Hi,
The FunctionAdvisor project is currently developing at full speed. During the last two months, a significant amount of new conversion routines and mathematical information for Jacobi elliptic and Jacobi Theta functions, on identities, periodicity, transformations, etc. got added to the conversion network for mathematical functions and to the FunctionAdvisor. The previous months was the turn of the set of complex components, added to the network. Developments regarding the simplification and integration of special functions (e.g SphericalY for computing spherical harmonics or Dirac), as well as fixes to the numerical evaluation of JacobiAM, `assuming` and to differential equation subroutines are also part of the update.

These developments are available to everybody as usual in the Maplesoft R&D Differential Equations and Mathematical Functions webpage. Below there is a list of the latest developments as seen in the worksheet that comes in the zip with the DEsAndMathematicalFunctions update.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Greetings to all.

As some of you may remember I have posted several announcements concerning Power Group Enumeration and the Polya Enumeration Theorem this past year, e.g. at this MaplePrimes link: Power Group Enumeration.

I have continued to work in this field and for those of you who have followed the earlier threads I would like to present some links to my more recent work using the Burnside lemma. Of course all of these are programmed in Maple and include the Maple code and it is with the demonstration of Maple's group theory capabilities in mind that I present them to you (math.stackexchange links).

• Power Group Enumeration with two instances of the symmetric group by Burnside
• Multisets of n permutations of [n] with the symmetric group acting on the permutation elements
• Counting binary structures
• Primitive necklaces, the Mobius function, and Power Group Enumeration
• Edge colorings of the cube and Power Group Enumeration
• Counting functions by Simultaneous Power Group Enumeration
• Subsets of a standard 52 card deck wrt. suit permutation
• Systems of lottery tickets wrt. the symmetric group acting on the values
• Stirling numbers and Power Group Enumeration
• Binary matrices with a fixed number of ones per column under row and column permutations

The third and fourth to last link in particular include advanced Maple code.

The second entry is new as of October 30 2015.

With my best wishes for happy group theory computing with Maple,

Regards,

Marko Riedel

Hi,
An interesting sequence of enhancements and new developments happened in the Physics package during this first half of the year. During the last month, improvements happened in the handling of Vectorial expressions and quantum mechanics using Dirac’s notation. During April and part of May it was the turn of general relativity enhancements.

Some of the developments are also interesting beyond Physics. For example: it is now possible to multiply equations. Suppose you have A = B   (1), and C = D   (2), multiplying as in (1) (2) now results in lhs((1)) lhs((2)) = rhs((1)) rhs((2)), saving a lot of typing. You can also perform (1)/(2) or (1)^2. Some enhancements in Physics related simplification, integration, `assuming`, and typesetting - e.g. the simplification and integration of spherical harmonics (SphericalY function) are also part of the update.

These developments are available to everybody as usual in the Maplesoft R&D Physics webpage. Below there is a list of the developments for the last month as seen in the worksheet that comes in the zip with the Physics update.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

I learned about this problem from Aser's post   See  page of tasks still without  Maple implementation. 

The procedure  game24  solves the problem. In the procedure Acer's  procedure  MyHandler is  used, which prevents the program to stop in case of 0 in the denominator.

game24:=proc(a,b,c,d)

local MyHandler,It, K, M, i, P;

uses StringTools, combinat;

 MyHandler := proc(operator,operands,default_value)

      NumericStatus( division_by_zero = false );

      return infinity;

   end proc;

   NumericEventHandler(division_by_zero=MyHandler); 

It:=proc(L1,L2)

local i, j, L;

L:=[];

for i in L1 do

for j in L2 do

L:=[op(L), op([Substitute(Substitute("( i + j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i - j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i * j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i / j )","i",convert(i,string)),"j",convert(j,string))])];

od; od;

L;

end proc; 

P:=permute([a,b,c,d]); 

K:=[];

for i in P do

K:=[op(K),op(It(It(It([i[1]],[i[2]]),[i[3]]),[i[4]])), op(It(It([i[1]],It([i[2]],[i[3]])),[i[4]])), op(It([i[1]],It(It([i[2]],[i[3]]),[i[4]]))), op(It([i[1]],It([i[2]],It([i[3]],[i[4]])))), op(It(It([i[1]],[i[2]]),It([i[3]],[i[4]])))];

od;

M:=[];

for i in K do

if parse(i)=24 then M:=[op(M), i] fi;

od;

if nops(M)=0 then return `No solutions` else

for i in M do

print(SubString(i,2..length(i)-1));

od; fi; 

end proc:

Two examples:

game24(2,3,8,9);

game24(2,3,3,4);

        No solutions

24.mws

http://vk.com/doc242471809_295040421

The new method and approach to the calculation of the geometry and kinematics linkages. It is based on the Draghilev method for solving systems of nonlinear equations.

