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Re: How do I encode negative numbers in content MathML?

From: <juanrgonzaleza@canonicalscience.com>
Date: Fri, 19 May 2006 11:20:05 -0700 (PDT)
Message-ID: <3028.217.124.88.203.1148062805.squirrel@webmail.canonicalscience.com>
To: <www-math@w3.org>
Cc: <lroffey1@ix.netcom.com>

Leane Roffey wrote:
> You write: A possibility for elimination of brackets is working only
> 2-ary operators
> in postfix form. The code (a kind of infix LISP):
>
> [Y \= [plus [times a \* x] \+ b]]

Sorry it would be

[Y = [[a * x] + b]]

> can be expressed in a FORTH-like way
>
> a x * b + Y =
>
> But last expression is less readable than Lot of Irritant Silly
> Parentheses ;-)
> *****
>
> I've worked with FORTH (back when the earth was cooling).

Is that when Ace Age I movie? ;-)

> Less readable, perhaps, but if you were a FORTH user, they
> were a breath of fresh air.

I mean less readable for 80-90% people. How many RPN calculators do you
know ? 2%?

> I think you have a point here worth looking
> at. (perhaps issued from the Bureau of Silly Random Walks :-)  )
> Those work for simple expressions, there is no doubt.
>
> The whole question of "greenfield" issues, like encoding
> negative numbers often involves the assignment of multiple uses
> to the same physical character. As I've seen before on this
> forum, sometimes that's important to clarify, and other times it isn't.
>
> I recently consulted for a nationally known tutoring center as a
> mathematics specialist, and in examining the arithmetic for
> grades K-12, found that for some time now, the children are
> shown negative integers as the integer with a superscripted
>  "minus sign" either in front or back of the number. It varied
> by textbook.
>
>  When presented then, with expressions like "some positive
> number minus some negative number" or "some negative
> number minus some negative number" the resulting confusion
> was the stuff of legend. This concerned me because the
> ultimate goal of content MathML, in my applications, would be to be able
> to present interactive learning to any audience, integrating
> both correct representation of intent by the user and ensuring the
> answer would be correctly interpreted by any scripting compiler
> running the page by any browser anywhere. Richard has
> already pointed out the issues about browsers.

What issues?

> Documentation,
> for which both style and content would be important, for me, is
> vital. Short of representing any negative integer by the mirror
> image of its positive integer around zero, I can't think of any
> way around this difficulty offhand.

 - 1 = 0 - 1

"some positive number minus some negative number"

 a - (- b)

 a - (0 - b)

"some negative number minus some negative number"

 -a - (- b)

 (0 - a) - (0 - b)

> Your points on compilers are well-taken. They are tricky devils,
> depending on the language and how run-time oriented they are.
> I could wax for hours on the differences, but that would really
> be off topic for this thread.
>
> Leane
>
> Leane Roffey Line, Ph.D.
> Research Engineer
> www.bioelektronika.com
> Neuro Magnetic Systems
> San Antonio, TX 78209


Juan R.

Center for CANONICAL |SCIENCE)
Received on Friday, 19 May 2006 18:20:23 GMT

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