Our previous article described the design of fast algorithms for multiplying and dividing sparse polynomials. We have integrated these algorithms into the expand and divide commands of Maple 14. In this post I want to talk a bit about what you might see when you try Maple 14. Keep in mind that the product isn't released yet and I don't work for Maplesoft, so general disclaimers apply. Nevertheless, one of the first things you may notice is this.

Consider  S=sum((-1)^n*(n^(1/n)-a),n=1..infinity).
S=1/2*(a+2m-1), where m is the MRB constant.

Let m = MRB constant = sum((-1)^n*(n^(1/n)-1),n=1..infinity)

Notice the sequential patterns Maple gives for an output to the following:

Digits := 96; floor(evalf((10^100+1)*(1/9801)))

which gives 1020304050607080910111213141516171819202122232425262728293031323334353637383940414243444546474850

and

evalf((10^100+1)*(1/9801)-floor((10^100+1)*(1/9801)))

which gives 0.505254565860626466687072747678808284868890929496990103050709111315171921232527293133353739414345

.

In honor of Pi Day, in this blog I would like to show that the MRB constant has some meaning in our day to day lives. The first two messages are lifted from a discussion group.

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.

 Consider the sequence of divergent 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(f1);

and

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

The Maple output, which is the MRB constant

I'm not sure why maple opted not to include the color option in the colormap when browsing an array?

The only available options are Grayscale, Hue, Hot and Cool.  Does anyone know why color was not included as an option?

i have two quotes :

#1:

You confuse science with engineering, publication with patents. Intellectual property law does not recognize ownership of scientific truth. Your theory is true, or it isn't. You don't 'own' it. An apple does not need Isaac Newton's permission to fall to the ground. The primary protections for inventions are trade secret and patents. The primary protection for other intellectual property is copyright, and wise choices in how you use it and publish it.

Q1) Why doesn't this subthread show up when putting MPFR in the Mapleprimes Search?

Q2) How does Maple make use of these?

> # on a system with `ls`
> system(cat("ls ","bin*/*mpfr*"));
bin.APPLE_UNIVERSAL_OSX/libmmpfr.dylib
bin.APPLE_UNIVERSAL_OSX/libmpfr.1.0.0.dylib
bin.IBM_INTEL_LINUX/libmpfr.so.1
bin.IBM_INTEL_LINUX/libmpfr.so.1.0.0
bin.SUN_SPARC_SOLARIS/libmpfr...

I've spent two days trying to figure out why Maple won't allocate more than 512 MB of memory on my Mac. I've checked all the forums here an on Apple and it seems that this is a problem which has been around for at least two years, without being properly resolved. Previous posts can be found here:

http://www.mapleprimes.com/forum/memoryproblemsmac

http://www.mapleprimes.com/blog/mathgeek/macandmaplekernelissue

See the following PDF for the geometry of the MRB constant.

http://www.marvinrayburns.com/what_is_mrb.pdf

If you have any questions, I would like to hear them.

Marvin Ray Burns

Please let me know if Maple 11 will work in 64-bit Windows 7, and if there are any compatibility issues.

I'm moving my Maple from 32-bit Windows XP to a new 64-bit Windows 7 system.

Thanks,

Tim

Does anybody knows of a method using ImageTools to correct an image for lens distortion?