( 10-bar linkage spherical mechanism animation. Program text for professionals only.)

MECHAN123_SPHERE_10.mw

you can change help of older maple version to 18 by this command:

HelpTools:-Database:-ConvertAll():

for example if you download DirectSearch optimization package it's help don't open in maple 18 because in maple 18 .hdb converted to .help and you can do this convert by HelpTools:-Database:-ConvertAll():

DirectSearch version 2 created for maple 13 and i converted it's help to 18.

after i typed this command maple 18 wrote: 

"Converting G:\\Program Files\\Maple 18\\lib\\DirectSearch.hdb to G:\\Program Files\\Maple 18\\lib\\DirectSearch.help"
Warning, .hdb help databases are deprecated, 'G:\Program Files\Maple 18\lib\DirectSearch.hdb' will not be used, see ?HelpTools,Migrate help page for more information.

and when try again it worked properly and DirectSearch help opened.

DigiArea Team is proud to present Maple WWW Net. 

Maple WWW Net is a part of Maple WWW technology that brings integration with MapleNet. Now you can access the power of Maple core directly from your worksheets in the internet. Maple WWW Net allows you to develop Maple worksheets enriched by live computations and interactive controls.

You can read more about the technology here:
http://digi-area.com/light/MapleWWW/

Take a look at this link.

We have just released an all-new, second edition of the Calculus Study Guide.

This guide has been completely rewritten and greatly expanded and to take full advantage of Maple’s Clickable Math approach.  It covers all of Calculus I and Calculus II and has over 450 worked examples, the vast majority of which are solved using interactive, Clickable Math techniques. 

Not only is this guide useful for students learning calculus, but it can also serve as a guide for instructors interested in pursuing a syntax-free approach to using Maple in their teaching.

See Clickable Calculus Study Guide for more information.  For even more information, you could also attend a live webinar about the new study guide next Wednesday.

eithne

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on some upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Hollywood Math (with more new examples!)

Over its storied and intriguing history, Hollywood has entertained us with many mathematical moments in film. John Nash in “A Beautiful Mind,” the brilliant janitor in “Good Will Hunting,” the number theory genius in “Pi,” and even Abbott and Costello are just a few of the Hollywood “mathematicians” that come to mind.

Although the widespread presentation of mathematics on the silver screen is not always entirely accurate, it does serve as a great introduction to the study of mathematics in general. During this webinar Maplesoft will present a number of examples of mathematics in film. See relevant, exciting examples that you can use to engage your students.At the end of the webinar you’ll be given an opportunity to download an application containing all of the Hollywood examples that we demonstrate.

To join us for the live presentation, please click here to register.

Applications of Symbolic Computation in Control Design

You may already use Maple and/or MapleSim within your organization to solve various problems, but did you know that they have capabilities for control design as well? In one of our upcoming featured webinars for this month, we will explore the Control Design toolbox including the ability to extract symbolic equations of plant models, perform symbolic linearization, design symbolic controllers, and generate very fast code for HIL testing.

The following examples will be demonstrated:

• PID Control

• LQR, Kalman filter design

• Gain scheduling

• Feedback linearization

To join us for the live presentation, please click here to register.

This is the first presentation of updates for the DE and Mathematical Functions programs of Maple 18. It includes several improvements, all in the Mathematical Functions sector, as well as some fixes. The update and instructions for its installation are available on the Maplesoft R&D webpage for DEs and mathematical functions. Some of the items below were mentioned here in Mapleprimes - you are welcome to present suggestions or issues; if possible they will be addressed right away in the next update.

