OpenAxiom: The Open Scientific Computation Platform

1. Base Reference Document

OpenAxiom is a descendent of the AXIOM computer algebra system as described by Richard Jenks and Robert Sutor in AXIOM: The Scientific Computation System. That book is the base reference document for OpenAxiom.

2. Changes From The Base Document

2.1. OpenAxiom-1.4.0

This release introduces the following changes from the base document

2.1.1 Interpreter

2.1.2. Compiler

The compiler now accepts interpreter-style unnamed functions.
The compiler now generate far better (Lisp) codes for Spad libraries or scripts. The compiler now applies more aggressive (but sound) optimizations, including domain inlining, type propagations.
The compiler now accepts interpreter-style unnamed functions.
Parameterized macros are now supported by the compiler.
The compiler now support exception handling. In particular, the try/finally programming construct was added to support reliable resource management (e.g. opening/closing or creating/removing files.)

2.1.3. Algebra

In addition to novelties in OpenAxiom-1.3.0, the following types have been added to OpenAxiom-1.4.0:

The category BooleanLogic has been added. It is now extended by PropositionalLogic and BitAggregate. The domain SingleInteger now satisfies BooleanLogic.
It it now possible to obtain the string representation of a DoubleFloat value. The function
```
           string: DoubleFloat -> %
       
```
was added to the domain String
A function matrix is now exported by the category MatrixCategory to allow construction of matrices whose entries can be succinctely described by a function. For instance, the 4-by-4 Hilbert matrix may be expressed as
```
           m: Matrix Fraction Integer := matrix(4,4,(i,j) +-> 1/(i+j))
       
```
Note that the third argument is a function that computes the value of the (i,j)th entry.
The category StringCategory was removed as it was essentially redundant with the category StringAggregate.
The category MappingCategory is now part of the algebra as a builtin category constructor.

The following operators

           less?: (%,NonNegativeInteger) -> Boolean
           more?: (%,NonNegativeInteger) -> Boolean
           size?: (%,NonNegativeInteger) -> Boolean

have been moved from the category Aggregate to StreamAggregate where they seem more appropriate.

The domain InnerTaylorSeries now satisfies the category BiModule.
The domains FreeModule and OrderedFreeMonoid now satisfy the newly added FreeMonoidCategory.
The list of domains for OpenAxiom program manipulation has been expanded.
Support for range and segment bindings now includes RangeBinding.

2.1.4. Boot

Boot, the programming language used to write the OpenAxiom compiler, has been vastly improved. Lisp codes are being phased out.