The well-known  combinat[composition]  command computes and returns a list containing all distinct ordered  k-tuples of positive integers whose elements sum equals  n . These are known as the compositions of  n .  For some applications, additional constraints are required for the elements of these k-tuples, for example, that they are within a certain range.

The  Composition  procedure solves this problem. Required parameters:  n - a nonnegative integer, k - a positive integer. The parameter  res  is the optional parameter (by default  res is  0 ). If  res  is a number, all elements of  k-tuples must be greater than or equal  res .  If  res  is a range  a .. b ,   all elements of  k-tuples must be greater than or equal  a  and  less than or equal  b .  Composition(n,k,1)  is equivalent to  combinat[composition](n,k) .

The code of the procedure:

Composition := proc (n::nonnegint, k::posint, res::{range, nonnegint} := 0)

local a, b, It, L0; 

if res::nonnegint then a := res; b := n-(k-1)*a  else a := lhs(res); b := rhs(res) fi;

if b < a or b*k < n then return `No solutions` fi; 

It := proc (L)

local m, j, P, R, i, N;

m := nops(L[1]); j := k-m; N := 0;

for i to nops(L) do

R := n-`+`(op(L[i]));

if R <= b*j and a*j <= R then N := N+1;

P[N] := [seq([op(L[i]), s], s = max(a, R-b*(j-1)) .. min(R, b))] fi;

od;

[seq(op(P[s]), s = 1 .. N)];

end proc;

L0 := [[]];

(It@@k)(L0); 

end proc:

Three simple examples:

Composition(10,3); ``;   # All terms greater than or equal 0

Composition(10,3, 2);   # All terms greater than or equal 2

Composition(10,3, 2..4);   # All terms greater than or equal 2 and less than or equal to 4 

A more complex example. The problem - to find all the numbers in the range  1 .. 99999999  whose digits sum is equal to 21 .

Each number is represented by a list of digits from left to right, replacing missing digits at the left with zeros.

M:=Composition(21,8, 0..9):  

nops(M);  # The number of solutions

[seq(M[1+100000*i], i=0..9)]; # 10 solutions from the list M starting the first one

seq(add(%[i,k]*10^(8-k), k=1..8),i=1..nops(%));  # Conversion into numbers

Composition.mws

Greetings to all.

I am writing to alert MaplePrimes users to a Maple package that makes an remarkable contribution to combinatorics and really ought to be part of your discrete math / symbolic combinatorics class if you teach one. The combstruct package was developed at INRIA in Paris, France, by the algorithmics research team of P. Flajolet during the mid 1990s. This software package features a parser for grammars involving combinatorial operators such as sequence, set or multiset and it can derive functional equations from the grammar as well as exponential and ordinary generating functions for labeled and unlabeled enumeration. Coefficients of these generating functions can be computed. All of it easy to use and very powerful. If you are doing research on some type of combinatorial structure definitely check with combstruct first.

My purpose in this message is to advise you of the existence of this package and encourage you to use it in your teaching and research. With this in mind I present five applications of the combstruct package. These are very basic efforts that admit improvement that can perhaps serve as an incentive to deploy combstruct nonetheless. Here they are:

• A parity bias for trees
• Number of nodes with even offspring
• Trees with odd degree sequence
• Ordered rooted trees with all nodes having at least two child nodes
• Average depth of a leaf in an ordered binary tree

I hope you enjoy reading these and perhaps you might want to feature combstruct as well, which presented the first complete implementation in a computer algebra system of the symbolic method, sometimes called the folklore theorem of combinatorial enumeration, when it initially appeared.

Best regards,

Marko Riedel.

Currently calculations: equations, regression analysis, differential equations, etc; to mention a few of them; are developed using traditional methods ie even are proposed and solved by hand and on paper. In teaching our scientists and engineers use the chalkboard as a way to reach students and enable them to solve their calculation. To what extent Maple contributes to research on new mathematical models applied science and engineering ?. Maplesoft appears as a proposal to resolve problems with our traditional proposed intelligent algorithms, development process, embedded components, and not only them but also generates type applications for Apple ipad tablets signature. Based on the computer algebra system Maple Maplesoft gives us the package which works exactly like we were on our work. I will show how mathematics is developed from a purely basic to reach modeling differential equations applied to education and engineering. Also visualizare current techniques for developing applications for mobile devices.

link: https://www.youtube.com/watch?v=FdRUSgfPBoc

ECI_2015.pdf

Atte.

Lenin Araujo Castillo

Physics Pure

Computer Science

We are happy to announce the first results of a partnership between Maplesoft and the University of Waterloo to provide effective, engaging online education for technical courses.

Combining rich course materials developed by the University with Maple T.A. and Maplesoft technology for developing, managing, and displaying dynamic content, the Secondary School Courseware project supports high school students and teachers from around the world in their Precalculus and Calculus courses. The site includes interactive investigations, videos, and self-assessment questions that provide immediate feedback.

Feel free to take a look. The site is free, and no login is required.  

