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Lush is a Lisp dialect with extensions for object-oriented and array-oriented programming. Lush is intended for prototyping numerically intensive applications and is designed for easy integration of existing C/C++/Fortran codes.
A Portable General-Purpose Computer Algebra System
...Since then, many scientists from all over the world have contributed to its development. REDUCE has a long and distinguished place in the history of computer algebra systems. Other systems that address some of the same issues but sometimes with rather different emphasis are Axiom, Derive, Macsyma (Maxima), Maple, Mathematica and MuPAD.
REDUCE primarily runs on either Portable Standard Lisp (PSL) or Codemist Standard Lisp (CSL), both of which are included in the SourceForge distribution. By modern standards, REDUCE is a surprisingly small and compact application, which runs well on all major operatingsystems.
Axiom is a computer algebra system. It consists of an interpreter,
a compiler and a library of algorithms. Axiom is an excellent research
platform as well as a useful tool for scientific programming.
CLISP is a portable ANSI Common Lisp implementation and development environment by Bruno Haible. Interpreter, compiler, debugger, CLOS, MOP, FFI, Unicode, sockets, CLX. UI in English, German, French, Spanish, Dutch, Russian, and Danish.
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MatLisp is a package for Common Lisp for handling matrices with real-valued or complex-valued elements. BLAS is used for elementary matrix operations and LAPACK is used for linear algebra routines.
FrAid(FRactal AID) is an interface to Java, allowing it to proc. math. data(functions/equations). A compl. standalone system utilizing the FrAid prog. lang. is available(no need to be Java programmer to use it!). Use instead of Matlab. High res. graphics