Amdahl's Law is a formula for determining the theoretical speed up when parallelizing a function. For example, imagine we wanted to parallelize a function that spends 90% of its time in one algorithm. If there is a parallel version of that algorithm, how much faster would the entire function run with 2, 4 or more cores?

In our previous article we described a packed representation for sparse polynomials is designed for scalability and high performance. The expand and divide commands in Maple 14 use this representation internally to multiply and divide polynomials with integer coefficients, converting to and from Maple's generic data structure described here. In this post I want to show you how these algorithms work and why they are fast. It's a critical stepping stone for our next topic, which is parallelization.

Back in September, I posted an announcement about our plans for the new version of MaplePrimes.  Well a few months and many, many hours of development later, we are approaching the end point!

In the book Introduction to Maple by Andre Heck books.google.co.uk/books  the author manage to plot the canadian flag
in maple by using the following code:
 

This is an update to my earlier post on the Rossler system, one of the simplest examples of a dynamical system in 3 dimensions that can exhibit deterministic chaos.

restart;

interface(displayprecision=10):

PDEtools:-declare(prime=t,quiet):

ross_x:=diff(x(t),t)=-y(t)-z(t):

ross_y:=diff(y(t),t)=x(t)+a*y(t):

ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t):

rossler_sys:=ross_x,ross_y,ross_z;

#Find fixed points:

Consider the following situation.  A thread acquires a mutex, then enters a critical section.  However when executing in the critical section, the thread access a memory location.  If that memory location is not in cache, the thread will wait for a few hundred cycles.  If accessing the memory location causes a page fault (the memory was swapped out to disk), the thread may need to wait a few million cycles.  However while this thread is waiting, it is still holding the mutex.  This means that other threads will not be able to enter the critical section, and may

The following interaction with Maple's Excel link came to my attention today.  I thought it had many interesting points that lead to insights about Excel and Maple that are worth sharing. 

The Maplesoft corporate blog has seen the addition of many interesting new posts recently, and I thought I'd share a few of the most recent ones with MaplePrimes.

Visualizing a Parallel Field in a Curved Manifold
Posted by Robert Lopez, Maple Fellow

Speaking of Languages...
Posted by Tom Lee, Chief Evangelist

An analytical model of mornings in the Wright household
Posted by Derek Wright, Application Engineer

It has been a while since my last post.  I'm sorry about that, but I have been busy trying to the fix bugs reported as part of the Maple Beta program.  I'm also running low of good parallel programming topics.  So, as always, if you have topics you'd like to hear about (or hear more about) feel free to ask.

Today I am going to post a brief note about a blog that I find quite interesting.

Cliff Click Jr's Blog: http://blogs.azulsystems.com/cliff/

Here is the Rossler system, one of the simplest examples of 3 dimensional deterministic chaos (under certain conditions according to "params"). Thanks to Doug and Joe for various assists. Comments and critiques most welcome !