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Message-ID:  <539432A6.7030205@clear.net.nz>
Date:         Sun, 8 Jun 2014 21:53:42 +1200
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From: aparsloe <aparsloe@CLEAR.NET.NZ>
Subject: Juxtaposition in l3fp
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Status: R

Should l3fp use juxtaposition *at all* to indicate multiplication? I am 
an enthusiast for l3fp. I am using it constantly (in LyX using LyX's 
instant preview to evaluate formulas), but that has simply heightened my 
unease about using juxtaposition to indicate multiplication, 
particularly as part of a kernel package.

Most people using numbers have their mental reflexes shaped either by 
mathematical usage or calculator or spreadsheet usage. The last two, to 
my knowledge, don't allow juxtaposition. Multiplication must be 
explicitly indicated with an asterisk.

Mathematical usage is variable and often irregular but there is a 
certain core understanding. In a polynomial like 2x^3-5x^2-9 it is 
universally understood that the cubing and squaring applies only to the 
x, not the coefficients. In l3fp, however, because juxtaposition has the 
highest precedence, the coefficients are "glued" to the x so that it is 
2x that is cubed and 5x that is squared (e.g. on putting (2+3) for x). 
Usually the answers from "normal" and l3fp evaluation will be 
sufficiently different to alert one to the fact that something has gone 
wrong, but occasionally they will be "in the same ball park" and may 
lead to overlooking an error.

For instance scaling paper sizes or text blocks may lead one to seek the 
length of the diagonal of a rectangle, say the initial one with sides 
21cm and 29.7cm and a larger one with sides 1.2 times greater. What is 
the larger diagonal? By similarity, it is 1.2 times the length of the 
smaller diagonal. It is very easy to write 1.2(21^2+29.7^2)^.5 (with 
1.2\times\sqrt{21^2+29.7^2} in mind), evaluate it with fp and get 
39.85cm. This is wrong but not too obviously different from the correct 
43.65cm.

Juxtaposition also produces conflicts with established practice 
(calculators, spreadsheets) for function calls. Yes, sin2pi evaluates to 
0 as does sin(2pi), but sin(2pi)(2pi) = 0.978... does not, so that a 
function's argument is not delimited by parentheses, even when 
parentheses are used. That also breaks a long-established practice and 
seems like a source of error for the unwary.

I find myself now shunning juxtaposition and making a point of 
explicitly indicating multiplication with an asterisk, even in cases 
like 2*pi -- in other words making it a habit of mind precisely to avoid 
these "traps for the unwary". I imagine the juxtapositional horse has 
well and truly bolted, but I find myself wondering if it still might be 
possible to graft a strict "calculator front end" onto l3fp to align its 
operations with more familiar habits of mind?

Andrew Parsloe