To judge results of functions coded in double precision against precise results (as they may be given by Maple) one has to respect decimal presentations on one side and IEEE on the other side.

For that one can use routines developed by Florent de Dinechin, which are worth to be better known.

Here is a Maple sheet showing how one can do it (looking at the complex valued power function using evalhf versus using MS VC2005 as an example).

There was some recent discussion about Maple's Standard GUI having two parsers. (See here, and its parent.)

I've been accumulating a list of some differences between the parsers of 2D Math and 1D Maple notation, for the same given pasted input.

In particular, I'm interested here in differences...

Using Maple 12 I have the following behaviour, which I find odd:


1. 'evalb' is correct, 'is' turns out to be false (by example):

  eq:=1/2*I*(-z+ln(exp(z)))/Pi = -1/2*I*(z+ln(exp(-z)))/Pi;

  evalb(eq);
                                false
  is(eq);

I realized the other day that I had not mentioned the Threads:-Add, Threads:-Map, Threads:-Mul and Threads:-Seq functions.  These are parallel implementations of the standard Maple functions, add, map, mul and seq.  They expect the sam

On and off over the last few months I've been meaning to learn about computing a center manifold approximation and normal form of a dynamic system of three differential equations.

My main reading: Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Second Edition, Springer, 2003.

I want to apply the technique to a system I derived from an optimal control problem. As a first step, I decided to reproduce the steps for the following system, for which the solution has been published.

Below is the latest version of the code to draw iso-chrone lines and a salvo of arrows onto the phase diagram of a two-dimensional system of ordinary differential equations.

I have greatly benefited from inputs by Robert Israel (who wrote the first incarnation of the procedure), Joe Riel, and pagan. A big thankyou!

The procedure is sufficiently developed for my current purpose, so I don't plan to modify it much in the near future.

Tested on Maple 13/ Classic. The last plot combines the isochrones and the salvo.

what I learned today is that you cannot write 1e-i, where i is an unassigned variable (at least not like that):

I've created a Maple help page, saved in a small hdb file, that describes the hierarchy of Maple's numerical types.  Insert it into the path assigned to ?libname.  Access the help page with ?numer-hier. To make it compact, I took some liberties with the notation.  Here is what it looks like

I'm posting it here to keep a record for myself.

my second blog post, aka "the lost blog post", is here.

Still some way to go. The following still needs to be tweaked case by case. And it can be made more compact too. Are the arrows flying so much faster in the top triangular area or are the arrows not printing where I expected them to ...

funny that, how do I go from first blog post to third blog post!?!?!

that's because my second blog post appears as a comment to my first blog post.

you've just got to learn...

Since much of what I post couldn't possibly be of interest to anyone else, I thought I'd use the blog. If I remember its existence, I'll try to post here stuff to myself. After all it's less likely to be lost here than in the maze of my harddrive.

Every year my extended family does a "secret santa" gift exchange. Each person draws another person at random and then gets a gift for them. At first, none of my siblings were married, and so the draw was completely random. Then, as people got married, we added the restriction that spouses should not draw each others names. This restriction meant that we moved from using slips of paper on a hat to using a simple computer program to choose names. Then people began to complain when they would get the same person two years in a row, so the program was modified to keep some history and avoid giving anyone a name in their recent history. This year, not everyone was participating, and so after removing names, and limiting the number of exclusions to four per person, I had data something like this:

Corless & Davenport provide a whole bestiarium of rules. This is a small part of the most simple cases, which I sampled more or less for 'all day use' as reference. They are based on the 'unwinding number' (which is a sheet number of according Riemannian surfaces). It turns out, that Maple can 'proof' the identities, if one does not use the definition, but uses the version given in the help pages (= version 2 in the following).

While running Maple (13.0 and 13.02) on a Linux system that has IPv6 enabled (Debian Sid AMD64 as of December 8, 2009) I found that the xmaple interface was unable to connect to the Maple kernel.  Command line maple worked fine with a simple test of 2 + 2.  Xmaple had some odd behavior as the kernel connection issue is not reported until running a calculation.  Aslo I found the many of the menu items were dimmed out such as "Help" -> "About" and "Help" -> "Maple Help."  Further selection of the "Tools" menu caused t