For more information about the project, see Online Mathematical Courseware.

eithne

Hello Everyone, I am new one in the community..

In this work we show you what to do with the programming of Embedded Components applied to graphics in the Cartesian plane; from the visualization of a point up to three-dimensional objects and also using the Maple language generare own interactive applications for touch screen technology in mobile devices techniques. Given that computers use multicore and designed algorithms that solve calculus problems with very good performance in time; this brings programming to more complex mathematical structures such as in the linear algebra, analytic geometry and advanced methods in numerical analysis. The graphics will show real-time results for the correct use of the parallel programming undertook to bear the procedural technique is well suited to the data structure, curves and surfaces. Interaction in a single graphical container allowing the teaching and / or research the rapid change of parameters; giving a quick interpretation of the results.

FAST_UNT_2015.pdf

Programming_Embedded_Components_for_Graphics_in_Maple.mw

Atte.

L.Araujo C.

Physics Pure

Computer Science

Happy New Year! Now that 2014 is behind us, I thought it would be interesting to look back on the year and recap our most popular webinars. I’ve gathered together a list of the top 10 academic webinars from 2014 below. All these webinars are available on-demand, and you can watch the recording by clicking on the webinar titles below.

-----------------------------------------------

See What’s New in Maple 18 for Educators

In this webinar, an expert from Maplesoft will explore new features in Maple 18, including improved tools for developing quizzes, enhanced tools for visualizations, updated user interface, and more.

Introduction to Teaching Calculus with Maple: A Complete Kit

During this webinar you will learn how to boost student engagement with highly interactive lectures, reinforce concepts with built-in “what-if” explorations, consolidate learning with carefully-constructed homework questions, and more.

Maplesoft Solutions for Math Education

In this webinar, you will learn how Maple, The Möbius Project, and Maplesoft’s testing and assessment solutions are redefining mathematics education.

Teaching Concepts with Maple

This webinar will demonstrate the Teaching Concepts with Maple section of our website, including why it exists and how to use it to help students learn concepts more quickly and with greater insight and understanding.

Revised Calculus Study Guide - A Clickable-Calculus Manual

This webinar will provide an overview of the Revised Calculus Study Guide, the most complete guide to how Maple can be used in teaching and learning calculus without first having to learn any commands.

Clickable Engineering Math: Interactive Engineering Problem Solving

In this webinar, general engineering problem-solving methods are presented using clickable techniques in the application areas of mechanics, circuits, control, and more.

Hollywood Math 2

In this second installment of the Hollywood Math webinar series, we will present some more examples of mathematics being used in Hollywood films and popular hit TV series.

Robotics Design in Maple and MapleSim

In this webinar, learn how to quickly create multi-link robots by simply defining DH parameters in MapleSim. After a model is created, learn to extract the kinematic and dynamic equations symbolically in Maple.

Introduction to Maple T.A. 10

This webinar will demonstrate the key features of Maple T.A. from both the instructor and student viewpoint, including new features in Maple T.A. 10.

The Möbius Project: Bringing STEM Courses Online

View this presentation to better understand the challenges that exist today when moving a STEM course online and to find out how the Maplesoft Teaching Solutions Group can help you realize your online course vision.

-----------------------------------------------

Are there any topics you’d like to see us present in 2015? Make sure to leave us a comment with your ideas!

Kim

D_Method.mw

The classical Draghilev’s method.  Example of solving the system of two transcendental equations. For a single the initial approximation are searched 9 approximate solutions of the system.
(4*(x1^2+x2-11))*x1+2*x1+2*x2^2-14+cos(x1)=0;
2*x1^2+2*x2-22+(4*(x1+x2^2-7))*x2-sin(x2)=0; 
x01 := -1.; x02 := 1.;

Equation: ((x1+.25)^2+(x2-.2)^2-1)^2+(x3-.1)^2-.999=0;



a_cam_3D.mw

Cam mechanism animation.   Equation:  (xx2-1.24)^10+5*(xx1-.66)^10-9.=0
a_cam.mw

Transformation and rotation.

transformation.mw

The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the world (regardless of the students' nationalities). One can see some problems and answers here. I find it remarkable that a lot of these problems can be done with Maple. Here is a sample (The DirectSearch package should be downloaded from http://www.maplesoft.com/applications/view.aspx?SID=101333 and installed in your Maple.).

Hope the reader will try to continue the above.

Download Putnam_done_with_Maple.mw

Today science professionals in engineering software used to only work on the desktop and even just looking to download and use mobile apps math; but they are not able to design their own applications.Maplesoft to set the solution to it through its Maple package; software supports desktop and mobile; solves problems of analysis and calculation with Embedded Components. To show this we have taken the area of different mathematical topics; fixed horizontally to a certain range of parameters and not just a constant as it is customary to develop. This paper shows how the Embedded Components allow us to develop mathematics in all areas. Achieving build applications that are interactive in mobile devices such as tablets; which are used at any time. Maple gives us design according to our university or research need, based on contemporary and modern mathematics.With this method we encourage students, teachers and researchers to use graphics algorithms.

