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Subject: Re: OASIS: Infix Operator "^"

• From: Andreas J Guelzow <aguelzow@math.concordia.ab.ca>
• To: Leonard Mada <discoleo@gmx.net>
• Date: Thu, 22 Feb 2007 13:14:48 -0700

```On Thu, 2007-22-02 at 21:09 +0200, Leonard Mada wrote:
> Chapter 6.3.5 of the OASIS OpenFormula document (version 2007-02-14)
> describes the Infix Operator (^).
>
> However, it contains a lot of mathematical ERRORS:

Considering that the document contains definitions there is no claim
that the terms match what others may define. Unfortunately there is a
significant discrepancy of the normal mathematical definitions and what
is used in spreadsheets.

In any case, OpenFormula describes the syntax used in a file. There is
no absolute requirement that this is what the user sees. As noted below,
Gnumeric includes aditional parentheses in case were precedence is
unexpected.

[Of course there is an issue here: in OOo ^ appears to be
left-associative while in Gnumeric it is right-associative.]
>
> 1. “^” is left-associative, not right-associative!!!

Wherever I look I find that ^ is indeed right-associative contrary to
your claim. Of course this does nean that =2^3^2 should return =2^(3^2)
= 512 not 64.

> Therefore: =2^3^2 should return =2^(3^2) = 512 and NOT 64 !!! The second
> "^" left associates with "3", so first "3" gets squared and thereafter
> the first "2" gets to the power 9.
>
> 2. The classic ERROR: -4^2
> Mathematically, this yields always -(4^2)=-16, NEVER +16!!!
> There is NO unary operator in mathematics that converts a number to its
> negative, like described in the documents.

This is utter nonsense. Of course there is such a unary operator. How
else is  - (x^2+1) to interpret. Pick any universal algebra text, look
for unary operators and you will likely find the negation operator as an
example.

Personally I don't care whether -4^2 in an odf file means (-4)^2 or
-(4^2) as long as the user is not exposed to -4^2 with the former
meaning. Unfortunately in Excel-land the -4^2 is interpreted as (-4)^2.

By the way, if you were right that there is no unary negation operator
that the only way to interpret -4^2 would be as the square of the
negative number -4 rather than the negation of the square of 4.

>  I would suggest consulting a
> dedicated mathematical program. As stated in issue
> http://www.openoffice.org/issues/show_bug.cgi?id=66735 on the OOo website:
> *Mathematica* v5.(x) returns -16
> *R* v2.4.0 returns -16
> other software (like Scilab, maxima, octave, as pointed in that Calc
> issue) report -16, too.
>
> gnumeric takes an interesting approach: it converts the first expression
> to =(-4)^2, which indeed is then +16. So, this last is mathematically
> correct and, at the same time, users who know a bit more about
> mathematics, recognize that gnumeric did NOT calculated what they
> expected. (it is transparent what has happened)
>
> Stating however, that -4^2 = +16 is plain wrong!!! And inventing various
> mathematical rules that break the old ones is really NOT good for a
> standard.

And inventing a syntax that break what historically has been done in the
field (in this case in spreadsheets) isn't good for a standard either.

Andreas

--

Prof. Dr. Andreas J. Guelzow
Dept. of Mathematical & Computing Sciences
Concordia University College of Alberta

```

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