TORRIX and SPARSE

[Remington Furman]

Hi Jose,

This is very interesting.  I've only read the first dozen pages of 
TORRIX 1 and section 2.1, but it looks useful for doing finite field 
math for error-correcting codes, etc.

Error correcting codes were my introduction to abstract algebra, and 
it's cool to see such an early system based on abstract algebra 
foundations.  Few modern languages are as advanced.  It's compelling 
that they chose Algol68 for this.

(Of course, part of the appeal of GF(2) is that standard bit-wise 
operators suffice to implement it, so it can be done with simpler tools.)

This past year I've been studying and using the J programming language 
(a descendant of APL), and now I'm curious how TORRIX compares to APL 
and the array language family.

The TORRIX 1 bibliography does cite "{10} IVERSON, K.E., A programming 
language, John Wiley & Sons, New York, 1962", but I haven't found 
references in the text yet.

Thanks for sharing.

-Remington

On 5/1/26 2:41 PM, Jose E. Marchesi wrote:
> Hello.
>
> As mentioned in the meetup call, these are the two TORRIX
> articles/books:
>
>    TORRIX 1: A programming system for operations on vectors and matrices
>              over arbitrary fields and of variable size
>              - By S.G. van der Meulen and M. Veldhorst
>
>              https://jemarch.net/torrix-1.pdf
>
>    TORRIX 2: An analysis of sparse matrix storage schemes
>              - By M. Veldhorst
>
>              https://jemarch.net/torrix-2.pdf
>
>
> The first torrix is a system written in Algol68 that provides Vec and
> Mat modes, for "vector" and "matrix" respectively, which are
> variable-sized in the sense they are "total" arrays/matrices, i.e. they
> conceptually expand in all directions to infinite, containing zeroes.
>
> I have transcribed and ported Torrix to ga68.  It compiles.  I cannot
> publish it until I clarify the copyright with the CWI though.
>
> The second torrix book (SPARSE) studies the efficient storage of sparse
> torrix Matrices, i.e. in which there are many zeroed areas.  It develops
> storage algorithms.  In principle our Torrix implementation could be
> expanded with it.  The mode it provides is Rowmat, and some others.
>
> Salud!