CSMP_PUCP_2014.pdf

Coloquio_PUCP.mw

Lenin Araujo Castillo

Physics Pure

Computer Science

The procedure  NumbersGame  generalizes the well-known 24 game  (implementation in Maple see here), as well as related issues (see here and here).

Required parameters of the procedure:

Result is an integer or a fraction of any sign.

Numbers is a list of positive integers.

Optional parameters:

Operators is a list of permitted arithmetic operations. By default  Operators is  ["+","-","*","/"]

NumbersOrder is a string. It is equal to "strict order" or "arbitrary order" . By default  NumbersOrder is "strict order"

Parentheses is a symbol  no  or  yes . By default  Parentheses is  no 

The procedure puts the signs of operations from the list  Operators  between the numbers from  Numbers  so that the result is equal to Result. The procedure finds all possible solutions. The global  M  saves the list of the all solutions.

Code the procedure:

restart;

NumbersGame:=proc(Result::{integer,fraction}, Numbers::list(posint), Operators::list:=["+","-","*","/"], NumbersOrder::string:="strict order", Parentheses::symbol:=no)

local MyHandler, It, K, i, P, S, n, s, L, c;

global M;

uses StringTools, ListTools, combinat; 

 MyHandler := proc(operator,operands,default_value)

      NumericStatus( division_by_zero = false );

      return infinity;

   end proc;

   NumericEventHandler(division_by_zero=MyHandler); 

if Parentheses=yes then 

It:=proc(L1,L2)

local i, j, L;

for i in L1 do

for j in L2 do

L[i,j]:=seq(Substitute(Substitute(Substitute("( i Op j )","i",convert(i,string)),"j",convert(j,string)),"Op",Operators[k]), k=1..nops(Operators));

od; od;

L:=convert(L, list);

end proc; 

P:=proc(L::list)

local n, K, i, M1, M2, S;

n:=nops(L);

if n=1 then return L else

for i to n-1 do

M1:=P(L[1..i]); M2:=P(L[i+1..n]);

K[i]:=seq(seq(It(M1[j], M2[k]), k=1..nops(M2)), j=1..nops(M1))

od; fi;

K:=convert(K,list);

end proc;

if NumbersOrder="arbitrary order" then S:=permute(Numbers); K:=[seq(op(Flatten([op(P(s))])), s=S)] else  K:=[op(Flatten([op(P(Numbers))]))] fi; 

else 

if NumbersOrder="strict order" then

K:=[convert(Numbers[1],string)];

for i in Numbers[2..-1] do

K:=[seq(seq(cat(k, Substitute(Substitute(" j i","j",convert(j,string)),"i",convert(i,string))), k in K), j in Operators)]

od;   else 

S:=permute(Numbers);

for s in S do

L:=[convert(s[1],string)];

for i in s[2..-1] do

L:=[seq(seq(cat(k, Substitute(Substitute(" j i","j",convert(j,string)),"i",convert(i,string))), k in L), j in Operators)]

od; K[s]:=op(L) od; K:=convert(K,list) fi;  

fi; 

M:='M'; c:=0;

for i in K do

if parse(i)=Result then c:=c+1; if Parentheses=yes then M[i]:= convert(SubString(i,2..length(i)-1),symbol)=convert(Result,symbol) else M[i]:=convert(i,symbol)=convert(Result,symbol) fi; fi;

od; 

if c=0 then M:=[]; return `No solutions` else M:=convert(M,list);  op(M) fi; 

end proc:

Examples of use.

Example 1:

NumbersGame(1/20, [$ 1..9]);

     1 * 2 - 3 + 4 / 5 / 6 * 7 / 8 * 9 = 1/20

Example 2. Numbers in the list  Numbers  may be repeated and permitted operations can be reduced:

NumbersGame(15, [3,3,5,5,5], ["+","-"]);

         3 - 3 + 5 + 5 + 5 = 15

Example 3. 

NumbersGame(10, [1,2,3,4,5]);

         1 + 2 + 3 * 4 - 5 = 10

If the order of the number in Numbers is arbitrary, then the number of solutions is greatly increased (10 solutions displayed):

NumbersGame(10, [1,2,3,4,5], "arbitrary order"):

nops(M);

for i to 10 do

M[1+50*(i-1)] od;

If you use the parentheses, the number of solutions will increase significantly more (10 solutions displayed):

NumbersGame(10, [1,2,3,4,5], "arbitrary order", yes):

nops(M);

for i to 10 do

M[1+600*(i-1)] od;

Game.mws

A new release of the Maple T.A. MAA Placement Test Suite  is now available.

The latest release takes advantage of the streamlined interface, accessibility from tablets, and other new features of Maple T.A. 10. It also includes new testing content to determine if your students understand the concepts needed for success in their algebra and precalculus courses; new parallel versions of the calculus concepts readiness test; and improved searching and browsing of testing content.

To learn more, visit What’s New in Maple T.A. MAA Placement Test Suite 10.

eithne