• Filling gaps in the FunctionAdvisor regarding all the 6 complex components: abs, argument, conjugate, Im, Re, signum, as well as regarding Heaviside (step function), Dirac, min and max.
• Fix the simplification and differentation rule for doublefactorial
• Make convert(..., hypergeometric) work the same way as convert(blabla, hypergeom)
• Implement integral forms for Heaviside(z) and JacobiAM(z, k) via convert(..., Int)
• Implement appropriate display for the inert %intat function as well as its conversion to the inert Int
• Make the FunctionAdvisor/DE return not just the PDE system satisfied by f(z, k) = JacobiAM(z, k)and also (new) the ODE satisfied by f(z) = JacobiAM(z, k)
• Fix conversion rule from Heaviside(z) to Sum
• Fix unexpected error interruption when differentiating min(...) and max(...) containing more than three arguments
• Fix issue in simplify/conjugate
• Improvement in expand/int: factors in disguise are put outside the integration sign
• Various improvements in the case of multiple integrals involving the Dirac function
• Make Intat fully inert (before it was evaluating its arguments)
• Make value of inert indexed objects work

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

DigiArea Team is proud to present new modern web technology for Maple Worksheets - Maple WWW. 

Maple WWW is a technology that brings Maple Worksheets to the World Wide Web. The technology provides a web application to view and share interactive scientific documents across the web. Maple WWW allows to open Maple worksheets in your browser without any additional plugins or extensions.

You can read more about the technology here:
http://digi-area.com/light/MapleWWW/

You can see the technology in action right here using the following embedded Maple Worksheet!

Voting is now open for the next individual prize to be awarded as part of the Möbius App Challenge.  The winner will receive an Xbox One Prize Pack! 

Here are the finalist Apps:

• Fixed Point Equation
• Testing Convergence of a Series
• Mod-N-Calulator
• Epsilon-delta Limit Definition

Note that, if you ever have any problems viewing Apps in your browser, or simply want to work offline, you can always download a Möbius App and view it in Maple or the free Maple Player. To download a Möbius App, follow the link to the App and then click on the Download button near the top left of the page.

You can vote for your favorite through our Facebook page or, if you’re not on Facebook, send an email with your vote to Mobius-Project@maplesoft.com.

And remember, we are now accepting entries for the next quarterly prize. You could win a Music Prize Pack, including the 64GB 5th Generation Apple iPod Touch, Sennheiser In-Ear Noise Cancelling Headphones and the Bose SoundLink Bluetooth Speaker III!  See the Möbuis App Challenge for details.

Voting closes April 25^th, 2014.

This is a little more than a new game it potentially uncovers a new class of numbers -- though determining membership might become a hard problem.

A number that possesses the solitaire property can be written in as ...,0,...1,...2,...etc, or ...,0,...1,...10...11,...etc,(where the "0" is the first zero in the number), with a radix point anywhere. We are free to pick the base and say it is solitaire with respect to that base. After the initial 0, the subsequent ordinals (the 1,2, etc or the 1,10,11, etc) used to write the solitaire number don't have to be the first ones. For example:

pi=3.1415926535897932384626433832795
0 2884
1 971693993751058
2 0974944592
3 078163860
4 ...
etc.,

or

pi=3.1415926535897932384626433832795

0 2884197

1 6939937510582 097494459

2 3 07816

3 860
4 ...
etc.,are both acceptable. (If the number can be written as  ...,0,...1,...2,...etc, or ...,0,...1,...10...11,...etc. it is solitaire.)

The Champernowne constant with respect to base 10 has only one representation:

0.

1

2

3

4

5

6

7

8

9

10

11...

etc. .

I know Base 10 Champernowne constant is base 10 solitaire. I can not say the same with certainty for Pi.

I also propose we can measure the solitude of a number by the average amount of numbers between the 0,1,2,3..., and give a perfect solitude score to Base 10 Champernowne constant. Other constants can be given additional credit, of some kind, if the amounts of numbers between the 1,2,3... follow a specific preset pattern.

marvinrayburns.com

The attached presentation is the last one of a sequence of three on Quantum Mechanics using Computer Algebra, covering the field equation for a quantum system of identical particles, its stationary solutions and the equations for small perturbations around them and, in this third presentation, the conditions for superfluidity of such a system of identical particles at low temperature. The novelty is again in how to tackle these problems in a computer algebra worksheet.

Download QuantumMechanics3.mw   QuantumMechanics3.pdf

Edgardo S. Cheb-Terrab
Physics, Maplesoft