Diff for "padicSageDays/Projects"

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.