## [REBOL] Matrix Arithmetic Rules? Help needed!

### From: robbo1mark:aol at: 10-Jan-2002 12:57

After reading Joel Neely's most recent excellent article on REBOL forces on Iterators, Recursion & Algebra, I hit upon the idea of expanding the REBOL arithmetic & logic functions to handle series & matrix arguments as well as their current scalar arguments. There's a little bit synchronicity here as I've recently been reading & studying Kenneth Iverson's "J" programming language which is a dialect of APL, surely one of the wierdest notations yet with the some of the most powerful built-in functions for computing maths expressions in any programming language that I've seen. Anyway, I would like to redefine the prefix REBOL arithmetic & logic functions to be able to handle series & matrix arguments as well as scalar arguments, trouble is I can't figure out all the correct "RULES" for series & matrix operations and Iam looking for HELP from list members to design correct behaviour & optimal functions. Here's some examples of what I would like to be able to say in REBOL.>> add 1 [2 3]== [3 4]>> add [2 3] [2 3]== [4 6]>> multiply 2 [2 3]== [4 6]>> multiply [2 3] [2 3]== [4 9]>> subtract 1 [2 3]== [-1 -2]>> subtract [2 3] 1== [1 2]>> subtract [4 5] [2 3]== [2 2]>> divide 12 [2 3]== [6 4]>> divide [36 24] 12== [3 2]>> greater? 4 [3 5]== [true false]>> equal? 4 [3 4 5]== [false true false]>> equal? [2 3 4] [2 4 6]== [true false false] I'm sure you get the picture of what I mean here and to be honest these funcs are pretty trivial examples of what Iam looking for and can be coded quite easily. MY PROBLEM / QUERY are these Firstly What is the correct behavior of performing arithmetic and logic functions on arbitarily nested blocks, ie matrixes, and secondly what is the correct behaviour when series or matrix are of differing lengths, ie missing arguments. Here's some examples of what I mean, how should these evaluate?>> multiply [2 3] [3 4 5]== ????>> add [2 3] [3 4 5]== ????>> add [2 3] [3 [4 [5]]]== ????>> greater? [2 3 4] [2 1]== ????>> equal? [2 [3 4]] [[2 3] 4]== ????>> subtract [3 4 5] [2 2 2 2]== ???? Even these are fairly trivial examples of problems compared to some deeply nested matrix or huge series operations you could imagine. Rules I have ascertained are these; 1. If any argument is a series! then the result is a series! 2. If one arg is a scalar and the other arg is a series then the function applies the operation on the scalar to each value in the series resulting in a series!. Please help me to flesh out these rules / logic and point out any flaws or mistakes you can see in my examples, and also if your willing to help design these functions and their attributes. Anybody interested? Joel, Ladislav, Larry........? thanks, Mark Dickson