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!

I am trying to solve a set of 4 coupled ordinary differential equations, starting from certain set of initial conditions for certain parameter values.  i have to evolve the system for a very long time (higher number of iterates are needed).

For a certain set of initial conditions the following error occurs

"Error, (in sol12) cannot evaluate the solution further right of 2939.9221, probably a singularity"

what could be the possible way to get rid of this error.......

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:
 

In this blog we will consider what happens when the formula for the MRB constant is iterated infinitely. This will invoke divergent series, but we will use an analytic extension of the formula to continue our iterating. We will also find a new use for MRB2=1-2*MRB constant.( Sloane's A173273 )

I think Maple should emphasize occupational and problem specific packages, like its TA software for teachers. Maple should have a package or set of packages for each type of engineer: electrical,hydrological, etc. Actually, Maple should promote packages for all professions that tend to need it. An abundance of packages would enable many new users to benefit from the power of maple with the experience of the advanced users who helped develop the packages.

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 sequence of divergentt series in part evaluated by the following maple input.

f1 := seq((1-a)*(1/2)+sum((-1)^n*(n^(1/n)-a), n = 1 .. infinity), a = 1/10 .. 9*(1/10), 1/10): evalf(f): where abs(a)<1

and

f2 := `$`((1-a)*(1/2)+sum((-1)^n*(n^(1/n)-a), n = 1 .. infinity), a = 2 .. 10): evalf(f2); where abs(a)>1 .

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