The following limit does not return a value. Then the evalf gives a wrong answer.

The answer should be "undefined" or -infinity .. infinity.

limit(exp(n)/(-1)^n, n = infinity) assuming n::posint; evalf(%);

                       /exp(n)              \
                  limit|------, n = infinity|
                       |    n               |
                       \(-1)                /

                               0.

The same happens if you delete the assumption.

A similar problem occurs with

limit(sin(Pi/2+2*Pi*n), n = infinity) assuming n::posint;
                            -1 .. 1
without the assumption this would be appropriate.

A little late in the game, with no Maple 18 wishlist yet I'd like to get it started

granted all wishes for previous versions not yet applied should still, hopefully, be under consideration.  

1 - The abitlity to angle x-axis labels.

2 - Textplot option for text to rotate with graph as it is rotated.  Currently all textplot texts are held to the horizontal

Thanks to the community through Maplesoft Mapleprimes that could develop in Computational Mathematics Achievement Day at our institution.

libro de geometrias:

http://www.slideshare.net/kaizzerz/geometria-analitica-charles-h-lehmann

Greetings to all.

This past year I have on occasion shared mathematical adventures with cycle index computations and Maple, e.g. at these links:

• Fascinating cycle indices with Maple
• The enumeration of non-isomorphic graphs
• Automorphisms of the Petersen Graph.

Befitting the season I am sending another post to continue this series of cycle index computations. I present two Maple implementations of Power Group Enumeration as described by Harary and Palmer in their book "Graphical Enumeration" and by Fripertinger in his paper "Enumeration in Musical Theory." It was a real joy working with Maple to implement the computational aspects of their work, i.e. the Power Group Enumeration Theorem. Moreover the resulting software is easy to read, simple and powerful and has a straightforward interface, taking advantage of many different capabilities present in Maple.

The problem I am treating is readily described. Consider a cube in 3 space and its symmetries under rotation, i.e. rigid motions. We ask in how many different ways we may color the edges of the cube with at most N colors where all colors are completely interchangable, i.e. have the symmetric group acting on them in addition to the edge permutation group of the cube. At the following Math Stackexchange Link  I have posted the Maple code to implement the algorithms / formulas of Harary / Palmer / Fripertinger to solve this problem. The reader is invited to study and test these algorithms. It seems to me an excellent instance of computational combinatorics fun.

To conclude I would like to point out that these algorithms might be candidates for a Polya Enumeration Theorem (PET) package that I have been suggesting for a future Maple release at the above posts, the algorithms being of remarkable simplicity while at the same time providing surprisingly sophisticated combinatorics and enumeration methods.

Season's greetings!

Marko Riedel

I find this very strange. I see questions posted at Maple prime using a language other than English.

I do not know if this is a Mapleprime bug, or not. If this is not a bug, why is it allowed to post questions in a language other than English?
 

It would be nice if Maple had a procedure which could turn a procedurelist into a listprocedure.
I use these words in the sense they are used in dsolve/numeric.
Thus by a procedurelist I mean a procedure returning lists (of numbers).
By a listprocedure I mean a list of procedures all having the same formal parameters and each returning one number.
Thus a `convert/listprocedure`should accept a procedurelist p as input and give as output the corresponding listprocedure [p1,p2, ... pN] where N is the number of elements in the output from p.

I tried making a `convert/listprocedure` myself and in doing so found that it was not totally trivial.
I had lots of problems but did end up with something that seems to work.

convert-listprocedur.mw

But my main point is that Maple ought to have some such facility either as described available to the user or by changing fsolve, complexplot or what have you, so that procedurelists are accepted.

Hi

It's been 3+ months since we launched this new, experimental, Maple Physics: Research & Development webpage, containing fixes and new developments around the clock made available to everybody. Today we are extending this experience to Differential Equations and Mathematical functions, launching the Maple Differential Equations and Mathematical Functions: Research & Development Maplesoft webpage. Hey!

With these pages we intend to move the focus of developments directly into the topics people are actually working on. The experience so far has been really good, putting our development at high RPM, an exciting roller-coast of exchange and activity.

As with the Research version of Physics, when suggestions about DEs or Mathematical Functions are implemented or issues are fixed, typically within a couple of days when that is possible, the changes will be made available to everybody directly in this new Maplesoft webpage. One word of clarification: for now, these updates will not include numerical ODE or numerical PDE solutions nor their numerical plotting. Sorry guys. One step at a time :)

This first update today concerns Differential Equations: dsolve and pdsolve can now handle linear systems of equations also when entered in Vector notation (Matrices and Vectors), related to a post in Mapleprimes from October/29. Attached is a demo illustrating the idea.

Everybody is welcome to bring suggestions and post issues. You can do that directly in Mapleprimes or writing to physics@maplesoft.com. While Differential Equations and Mathematical Functions are two areas where the Maple system is currently more mature than in Physics, these two areas cover so many subjects, including that there are the Research and the Education perspectives, that the number of possible topics is immense. 

