[seqfan] Style sheet lacks much of anything on "vertical bar"
Robert Munafo
mrob27 at gmail.com
Wed Mar 27 00:00:21 CET 2024
No-one noticed on oeis.org/wiki/Talk:Style_Sheet therefore I now ask here.
Can we add to the "Spelling_and_notation" section of
oeis.org/wiki/Style_Sheet, to sanction more uses of the vertical bar
"|"?
I happen to have looked for precedent specifically of the form
"min_{a|b} {expression}" and ran across the lack of clarity on whether
"|" can be used apart from set cardinality.
Searching the OEIS I find that "|" has been used for the "divides"
relation 10 or more years ago, e.g. in the formula for A117498 we
find: "min_{d|n, 1<d<n} a(d)+a(n/d)".
In the OEIS, for a similarly long amount of time, the bar has also
been used often for "such that", e.g. name of A071893 "Min{k |
A071891(k)=n}".
I would recommend these uses, in no particular order, as most seem to
be already in common use, usually in an unambiguous way:
x|<expr> for "x divides an expression" (i.e. <expr>/x is an integer)
which could be a statement, or a set definition as when "written
below" Sigma or Pi or as a subscript to a function like "min"
x|<statement> for "x such that <statement>" as might be used in a
set definition "for all x such that...", or existence assertion e.g.
"there exists x such that"
|<expr>| for the absolute value of a scalar-valued expression or
field members for which something similar is well-defined
||<expr>|| for the norm of a vector-valued expression
|M| for the determinant of a matrix
|S| for the cardinality of a set S
and I would recommend against:
<expr>|<expr> for bitwise "or" as in some programming languages
<statement>||<statement> for boolean disjunction "or" as in some
programming languages
--
Robert Munafo, mrob27 at gmail.com
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