs in the p-adics]] -- some of our funding comes from this objective. |
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.
Function Fields -- Hess' automorphism algorithm for finding isomorphisms between function fields.
Witt Vectors -- Witt vectors over general rings.
Hilbert symbols -- General Hilbert symbols for p-adic fields.
Completions -- Completions of number fields.
Linear Algebra -- think. then implement.
Inversion -- Speed up inversion.
Panayi's root finding algorithm -- 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)
Trac 812: p-adic L-series via overconvergent modular symbols (William Stein, Jennifer Balakrishnan)
Report and fix bugs in the p-adics -- some of our funding comes from this objective.