Re: math alphabets, WAS: Proprietary Card Decks

From: Philippe Verdy (
Date: Sun Apr 17 2011 - 18:29:05 CDT

  • Next message: Hans Aberg: "Re: math alphabets, WAS: Proprietary Card Decks"

    2011/4/15 Hans Aberg <>:
    > Parenthesizes can be semantic, for example f^(k) (f superscripted with (k)) might denote the n-th derivative, while f^k the n-th composite or power of f.
    Actually when *extra* parentheses are used in a superscript (i.e.
    parentheses that are not needed to correctly evaluate the value of the
    inner expression which is already self-contained by the superscript),
    this gives a different semantic to those parentheses, which are not
    used for their function of grouping, but to change the semantic into a
    n-th derivative.

    If you transcribe such expression into plain-text only, without
    support for superscripts/exponent, you usually use the "^" symbol, but
    then nothing can help make the distinction between grouping
    parentheses and nth-derivative, because the inner expression is no
    longer self-contained. The only way to preserve this, is to use extra
    parentheses (exactly like for the case when superscripts are
    available). So you should write: f^((n)).

    If you write f^(n) only, it's not clear if this is the n-th exponent
    or the n-th derivative of function f. This may be implicit in some
    contexts, but specifying such formula without expliciting this context
    will cause problems. Notably when both interpretations are used in the
    same text (n-th derivatives and n-th exponentiations are heavily used
    concurrently, for example when working with limited developments, or
    with convergence of series, in probabilities...)

    I've seen also f^('n), where the prime is denoted by some single quote
    or apostrophe at the beginning of the inner expression. This preserves
    the parentheses for their usual grouping-only meaning. If the inner
    expression is simple enough (such as a single number or variable name,
    you can even remove these parentheses and write f^'n directly. This
    also preserves the distinction with f'^n (which denotes the n-th
    exponent of the first derivative of function f, because the prime
    operator is left-associative only).

    I've also seen the even shorter notation f('n), without any ^ symbol
    which then remains reserved to exponentiation only. (I will leave out
    of this discussion the choice of the "correct" character to use for
    the prime symbol, but it you cannot use true superscripts, then you're
    also likely to use basic text encoding. Other notations like f^[n] or
    f^{n} may be found (sometimes without the ^ symbol as well), provided
    that square brackets and braces are not used as alternative grouping
    parentheses to help reading complex formulas with multiple nesting
    levels, or to denote vectors/matrices, or value ranges and sets, or to
    denote indices/subscripts for terms of series.


    This archive was generated by hypermail 2.1.5 : Sun Apr 17 2011 - 18:36:06 CDT