Now, how does this match up with the result from Alec's suggestion?

int(2/(1-k^2*sin(2*t*phi/Pi)^2)^(1/2)/Pi*phi,
t=0..1/2*Pi,AllSolutions) assuming k>0, k<1, phi>0;
simplify(%,symbolic);

Would just mean hard coding in those results? Could Maple then subsequently be used to derive much else significant (and significantly different) from that?

Would just mean hard coding in those results? Could Maple then subsequently be used to derive much else significant (and significantly different) from that?

Just a small note on the PS. above and the sentence about public domain and copyright statements. It may be wise to ask wiki submitters to explicitly state that code they write and post is in the public domain (or, say, might be copied only if retaining some authorship note, etc), as far as redistribution goes.

It is my understanding that under Canadian (for example) copyright law no explicit statement of copyright is necessary for the author to have and retain certain rights over the redistribution of the material. In other words, it may not always be true that omission (in and of itself) to include an explicit copyright statement automatically places code in the public domain. In such situations it may be prudent to ask submitters either to agree to a sweeping release over redistribution rights or to include explicit release on a post-by-post basis.

And (slightly off topic), that doesn't seem to conflict with Will's attitude toward this site, which in one comment he has couched as, "Authors retain the copyright on all posts on MaplePrimes, you are free to re-use your posts on the site as you see fit."

I don't know why I missed the explanation that Robert gave below, about U being a number. Sorry, please ignore my response about evaluation levels of procedure locals. Running both ways (properly) would have clued me in.

I don't know why I missed the explanation that Robert gave below, about U being a number. Sorry, please ignore my response about evaluation levels of procedure locals. Running both ways (properly) would have clued me in.

I entered f:=x->2*x+2 in Maple 12, and then chose the context-menu item Plots -> 2-D Plot. Using the plots own context-menu (right-click) I toggled the checkbox under Manipulator -> Scale. At that point, when over the plot, the cursor because a foreshortened double-arrow and moving it up and down would zoom in and out.

I entered f:=x->2*x+2 in Maple 12, and then chose the context-menu item Plots -> 2-D Plot. Using the plots own context-menu (right-click) I toggled the checkbox under Manipulator -> Scale. At that point, when over the plot, the cursor because a foreshortened double-arrow and moving it up and down would zoom in and out.

I shouldn't have written to imply that the need for extra information was obvious. I apologize, if that gave an insulting impression.

I shouldn't have written to imply that the need for extra information was obvious. I apologize, if that gave an insulting impression.

Yes, that is why I asked about the number of cores/CPUs. Because (I believe that) the Windows task manager reports 50% CPU use when a single core of a dual-core system is running flat out.

There are one or two ways to make Maple utilize more than just a single core. And in doing so that would provide a test to confirm this hypothesis. One way (for 32bit Windows, or 32bith or 64bit Linux) is to make Maple use multiple cores concurrently during hardware floating-point datatype LinearAlgebra computations. Another way is to run some example from the Maple Threads package.

Running 64bit Maple is quite orthogonal to the issue of how many cores get used. Running 64bit Maple on 64bit Linux would not in itself make the Maple kernel use more than a single core.

The Maple GUI (Standard, Classic, or command-line) can all run as separate processes from the Maple kernel. So that brings one benefit of running Maple under multiple cores. For example the GUI could still be able to save worksheets and be responsive even if the kernel were to get locked up and unresponsive.

Yes, that is why I asked about the number of cores/CPUs. Because (I believe that) the Windows task manager reports 50% CPU use when a single core of a dual-core system is running flat out.

There are one or two ways to make Maple utilize more than just a single core. And in doing so that would provide a test to confirm this hypothesis. One way (for 32bit Windows, or 32bith or 64bit Linux) is to make Maple use multiple cores concurrently during hardware floating-point datatype LinearAlgebra computations. Another way is to run some example from the Maple Threads package.

Running 64bit Maple is quite orthogonal to the issue of how many cores get used. Running 64bit Maple on 64bit Linux would not in itself make the Maple kernel use more than a single core.

The Maple GUI (Standard, Classic, or command-line) can all run as separate processes from the Maple kernel. So that brings one benefit of running Maple under multiple cores. For example the GUI could still be able to save worksheets and be responsive even if the kernel were to get locked up and unresponsive.

Hi Alec,

Have you seen the mechanism on mapleprimes introduced during your quiet period, called "Submit Maple Software Change Request"? It's a euphemism for "submit a bug report".

As far as I know, the principal danger during computation of the roots of a quadratic is catastrophic cancellation of terms during addition. This can be side-stepped by ensuring that the terms have the same sign.

Take the quadratic a*x^2+b*x+c . Let,

 d := -1/2 * (b+signum(b)*sqrt(b^2-4*a*c));

Then the roots may be taken as d/a and c/d.

Don't you think that a root-finder's handling of multiple close roots, bad conditioning and high degree, its particular deflation implementation, and whether it shows the final estimated accuracy will all determine its quality and robustness far more than does its lowermost quadratic step? Do you know of other specific dangers for the quadratic?

Well, it would have to depend upon what you know about the qualitative aspects of the given problem. If there were a reliable way to do it, then it wouldn't have to be an optional parameter. Isn't it obvious that it has to be an option since the exact extension possibilities are limitless, the precision of computation is variable, and the data is only approximate to a finite number of digits?