Progress on Mathemagix

1.What has been done

Basix

• Basic data types: symbols, lists, arrays, hash tables, etc.
• A system for generic objects.
• Parsers and pretty printers, together with a system for keeping track of locations in the source code and generating error messages.
• Important operators and categories for systematic use throughout the project.
• The Mathemagix glue facility, both for interpreters and functionality.

Mmxlight

• The basic interpreter: most control structures, declarations, function applications, loading files and dynamic libraries.
• A rudimentary type system with overloading, implicit conversion and a first form of genericity based on the generic type.
• An Emacs mode for Mathemagix.

Pack

• Remote libraries packaging for quick installation and easy update.

Gnumerix

• Interfaces with Gmp and Mpfr.
• Complexified numbers.
• Intervals and balls for certified arithmetic.
• Wrapper above intervals or balls for computable numbers.

Algebramix

• Vectors, matrices and dense polynomials.
• A start of modular arithmetic, algebraic numbers and quotient structures.
• Skew polynomials.
• Formal power series and a start of transseries and moulds.

Symbolix

• Basic arithmetic on symbolic expressions.
• Basic calculus: differentiation, substitution and an overly simple solver.

Analyzit

• Some first and improvable routines for numerical matrices and polynomials.
• Some basic utilities for holonomic functions.
• First slow version of analytic functions and analytic continuation.

More packages are to be found in the Mathemagix root directory

2.What has to be done

Basix

• Dispatch frequently used functions (addition, multiplication, etc.) from generic type.

Mmxlight

• Template types (as in an older version of the interpreter, which did not have generic types or implicit type conversion).
• User definable types and modules.
• Full exception system.
• Higher level constructs such as (limited) generators, continuations.
• Make the interpreter more efficient (byte-code?).
• Writing a compiler (already in progress).

Gnumerix

• More semantics and several types of semantics for interval and ball arithmetic.

Algebramix

• Asymptotically fast implementations for all basic operations on univariate (skew) polynomials.
• Several versions of fast multivariate polynomials.

Symbolix

• Basic differential and exterior calculus.
• Efficient manipulation of exp-log expressions and Risch' integration algorithm.
• Symbolic interfaces for standard data types, i.e. solve a differential equation using power series.

Analyzit

• Systematic implementation of numeric and certified versions of standard data types.
• Full library for holonomic and special functions.
• Progress on the subject of effective analytic continuation.

3.How to help

• Suscribe to the developers mailing lists and participate to the design of the language and the elaboration of good strategies for writing the compiler.
• Write interfaces for standard mathematical (or other) libraries.
• Help developing the standard libraries.
• Help us writing a compiler for Mathemagix.