DEsAndMathematicalFu.pdf   DEsAndMathematicalFu.mw

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

Thу post is the answer to  http://www.mapleprimes.com/questions/200355-Clever-Cutter-3?reply=reply

This message contains two procedures . The first procedure called  LargestIncircle  symbolically looks for the largest circle inscribed in a convex polygon . Polygon must be specified as a list of lists of its vertices . If the polygon does not have parallel sides , the problem has a unique solution , otherwise may be several solutions . It is easy to prove that there is always a maximum circle that touches three sides of the polygon . Procedure code based on this property of the optimal solution.

The second procedure called  MinCoveringCircle  symbolically seeking smallest circle that encloses a given set of points. The set of points can be anyone not necessarily being vertices of a convex polygon. Procedure code based on the following geometric properties of the optimal solution , which can easily be proved :

1) The minimum covering circle is unique.

2) The minimum covering circle of a set Set can be determined by at most three points in  Set  which lie on the boundary of the circle. If it is determined by only two points, then the line segment joining those two points must be a diameter of the minimum circle. If it is determined by three points, then the triangle consisting of those three points is not obtuse.

Code of the 1st procedure:

restart;

LargestIncircle:=proc(L::listlist)

local n, x, y, P, S, T, Eqs, IsInside, OC, Pt, E, R, t, Sol, P0, R1, Circle;

uses combinat, geometry;

n:=nops(L); _EnvHorizontalName := x; _EnvVerticalName := y;

P:=[seq(point(A||i, L[i]), i=1..n)];

if nops(convexhull(P))<n then error "L should be a convex polygon" fi;

S:={seq(line(l||i,[A||i, A||(i+1)]), i=1..n-1), line(l||n,[A||n, A||1])};

Eqs:=map(lhs,{seq(Equation(l||i), i=1..n)});

T:=choose({seq(l||i, i=1..n)}, 3);

IsInside:=proc(Point, OC, Eqs)

convert([seq(is(eval(Eqs[i], {x=Point[1], y=Point[2]})*eval(Eqs[i], {x=OC[1], y=OC[2]})>0), i=1..n)], `and`);

end proc;

OC:=[add(L[i,1], i=1..n)/n, add(L[i,2], i=1..n)/n]; 

R:=0; point(Pt,[x,y]);

   for t in T do

     solve([distance(Pt,t[1])=distance(Pt,t[2]),      distance(Pt,t[2])=distance(Pt,t[3])],[x,y]);

     Sol:=map(a->[rhs(a[1]), rhs(a[2])], %);

     P0:=op(select(b->IsInside(b, OC, Eqs), Sol)); if P0<>NULL then R1:=distance(point(E,P0),      t[1]);

     if convert([seq(is(R1<=distance(E, i)), i=S minus t)], `and`) and is(R1>R) then R:=R1;      Circle:=[P0, R] fi; fi;

   od; 

Circle; 

end proc:

Code the 2nd procedure:

MinCoveringCircle:=proc(Set::{set, list}(list))

local S, T, t, d, A, B, C, P, R, R1, O1, Coord, L;

uses combinat, geometry; 

if type(Set, list) then S:=convert(Set, set) else S:=Set fi;

T:=choose(S, 2);

   for t in T do

      d:=simplify(distance(point(A, t[1]), point(B, t[2]))); midpoint(C, A, B);

      if convert([seq(is(distance(point(P, p), C)<=d/2), p in S minus {t[1], t[2]})], `and`)   then return            [coordinates(C), d/2] fi;

   od;

T:=choose(S, 3);

R:=infinity;

   for t in T do

      point(A, t[1]); point(B, t[2]); point(C, t[3]);

      if is(distance(A, B)^2<=distance(B, C)^2+distance(A, C)^2 and        distance(A,C)^2<=distance(B,        C)^2+distance(A, B)^2 and distance(B, C)^2 <= distance(A, C)^2 + distance(A, B)^2) then

      circle(c, [A,B,C],'centername'=O1); R1:=radius(c); Coord:=coordinates(O1);

      if convert([seq(is(distance(point(P, p), O1)<=R1), p in S minus {t[1], t[2], t[3]})], `and`) and is(R1<R) then    R:=R1; L:=[Coord, R] fi; fi;

   od; 

L; 

end proc: 

Examples of using the first procedure:

L:=[[0,2],[1,4],[4,4],[5,1],[3,0]]:

C:=LargestIncircle(L);

A:=plottools[disk](op(C), color=green):

B:=plottools[polygon](L, style=line, thickness=2):

plots[display](A,B, scaling=constrained);

The procedure can be used to find the largest circle inscribed in a convex shape, bounded by the curves, if these curves are approximated by broken lines:

L:=[seq([k,k^2], k=-1..2, 0.1)]:

C:=LargestIncircle(L);

A:=plottools[disk](op(C), color=green):

B:=plottools[polygon](L, style=line, thickness=2):

plots[display](A,B, scaling=constrained);

Examples of using the second procedure:

L:=[[0,2],[1,4],[4,4],[5,1],[3,0]]:

C:=MinCoveringCircle(L);

A:=plottools[circle](op(C), color=red, thickness=2):

B:=plottools[polygon](L, color=cyan):

plots[display](A,B);

