Some time ago, I had a blog post about a compendium of inequalities,  Some people took a look and found problems in that paper.  So I took the time to track down the author and point him to the mapleprimes page.

He got back to me some time later, thanking me for pointing out the errors.  But in the same email, he pointed me to 2 other papers, http://xxx.lanl.gov/abs/0707.2098 and http://xxx.lanl.gov/abs/0707.2584 which contain (interesting?) conjectures which seem amenable to Maple exploration. I meant to look at these myself, but it has now become clear that I won't for quite some time yet. Perhaps these will pique the curiosity of some MaplePrimes member.

The following example arrived in my email inbox a few weeks ago. It spurred a short but lively thread of discussion amongst some Maple developers.

I thought that it was interesting enough to post here. I'll hold off on giving my own opinion right away, because I'm curious to read what other MaplePrimes members might write about it.

I recently submitted my work to Maple Application Center
and I received a bug report from a staff. Then, I resubmitted
it after fixing bugs. However, I have a bug report again (^_^;
Yes, this is because my work was poor, but in other words,
all applications in Maple Application center that passed
strict check by staff are all guaranteed to have good quality.

I am sure that everyone can find good tools for education and
research. We should utilize them. If we can not find applications
that we want, let us develop works and submit them !

Yasuyuki Nakamura

On his blog, Jaime Zawinski (of Netscape and XEmacs fame) relates a tale of finding limits in the (supposedly) unlimited big number representation on a TI Lisp machine in the early 1990s. It is an amusing story, and it makes me wonder if GnuMP is has a similar limit on a different scale.  Or in other words, is there a positive integer small enough to fit into memory  (assuming 64 bit address space) but that cannot actually be constructed in GnuMP due to limits in the implementation? Does someone here know enough about the GnuMP internals to give the answer?

A search I was doing dug up this old gem, involving a discussion between Gerald Edgar and I over a Maple problem 16 years ago!

Easy challenge: improve on my solution to Gerald's problem.

History challenge: my email address shows as wmsical!jjcarett@watmath.waterloo.edu.  Can you puzzle that out?  That is really two questions, a) how is that an email address and b) what is 'wmsical' ?

The recent thread A crossprod problem, although not directly related, inspired me to write this blog entry about bilinear cross products and their noticable property [see for instance P. Lounesto, Clifford Algebras and Spinors, 2nd ed. (Cambridge University Press, Cambridge, 2001)]:

Theorem: A bilinear cross product obeying the orthogonality property and the Pythagorean property, see below, exists only in 3 or 7 (real or complex) dimensions.

As many here know, Gaston Gonnet is a co-founder of Maple.  SIAM, in its History of Numerical Analysis and Scientific Computing project, has now published a very long interview with Gaston.  For those who like a good yarn, as well as details of the history of Maple and Maplesoft, it makes for fascinating reading.

My favourite quotes are:

Inspired by Jacques' blog entry Introduction to transseries, concerning a paper by Gerald A. Edgar, using Maple and published at arXiv, I here take the liberty to refer to a recent paper of mine which also uses Maple and is published at arXiv. The link is:

Linking electroweak and gravitational generators.

Most probably, this paper would not have existed without the possibility of performing lots of calculations in Maple, using for instance my own package COSVAM which deals with the octonions, the largest division algebra over the reals.

For instance, the pivotal Eq. (5) of the paper would probably not have been discovered by me using pen and paper. It was accidentally discovered while performing some Maple calculations with a different objective in mind.

Second note added: The issue below seems to have been resolved by clearing the cache of my Firefox browser, i.e., it seems to have been purely a local problem.

Inspired by the blog post Find a point in every region defined by a system of linear equations, I have come up with the following method to find a point inside each bounded region. The assumptions are:

• No two lines are parallel.
• No three lines are coincident.

Due to numerical instability, it seems, using floats, the coefficients of the equations of the lines are taken to be integers (they could also have been taken to be fractions, of course). Then the method goes like follows:

Hi there.
How are you?

I feel sorry since I purchased Maple. Let see if you would agree.
First of all, it is inferior to the Ti-89 in some aspects.

I have tried to use Maple 11.02 to solve the problems:

(sqrt(2)+1)^x+(sqrt(2)-1)^x = 3;

And Maple 11.02 fail to solve, then I tried to solve numerically, it missed one solution.
There must be 2 solutions for the problem above and Maple missed 1, the Ti-89 beats it hand down.

The second problem I tried was:
int(sqrt(sin(x))/(sqrt(sin(x))+sqrt(cos(x))), x = 0 .. (1/2)*Pi);

and Maple even stuck... The Ti-89 return answer correctly within about 20 secs.