On a recent trip to McGill University in Montreal, I had the pleasure of meeting Dr. Paul Oh of Drexel University in Philadelphia and the Director of the US National Science Foundation’s (NSF) robotics programs. During a fascinating presentation on the US robotics research landscape, Dr. Oh made a few comments that really made me think … and reflect.

Robotics has always been a “sweet spot” for Maplesoft technology. Between the necessary complex...

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.

That’s a mantra I need to have drummed into me, and perhaps tattooed on the inside of my car so I’m reminded every morning.  But I keep on making the same mistakes. 

 I seem to think that if I’ve “optimized” my portfolio with a few flashy calculations that I’ve done my due diligence, and the next stop is financial independence.  It’s the black box syndrome – trusting the output of a computer program without truly understanding the real issues.  Most portfolio analyses, for example, hinge on historical data, which of course doesn’t predict the sub-prime blow-up in the US or whether Brazilian coffee growers are on strike.  They’re all backward looking.

 However, in the absence of a neighbourhood scryer, historical analyses are a good indication of how to position a portfolio for the long term.

 Being a geek (however much I strenuously deny it), I tend leverage my tech skills wherever I can.  I wrote the attached worksheet to import stock quotes, including historical data, from Yahoo using the Sockets package.  Simply type in the appropriate NYSE stock tickers into the appropriate text boxes, check the quantities you want to download, and click the big gray button.

 All the stock quotes and historical data can be manipulated on the command-line and can be accessed via command-completion. 

 It then finds the best distribution of stocks in a portfolio by maximizing its Sharpe Ratio (through the Optimization package). 

The Sharpe ratio quantifies how effectively a portfolio of risky assets utilises risk to maximise return.  It’s defined as follows.

 

 

It essentially measures how effectively a portfolio uses risk to maximize return – the higher the ratio the better.  The expected portfolio return is predicted from historic data, the portfolio standard deviation is traditionally used as a proxy for risk, and the risk free return is the return that can be expected from a zero-risk investment (i.e. the interest on US Treasury Bills or the redemption yield on UK gilts).

What I find particularly fascinating is how Maple is now the centre of my technical desktop.  Through the combination of the interface and its math tools, I now use it for everything from the simplest calculations through to making wild guesses about my financial future.  If any of the developers are reading this, I want you to know there’s a lot riding on you...

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.

> q := (6*((1/3)*a-1/9))/(36*a-116+12*sqrt(12*a^3-3*a^2-54*a+93))^(1/3);
                                   6 (a/3 - 1/9...

Some time ago I was asked the question: do you know how to do a change of variables in a multi-dimensional definite integral?  I thought I knew, but I was wrong.  I only know how to do a change of variable in a multi-dimensional indefinite integral. 

This question really intrigued me.  Of course, this is such an obvious question, I just started pulling out textbook after textbook off my bookshelf, expecting to find the answer...

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.

Inspired by the post Re: the physics package I decided to have a closer look at the function FeynmanDiagrams. As the Lagrangian I thought I might as well take the QED Lagrangian for a massless spinor field Q[i](X) coupled to an external electromagnetic field A[mu](X):

restart:
with(Physics):
Setup(advanced):
L_QED :=
   +Dagger(Q[i](X)) * Dgamma[4] * Dgamma[mu][i,j] * I * diff(Q[j](X),X[mu])
   +Dagger(Q[i](X)) * Dgamma[4] * Dgamma[mu][i,j] * e * A[mu](X) * (Q[j](X));

My previous blog entry was a real success. Even though my original idea about multi-part MIME has not gotten anywhere, I do now have a concise way to package a maplet with supplemental files in a single package that can be downloaded via the WWW and automatically extracted and executed. Most of the ideas were presented by acer. acer first suggested that I look at the interactive interface to the InstallerBuilder. The idea here was to embed the maplet in a worksheet saved in a help database (hdb). This did work, but was not suitable for actual use due to the overhead of the installer. In the attempt to reduce this overhead, acer then supplied some code that used march and LibraryTools. To test the product of this interaction, download the file at the URL http://www.math.sc.edu/~meade/TEST/SimpleTest.mla.