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.

I see two recent items on the web about Mathematica and the rosettacode.org site. One was a Wolfram Inc. corporate blog post, and the other a post on Wolfram's relatively new community site.

There are many items on the page of tasks still without a submitted Maple implementation. It would be nice to see interesting implementations of some remaining tasks, as contributions from the Maple user base. The tasks remaining are of very mixed difficulty levels.

To date there are only 132 entries on the page for Maple implementations of that site's programming tasks. (Of these about 40 were submitted by one member while about 80 were submitted by another member.)

acer

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You can read more about the technology here:
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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.

Bring Statistics Education to Life!

This exciting new webinar will demonstrate some of the ways that educators can take advantage of Maple’s symbolic and numeric approach for statistics education. Examples will include basic statistics theory including descriptive statistics such as measures of central tendency and spread, hypothesis testing, as well as discrete and continuous random variables.

Many examples presented in this webinar will be taken from the new Student Statistics package that was introduced in Maple 18. The Student Statistics was designed with classroom use in mind, and features detailed explanations and instructions, interactive demonstrations, and visualizations, all of which are great learning tools for teaching a course involving probability and statistics.

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

Symbolic Computing for Engineering

As engineering applications become more complex, it is becoming increasingly difficult to satisfy the often-conflicting project constraints using traditional tools. As a result, we’ve found there is a growing interest within the engineering community for tools that make engineering calculations transparent and capture not just results but also the knowledge and analysis used throughout the engineering workflow. Engineering organizations are achieving this goal by making symbolic techniques an integral part of their tool set.

In this webinar, Laurent Bernardin will demonstrate how to enhance the early-stage design phase by making mathematical computations explicit and transparent, and then integrating the results into an existing tool chain.

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

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.

Updates are now available for both Maple 18 and MapleSim 6.4.

Maple 18.01 includes a variety of enhancements, including:

• Significantly enhanced  efficiency for many  numerical linear algebra computations
• New keyboard shortcuts for “Execute All” ([Ctrl or Cmd]+[Shift]+[Enter]) and for entering slideshow mode ([F11] or [Cmd]+[F11])
• Improved export of 2-D plots
• PDF export improvements for documents that include  code edit regions
• Enhancements to the limit command

 To get this update, you can use Tools>Check for Updates from within Maple, or visit Maple 18.01 Downloads.

MapleSim 6.4.01 includes:

• Improvements to the templates for creating custom components using discrete state space and discrete transfer function descriptions
• Improved handling of variable names that include both symbols and numbers
• UTF-8 filename support
• Improved backwards compatibility of the Parameter Inspector with older models

In MapleSim, use  Help>Check for Updates or visit MapleSim 6.4.01 Update. For best performance, we recommend that you run MapleSim 6.4.01 with Maple 18.01.

eithne

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

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Some years ago member William Fish started a long discussion in part about a numeric integral involving high parameter (high oscillation) Bessel J0. That numeric integration task appeared in a Bitwise Magazine article.

At that time even obtaining numeric results involved extra effort such as handling real and imaginary components of the integrand separately, and requesting particular methods (sometimes hacked, to bump up the subinterval limit, for very high parameter values).

That led to a post where I showed that the result could be obtained quickly by using a fast compiled BesselJ (J0) from an external library along with a modified low-level call to a particular evalf/Int solver.

And sometime after that a numeric result for the real & imaginary split integrand became much more readily (if not quickly) available by using a new `maxintervals` option of evalf/Int to specify the maximal number of subintervals for the particular solver.

Maple 18 has its own compiled implementations of the Bessel functions for "hardware" (double) precision arguments. So now the numeric evaluations of the integrand are computed much faster.

Using Maple 18.00 on 64bit Windows 7 the same numeric results obtain in under a second, in a simple, single call to evalf,Int.

restart:

CodeTools:-Usage(
  evalf(Int(BesselJ(0, 50001*x)*x*exp(I*(355*x^2*1/2)), x = .35 .. 1))
                 );
memory used=9.28MiB, alloc change=32.00MiB, cpu time=437.00ms, real time=441.00ms, gc time=0ns

                           -8                 -8  
             3.181753502 10   - 7.798301124 10   I

restart:

CodeTools:-Usage(
  evalf(Int(BesselJ(0, 10000*x)*x*exp(I*(355*x^2*1/2)), x = .35 .. 1))
                 );
memory used=6.83MiB, alloc change=32.00MiB, cpu time=218.00ms, real time=211.00ms, gc time=15.60ms

                            -7                 -7  
             -2.007752340 10   + 4.275388462 10   I

Of course the ramifications of fast, compiled Bessel functions at double precision extend much farther than just this one example. But I like seeing the speed improvement in terms of a concrete example.

acer