AMOEBA: A Matlab Package for Visualizing Alegbraic Plane Curves Over non-Archimedean Complete Fields

This is a preliminary release of some code co-authored with my research assistant Zhigang Zhang. The output is in OOGL format for visualization by Geomview. More documentation will appear soon but in the mean time please feel free to pester Zhigang or myself.

• pamoeba.m: a Matlab program which takes input lists of coefficients and exponent vectors and computes the p-adic amoeba of the resulting algebraic plane curve over the p-adic complex numbers.
• polytran2v.m: a Matlab program which takes the coefficient vector of exponent matrix of a bivariate polynomial f and computes the corresponding data for f(x+1,y+1). (Useful for verifying my theorem that the number of p-adic complex roots close to unity admits an upper bound depending on just the number of exponent vectors.)
• lowhull2file.m: computes the lower hull of the p-adic Newton polytope of an input polynomial and places the output in a file in OOGL format, ready for viewing by Geomview.
• sub2file.m: converts the precomputed mixed subdivision information into an OOGL file.
• padicorder.m: a small utility for computing p-adic valuations.