Re: Seriation

On 03/02/2025 09:00, David Entwistle wrote:

On Sun, 2 Feb 2025 10:06:03 -0000 (UTC), David Entwistle wrote:
 

I did have a bit of trouble with SCOS, not because it was hard to
decrypt,
but my implementation wasn't... There's a word, but I'm not sure what it
is... When you perform an operation on a set, the result of that
operation is should be guaranteed to belong to the same original set,
but in my case it wasn't. So in this case, when encrypting and
decrypting occasionally, due to some odd punctuation mark, or an
accented character, the result would lie outside the reasonable bounds
of characters. The web, which I often use as a source of plain text, is
full of such characters. That was my problem, not a problem with SCOS,
but it did cause me some grief.

 "Closure: In mathematics, a subset of a given set is closed under an
operation of the larger set if performing that operation on members of the
subset always produces a member of that subset".
 So, should an encryption / decryption operation always be closed? Maybe
SCOS was closed, but I think it would depend how you defined the full
character set and that may have to be quite wide.

In a sense, SCOS's character set is defined by these four lines:
#define UPPER "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
#define LOWER "abcdefghijklmnopqrstuvwxyz"
#define DIGIT "0123456789"
#define PUNCT "!\"$%^&*()_-+={}[]#~'@;:/?.>,<\|"
which isn't particularly wide, but any encryption of any of those characters will *always* produce a character drawn from the same set. When faced with something *not* from that set, SCOS leaves it unchanged. So I think I'm right in saying that by the above definition SCOS /is/ closed.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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