Magma

Magma is a computer algebra system. But unlike other systems, Magma treats algebraic structures in a mathematically rigorous way, so that you can make groups, rings, modules, fields, etc., and do efficient computations on those mathematical structures. My recent researches are all helped by extensive concrete computational experiments using Magma. The following are some Magma packages that I built during these experiments.

• Continued Fractions of Rational Functions: This Magma package adds a single intrinsic "ContineudFractionLinearTransform(s)". This implements the algorithm described in detail in my paper "Continued Fractions for Linear Fractional Transformations of Power Series". [Package] [Example]
• Minimal Polynomial Synthesis of Finite Sequences: This Magma package adds three intrinsics "EuclideanMPS(s)", "IterativeMPS(s)", and "IterativeMPSforDecoder(s)". These implement the algorithms described in my paper "Minimal Polynomial Synthesis of Finite Sequences". [Package] [Example]