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Topic: Mathematica and Lisp
Replies: 16   Last Post: Mar 7, 2013 3:58 AM

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Richard Fateman

Posts: 1,404
Registered: 12/7/04
Re: Mathematica and Lisp
Posted: Mar 7, 2013 3:58 AM
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On 3/6/2013 3:04 AM, David Bailey wrote:
<snip ... Fateman advocates preference for FullForm for some uses>
>
> So perhaps we should extend your principle to maths itself? Why risk
> students getting confused about the meaning of a + b c + d or f(a+b)-
> better to teach students to use a notation equivalent to FullForm!


This happens, to some extent, already. Students are advised to use
parentheses to try to limit ambiguity. I've seen power(x,y) instead
of x^y if x and especially y are long strings. Most mathematical
functions are probably parenthesized prefix, eg sin cos tan atan sinh
cosh.... There are a few where delimiters are kind of built in because
they are underlines or overlines like complex conjugate or
fractions. It is only
in the case of + and * that infix becomes so prevalent. Mathematica
of course makes a hash of this because sin(x) is a multiplication.

But in any case it is a false impression that mathematics beyond
(say) high-school level is presented in unambiguous formats.

This
> principle would be even more useful when they got to calculus, where
> notations like dy/dx and integrals are hopelessly ambiguous in that the
> terminating dx looks superficially as if it could commute with the
> integrand!


Actually this is not the problem, because context is a very big
help, and we know that dy/dx is not the same as (d*y)/(d*x). After
all, the d's would cancel producing y/x.
The real problem in integral tables and such is the REST of the
integral representation. You will see sin n x or x/ 2 pi .


These notations probably often encourage students to perform
> invalid manipulations - but even so, most people value them!

Not the students. It is just another burden on them. Like the
people who try to enrich the calculus courses with (say) Mathematica.
The majority of students, according to surveys, do not view it
as enrichment but merely another thing to learn. But that is
another story.

>
> I guess Mathematicians themselves realised why operator notation is so
> useful a long time back. It reduces the clutter and helps people to
> concentrate on what matters. Ultimately the choice between FullForm and
> operator form is a psychological question - not a math or computer
> science one. Those of us who do a lot of programming, also value
> operators that assist with that task too.


The nice thing about programming is that it gives you the opportunity
to name and re-use things like functions and subroutines. It allows you
to do this to essentially arbitrary depth. Hence "Solve" does whatever
it does, but you only have to remember one name. Mathematics allows
you to do this, but you must keep the notation either on paper or in
your head, and it is not usually "in the computer". In either case
the use of appropriate notation helps, and some would say is essential
in progress.
That does not mean that all notation is good. Some notation
increases the mental burden and may even increase the clutter. I have
read papers that advance the art and science not one millimeter, but
do nothing but lay claim to definitions and notations. Some editors
mistakenly view this as progress.
>
> The Mathematica language offers users a lot of choice - which you seem
> to abhor because some people don't choose to use it your way!


No, I have no problem in people making choices. I complain that the
design of the programming language EF is poor, at least in places. It
encourages incorrect choices (bugs) and the production of
unnecessarily difficult-to-read programs. Again I remind you that
I am talking about EF, not the library of
tools (like Solve).

RJF

>
> David Bailey
> http://www.dbaileyconsultancy.co.uk
>
>
>






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