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Topic: Work on Basic Mathematica Stephen!
Replies: 81   Last Post: Jun 4, 2013 5:59 AM

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David Bailey

Posts: 712
Registered: 11/7/08
Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Posted: May 31, 2013 3:19 AM
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On 28/05/2013 08:49, Richard Fateman wrote:
>
> I do not see any connection here. It is possible to write a linked list
> in Mathematica and still use its evaluation. e.g.
> consider using node[element,RestOfList]. Instead of [A,B,C] use
> node[A,node[B,node[C,Nil]]]. A node here is like a lisp "cons" cell.
> In fact there are other computer algebra systems written in lisp that
> use lisp lists and have similar evaluation strategies to Mathematica.
>


Yes you could, and you might find it instructive to do this, because you
would then see exactly why Stephen Wolfram chose to implement lists in a
different way!

Try using your implementation to implement some 1000 x 1000 matrix algebra!

OK - perhaps you wouldn't want to use your new list implementation for
linear algebra, but in that case, where would you want to use it? Lisp
lists are expensive to use unless the algorithm is tailored to generate
lists in reverse order, and consume them in forward order (OK you can
reverse a Lisp list, but that consumes space for a copy, but random
access is still inefficient).

Since the Lisp language was designed very early on, I would imagine its
list structure reflects the tiny memory spaces available at that time.
Garbage collection of varying sized objects is more complex and tends to
need some slack memory.

The decision to implement lists the Mathematica way, has been amply
vindicated in recent years. Because the mechanisms supplied to access
lists are not skewed towards sequential access, it has been possible to
produce packed arrays (and indeed sparse arrays) that work as drop in
replacements for the equivalent list structures - with enormous
performance gains.

Mathematica also gains from the decision to make lists mutable - again
this simplifies the design of algorithms and increases performance.

Clearly Mathematica lists also score in they must help internally to
avoid repeated evaluation. Clearly Mathematica must store some
information in the head of every object to keep track of objects that
need reevaluation, and you wouldn't want each list node to be bloated
out in that way.

Yes you could implement Lisp-style lists in Mathematica, and with a bit
more effort, you could also supply them with a nice syntax for
input/output, so try it and see how many people find them useful!

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





Date Subject Author
5/12/13
Read Work on Basic Mathematica Stephen!
David Park
5/13/13
Read Re: Work on Basic Mathematica Stephen!
psycho_dad
5/13/13
Read Re: Work on Basic Mathematica Stephen!
psycho_dad
5/14/13
Read Re: Work on Basic Mathematica Stephen!
Nasser Abbasi
5/15/13
Read Re: Work on Basic Mathematica Stephen!
szhorvat@gmail.com
5/16/13
Read Re: Work on Basic Mathematica Stephen!
szhorvat@gmail.com
5/16/13
Read Re: Work on Basic Mathematica Stephen!
Dr. Peter Klamser
5/17/13
Read Re: Work on Basic Mathematica Stephen!
Andrzej Kozlowski
5/17/13
Read Re: Work on Basic Mathematica Stephen!
Murray Eisenberg
5/17/13
Read Re: Work on Basic Mathematica Stephen!
Dr. Peter Klamser
5/18/13
Read Re: Work on Basic Mathematica Stephen!
Dr. Peter Klamser
5/19/13
Read Re: Work on Basic Mathematica Stephen!
Murray Eisenberg
5/19/13
Read Re: Work on Basic Mathematica Stephen!
paulmchale7@gmail.com
5/19/13
Read Re: Work on Basic Mathematica Stephen!
paulmchale7@gmail.com
5/23/13
Read Re: Work on Basic Mathematica Stephen!
szhorvat@gmail.com
5/24/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/20/13
Read Re: Work on Basic Mathematica Stephen!
Ingolf Dahl
5/20/13
Read Re: Work on Basic Mathematica Stephen!
David Annetts
5/22/13
Read Re: Work on Basic Mathematica Stephen!
mathgroup
5/23/13
Read expanding the use of symbolic computation in engineering .. was Re:
Richard Fateman
5/24/13
Read Re: expanding the use of symbolic computation in engineering .. was Re:
W. Craig Carter
5/23/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/23/13
Read Re: Work on Basic Mathematica Stephen!
mathgroup
5/24/13
Read Re: Work on Basic Mathematica Stephen!
Richard Fateman
5/25/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/25/13
Read Re: Work on Basic Mathematica Stephen!
Richard Fateman
5/25/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/28/13
Read Re: Work on Basic Mathematica Stephen!
Alexei Boulbitch
5/28/13
Read Re: Work on Basic Mathematica Stephen!
Alexei Boulbitch
6/4/13
Read Re: Work on Basic Mathematica Stephen!
Bill Rowe
5/24/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/27/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Noqsi
5/28/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Richard Fateman
5/31/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
David Bailey
6/1/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Richard Fateman
6/2/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
David Bailey
6/3/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Richard Fateman
6/3/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
David Bailey
6/4/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Andrzej Kozlowski
5/29/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
fd
5/30/13
Read Applying Mathematica to practical problems
Noqsi
5/31/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
5/31/13
Read Re: Applying Mathematica to practical problems
Kevin J. McCann
5/31/13
Read Re: Applying Mathematica to practical problems
Andrzej Kozlowski
6/1/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
6/1/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
6/2/13
Read Re: Applying Mathematica to practical problems
Andrzej Kozlowski
6/3/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
6/3/13
Read Re: Applying Mathematica to practical problems
Andrzej Kozlowski
6/1/13
Read Mathematica numerics and... Re: Applying Mathematica to practical problems
Daniel Lichtblau
6/2/13
Read Interval vs default, was Re: Mathematica numerics and... Re: Applying
Richard Fateman
6/2/13
Read Re: Applying Mathematica to practical problems
James Stein
6/3/13
Read Re: Applying Mathematica to practical problems
waku
6/3/13
Read Re: Interval vs default, was Re: Mathematica numerics and... Re: Applying
Daniel Lichtblau
5/27/13
Read Re: Work on Basic Mathematica Stephen!
Noqsi
6/2/13
Read Re: Work on Basic Mathematica Stephen!
David Bailey
5/28/13
Read Re: Work on Basic Mathematica Stephen!
fd
5/31/13
Read Re: Work on Basic Mathematica Stephen!
David Bailey
5/28/13
Read Re: Work on Basic Mathematica Stephen!
fd
6/2/13
Read Re: Applying Mathematica to practical problems
Mark McClure
6/3/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
6/3/13
Read Re: Applying Mathematica to practical problems
Joseph Gwinn
6/3/13
Read Re: Warsaw Univ. course, was Re: Work on Basic
lshifr@gmail.com
6/3/13
Read Re: Warsaw Univ. course, was Re: Work on Basic
lshifr@gmail.com

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