The smallest circle covering 30 random points:

> roll:=rand(1..10):

L:=[seq([roll(), roll()], i=1..30)]:

C:=MinCoveringCircle(L);

A:=plottools[circle](op(C), color=red, thickness=2):

B:=seq(plottools[disk](L[i],0.07,color=blue), i=1..nops(L)):

C1:=plottools[disk](C[1], 0.07, color=red):

T:=plots[textplot]([C[1,1]-0.2, C[1,2]-0.2, "C"], font=[TIMES,ROMAN,16]):

plots[display](A, B, C1, T);

The attached presentation is the second one of a sequence of three that we want to do on Quantum Mechanics using Computer Algebra. The first presentation was about the equation for a quantum system of identical particles, the Gross-Pitaevskii equation (GPE). This second presentation is about the spectrum of its solutions. The level is that of an advanced undergraduate QM course. The novelty is again in the way these problems can be tackled nowadays in a computer algebra worksheet with Physics.

QuantumMechanics.pdf     Download QuantumMechanics2.mw

Edgardo S. Cheb-Terrab
Physics, Maplesoft

MapleSim 6.3 includes substantial improvements to the MapleSim simulation engine, resulting in faster model pre-processing times, more flexible code generation, and expanded support for Modelica-based custom components. 

For more information, see What’s New in MapleSim.

eithne

Hi,
Relevant developments in Physics happened during the last month and a 1/2, some of them of interest beyond the use of this package. Among the most exciting things I can mention:

1. The redefinition of the derivative rule for the complex components (abs, argument, conjugate, Im, Re, signum) together with the introduction of Wirtinger calculus, as an user-option to work with complex variables. In other words: it is now possible to compute taking z and its conjugate as independent variables and in equal footing.
2. Introduction of textbook mathematical display for all the inert functions of the mathematical language, also for unknown functions f(x).
3. New options in Physics:-Setup to indicate that some mathematical objects are real (different from assume(x, real), while integrated with `is` and `coulditbe`).
4. A rather large number of micro developments advancing the integration of Physics with simplify, expand and combine.
5. Another large number of micro developments for quantum mechanics.
6. New options in Physics:-Setup to redefine sum as Physics:-Library:-Add, and with that have access to multiindex summation directly from sum, for instance as in sum(f(i, j), i + j <= n), including related typesetting copy & paste.

As usual the latest version of the package is available for download in the Maplesoft Physics: Research & Development webpage  and in the zip there is a worksheet illustrating all these developments. Below I'm copying the section related to the new redefinesum option of Physics:-Setup and multiindex summation.

Thanks to everyone who provided feedback, it has been of great value and at the root of this new round of developments.

Download sum_in_physics.mw

Edgardo S. Cheb-Terrab
Physics, Maplesoft

The attached presentation is the first one of a sequence of three that we wanted to do on Quantum Mechanics using Computer Algebra. The level is that of an advanced undergraduate QM course. Tackling this topic within a computer algebra worksheet in the way it's done below, however, is an entire novelty, and illustrates well the kind of computations that can be done today with Maple & Physics.

Edgardo S. Cheb-Terrab
Physics, Maplesoft

The DirectSearch package is a powerful Maple  tool. However, every soft has its advantages and disadvantages. In particular, the DS has problems in the case of a thin feasible set in higher dimensions. Recently a serious bug in the DS was detected by me. Solving an optimization problem, the DirectSearch produces the error communication

Warning, initial point [x1 = 1., x2 = 1., x4 = 2., y1 = 2., y2 = 3., y4 = 2.] does not satisfy the inequality constraints; trying to find a feasible initial point
Error, (in DirectSearch:-Search) cannot find feasible initial point; specify a new one
 while that initial point satisfies the constraints.

Download opti.mw

Greetings to all.

As some of you may remember I made several personal story type posts concerning my progress in solving enumeration problems with the Polya Enumeration Theorem (PET). This theorem would seem to be among the most exciting in mathematics and it is of an amazing simplicity so that I never cease to suggest to mathematics teachers to present it to gifted students even before university. My previous efforts are documented at your site, namely at this MaplePrimes link I and this MaplePrimes link II.

I have been able to do another wonderful cycle index computation using Maple recently and I would like to share the Maple code for this problem, which is posted at Math StackExchange.com (this post includes the code) This time we are trying to compute the cycle index of the automorphism group of the 3-by-3-by-3 cube under rotations and reflections. I suggest you try this problem yourself before you look at my solution. Enjoy!

I mentioned in some of my other posts concerning PET that Maple really ought to come with a library of cycle indices and the functions to manipulate them. I hope progress has been made on this issue. I had positive feedback on this at the time here at your website. Do observe that you have an opportinuity here to do very attractive mathematics if you prepare a worksheet documenting cycle index facilities that you may eventually provide. This is good publicity owing to the fact that you can include images of the many geometric objects that appear which all look quite enticing and moreover potential readers get rewarded quickly as they discover that it takes little effort to master this theorem and proceed to work with symmetries themselves and investigate them. This sort of thing also makes nice slides.

With best wishes for happy combinatorics computing,

Marko Riedel