http://lib.freescienceengineering.org/search.php?search_type=magic&search_text=maple&submit=Dig+for

Hi
Just finished updating the comparison between Maple 17.02 and Mathematica 9.01 in solving the 1390 Ordinary Differential Equations (ODEs) of Kamke's book:

• Mathematica solved 80% in 7 hours and 8 minutes
   
• Maple solved 97.5% in 43 minutes

While trying to solve the whole set, Mathematica hanged with 90 of these ODEs while Maple hanged with 6 ODEs. A pdf with a summarizing table and all the details is linked below

It is also relevant here that Maple's dsolve has close to half of its code implementing more modern methods, not found in Kamke, illustrated in the Maple 'what's new in DEs' help pages of the last 10 releases; for these other kinds of equations the difference is more impressive. I'll see to prepare another post about that.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

Comparison_Kamke.pdf

The question was "Let X be the random variable uniformly distributed in the disk centered at the origin O(0,0) with radius 1 and let Y be the random variable uniformly distributed in the square having its vertices A(6,-1), B(9,-2), C(8,-5), and E(5,-4). What is the PDF of the distance between X and Y? Is it possible to find that with Maple?"
Having a long think about the topic, I draw the conclusion that the exact closed form of the PDF/CDF, even the one can be found, would be useless because of its complexity.
Thus, an approximate formula for the CDF/PDF under consideration is a proper way. That formula can be derived in such a way. First,rotating the picture, we may consider the square having its sides horizontal or vertical: K((1/5)*sqrt(1410)-(1/2)*sqrt(10),1/sqrt(10)), L((1/5)*sqrt(1410)+(1/2)*sqrt(10),1/sqrt(10), M((1/5)*sqrt(1410)+(1/2)*sqrt(10),1/sqrt(10)-sqrt(10)), Q((1/5)*sqrt(1410)-(1/2)*sqrt(10),1/sqrt(10)-sqrt(10)). The geometry behind that is omitted.
We randomly choose a point P1 belonging to the square [-1,1] x [-1.1]. If the one belongs to the disk {(x,y):x^2+y^2 <=1}, then we randomly choose a point P2 from the square [K,L] x [Q,L]. Next, we calculate the distance between P1 and P2 (The  LinearAlgebra[Norm] command http://www.maplesoft.com/support/help/Maple/view.aspx?path=LinearAlgebra/Norm is used to this end.) and add it to the set S.This is repeated 2*10^4 times.

Converting S to an Array A, we constuct the empirical distribution X by A and find its mean mu and standard deviation sigma.

7.67568900820260

1.029831470

Let us compare the obtained empirical distribution and the normal distribution with the parameters mu and sigma.

The plot suggests a good fit between these. However, it is only semblance. Applying the Kolmogorov-Smirnov test (for example, see  http://www.mapleprimes.com/posts/119903-The-KolmogorovSmirnov-Test
), we  calculate

and

3.32619143372726

while the critical value equals 1.358098639 at the level 0.05. Thus, the hypothesis about the concordance should be rejected.

Also we draw the approximation to the PDF:

CDF.mw

Himmelblau.mw

     On the basis of Dragнilev method…

     Is there anyone interested in the algorithm to reduce the distance between the points of the given constraints? The algorithm is adapted for use in R ^ n. This is an example of its work on the surface:  
f = - (x1 ^ 2 x2-.3) ^ 2 - (x1 x2 ^ 2-.7) ^ 2 - 5;  

     Approximate description of the algorithm in pictures.

Greetings to all.

I have been using the numtheory package for quite some time now and it has helped me advance on a number of problems. Recently an issue came to my attention that I have known about for a long time but somehow never realized that it can be fixed. This is the fact that the numtheory package does not know about Dirichlet series, finite and infinite. Here are two links:

Fourteen Clickable Calculus examples have been added to the Teaching Concepts with Maple area of the Maplesoft web site. Four are sequence and series explorations taken from algebra/precalculus, four are applications of differentiation, four are applications of integration, and two are problems from the lines-and-planes section of multivariate calculus. By my count, this means some 111 Clickable Calculus examples have now been posted to the section.

A kryptarithm - this is an example of arithmetic, in which all or some of the digits are replaced by letters. The rule must be satisfied: the different letters represent different digits, the identical letters represent the identical digits. See the link  http://en.wikipedia.org/wiki/Verbal_arithmetic.

The following procedure, called  Ksolve , solves kryptarithms in which are used four operations ...

I just wanted to remind everyone that this quarter's Möbius App Challenge closes Sept. 30.  This quarter's prize is an iPad Prize Pack, which looks very cool but sadly, I'm not allowed to enter.

To enter the contest, all you need to do is:

1) Create an interactive App in Maple

2) While in Maple, log-in to the MapleCloud through the MapleCloud palette.

3) Click on the Send Document to the Cloud button

I think Maple is missing some lines and significant points. Here I leave another contribution to the possible implementation of a new algorithm to draw the circle of Taylor.

Circle_of_Taylor.mw

Atte.

L. Araujo C.

Other work done to demonstrate that using the correct syntax leads to corroborate all the principles and theorems found in the area of geometry. The Gergonne Point is another achievement developed by Maple procedure through GergonnePoint command and use. I hope your hand corrections if any.

Point_of_Gergonne.mw

Atte

Lenin

I would like to pay attention to the article "Words and More Words" by Joseph Malkevitch. Here are a few  intriguing references:

M. Morse, A solution of the problem of infinite play in chess, Bull. Am. Math. Soc., 44 (1938) 632.

M. Morse and G. Hedlund, Symbolic dynamics, Am. J. Math. 60, (1938) 815–866.

Lothaire, M. Applied Combinatorics on Words, Cambridge U. Press, New York, 2005.

https://www.facebook.com/pages/Matemática-Computacional-Trujillo/145132492343285

A user community of Maple I leave one of my contributions to the advancement of science. Here you see the true use of Mathematics in its real dimension Geometric. Just need to improve it with Components someone can help?.The_Point_of_Nage.mw

Aquí le dejo otro de mis trabajos hechos con puro matemáticas, creo que me parecio por demás plotear las alturas y medianas ya que eso se realizo en la recta de Euler.

Nueve_puntos_de_Feue.mw

Aqui les dejo La ecuación de la Recta de Euler, calculado desde su inicio hasta la comprobación con el comando EulerLine.

Recta_de_Euler.mw