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Date:         Fri, 11 Jul 2014 20:27:01 +1200
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From: aparsloe <aparsloe@CLEAR.NET.NZ>
Subject: Re: Juxtaposition in l3fp
To: LATEX-L@LISTSERV.UNI-HEIDELBERG.DE
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Status: R

On 11/07/2014 11:20 a.m., Bruno Le Floch wrote:
> Hello list,
>
> Sorry for the >1 month delay.  This is a followup to the thread asking
> whether letting juxtaposition denote multiplication was a good idea.
> I think it was, but I made a big mistake in making juxtaposition be
> multiplication with a _different precedence_ than the asterisk.
...
> In l3fp, I pushed the idea to its extreme, allowing juxtaposition for
> things other than units, and I kept the precedence as being the
> tightest possible.
>
> As Lars rightfully says it's "consistent, but not necessarily
> intuitive".  Andrew has given several cases where my choice leads to a
> terrible behaviour for l3fp, and there is basically no case where the
> current behaviour is better (well, there was one abusive one: with
> this rule, exp.5ln(...) computes the square root, but now that is not
> needed).
Actually, I've found this "abuse" quite a handy device, and despite the 
introduction of the sqrt function to l3fp, for n-th roots, exp(1/n)ln 
has a certain convenience.
> I'm keen on leaving juxtaposition = multiplication, because that
> allows to use dimensionful numbers directly inside fp expressions (pt,
> in, ... are defined as floating point constants).  I believe that we
> should change the precedence of juxtaposition-as-multiplication from
> what it currently is (the tightest) to being the same as
> multiplication.  In other words, juxtaposition would behave exactly
> identically to adding an asterisk.
>
> Would that make sense?  Am I missing something crucial (probably... I
> didn't realize when allowing juxtaposition what a mess I was
> creating)?
>
> Best regards,
> Bruno
Thanks for the response Bruno (but "terrible" is a strong word). The 
suggested new precedence would certainly take care of the examples that 
tripped me up and that seemed like traps for the unwary.

There is one other precedence which troubles me a little. I read an 
expression like

  ln(1+1/n)^n

as 'raise (1+1/n) to the n-th power then take the logarithm' ( = 
n*ln(1+1/n) ). l3fp treats this as

  ( ln(1+1/n) )^n

I realise that in the absence of clarifying parentheses there is an 
inherent ambiguity in such forms which needs to be resolved in a fixed 
manner one way or the other. I question whether l3fp has chosen the 
intuitive way, or the way of customary practice. For instance we write 
("incorrectly" but the practice is universal) sin^2 x rather than sin 
x^2 when we want to square the sine of x, presumably because sin x^2 
suggests the sine of x^2. In short, should the precedence levels of 
function calls and raising to a power be interchanged? With your 
proposed change to juxtaposition's precedence, this would bring l3fp 
into line with customary "habits of mind".*

Andrew

* Well, my mind!