Throughout the course of a year, Maple users create wildly varying applications on all sorts of subjects. To mark the end of 2018, I thought I’d share some of the 2018 submissions to the Maple Application Center that I personally found particularly interesting.

Solving the 15-puzzle, by Curtis Bright. You know those puzzles where you have to move the pieces around inside a square to put them in order, and there’s only one free space to move into?  I’m not good at those puzzles, but it turns out Maple can help. This is one of collection of new, varied applications using Maple’s SAT solvers (if you want to solve the world’s hardest Sudoku, Maple’s SAT solvers can help with that, too).

Romeo y Julieta: Un clasico de las historias de amor... y de las ecuaciones diferenciales [Romeo and Juliet: A classic story of love..and differential equations], by Ranferi Gutierrez. This one made me laugh (and even more so once I put some of it in google translate, which is more than enough to let you appreciate the application even if you don’t speak Spanish). What’s not to like about modeling a high drama love story using DEs?

Prediction of malignant/benign of breast mass with DNN classifier, by Sophie Tan. Machine learning can save lives.

Hybrid Image of a Cat and a Dog, by Samir Khan. Signal processing can be more fun that I realized. This is one of those crazy optical illusions where the picture changes depending on how far away you are.

Beyond the 8 Queens Problem, by Yury Zavarovsky. In true mathematical fashion, why have 8 queens when you can have n?  (If you are interested in this problem, you can also see a different solution that uses SAT solvers.)

Gödel's Universe, by Frank Wang.  Can’t say I understood much of it, but it involves Gödel, Einstein, and Hawking, so I don’t need to understand it to find it interesting.

i have two ode equations, when try to solve, i face this error
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system
any comment or help to solve this? ( or any simplifying comments to solve) . thnx in advance

 

Download zzv.mw

Hi!

I want to plot the approximation of a surface by polynomials. The surface is given by (x,y,f(x,y)) where f(x,y) is given by the following expression

proc (x) options operator, arrow; (sum(i*cos((i+1)*(-2+4*x[1])+i), i = 1 .. 5))*(sum(i*cos((i+1)*(-2+4*x[2])+i), i = 1 .. 5)) end proc

with both variables varying in the interval [0,1]. Then, by using the Bernstein polynomials of two variables (see, for instance, this paper for details  https://www.sciencedirect.com/science/article/pii/0021904589900956), the graph of the resulting (plot3d) surface (x,y,p(x,y))  it is not even like to the original surfaces.

Please, see this PDF of what I have done:  plots.pdf

Some idea or suggestion?

Thanks!

numeric.mws

Dear Colleagues,
Please give advice - How correct in Maple can be solve the heat nonlinear equation system with perfect thermal contact conditions?

Using procedure dsolve (numeric) Maple cannot determine type of problem (initial or boundary).

****
initial/boundary conditions specified at too many points 1
Error, (in dsolve/numeric/type_check) cannot determine type of problem (initial or boundary), as conditions are given at 4 points
****
 

In attachment Maple file - numeric.

Maybe anyone can get a simple exaple of the maple code for numeric solution of this  task?

Download numeric.mws

I am brand new to Maple Cloud and Maple Player.

I have uploaded two worksheets to the cloud, and my wife has just installed Maple Player on her laptop.

In Maple Player, the second worksheet shows the shareable symbol but the first doesn't even thought I uploaded both in the same way by clicking on the upload symbol in the Maple Cloud palette. Why is the first worksheet not shareable?

When my wife displays the second worksheet she is able to move its sliders but they do not change the display as they do when I move the sliders within Maple2016. How can she change the display?

Here is a link to the second worksheet:

Cassinian_oval.mw

Say I have 2 matrices, in which the elements themselves are vectors.

I'm looking for a way to perform matrix multiplication on these so that rather than having the first element as x11y11+x12y21+x13y31

It would be x11.y11+x12.y21+x13.y31 where . is the dot product on the elements of each matrix.

I know I could write a procedure to do this manually but I was wondering if there's any pre-made operations (or modifiers on the Multiply operation) to do this.

How do I plot the optimal control functions in an optimal control problem ?

Hello,

I have been working on Maxima and minima, I am able to extract the eigen values for the expression.
Based on following conditions I am able to find out the critical point is maxima or minima or saddle or inconsistant

If all the eigenvalues are positive, the point is a minimum.
If all the eigenvalues are all negative, it's a maximum.
If some eigenvalues are positive, some are negative, and none are zero, then it's a saddle point.
If any eigenvalues are zero, the test is inconclusive

I want to return all the critical points and their extrema.
just for example : For one perticular function I got a Eigen values as which I can find using sign function.

EigenValues := [[-.381966011250105+0.*I, -2.61803398874989+0.*I], [.414213562373095+0.*I, -2.41421356237309+0.*I]]
signDetails := [seq([seq(sign(EigenValues[i][j]), j = 1 .. nops(EigenValues[i]))], i = 1 .. nops(EigenValues))] #

 signDetails :=[[-1, -1], [1, -1]]

Now if I have a 0 in a list. Sign function returns 1 for 0, which is incorrect. How can I handle such conditions

if I have

EigenValues := [[-.381966011250105+0.*I, -2.61803398874989+0.*I], [.414213562373095+0.*I, -2.41421356237309+0.*I], [0, 2]]

I would like to have output [[-1, -1], [1, -1], [0, 1]],

I would like to know how is it possible return output based on above list

in this case my return shouble something like this [maxima, saddle, inconclusive].

Thank you

Here is a simple procedure that works fine if entered using 1D Maple input
> Q:=proc(x)
sin(x)
end proc;
but if you use 2D math input
> q:=proc(x)
sin(x);

  end proc;

Error, unterminated procedure
    Typesetting:-mambiguous(qAssignTypesetting:-mambiguous(

      procApplyFunction(x) sinApplyFunction(x),

      Typesetting:-merror("unterminated procedure")))
Error, unable to parse
    Typesetting:-mambiguous(  Typesetting:-mambiguous(end,

      Typesetting:-merror("unable to parse")) procsemi)

Ouch! But to confuse things further the following procedures may be entered using 2D math and work fine:
>H := proc (x) x^2*sin(x) end proc;
>K := proc (x) sin(x^2) end proc;
Doesn't make any sense to me. Perhaps 2D math is not ready for prime time?

 

So I have got the following integral:

around the square with corners 2, 2i, -2, -2i oriented counter-clockwise.

Do I need to tell Maple that z is complex? Do I need to manually parametrize z? Is Maple aware of Cauchy's theorem?

What is the quickest way of evaluating this sort of integrals.

I'm still a maple beginner and looking for a workable solution to the following problem. I have already solved these "by hand" and would now like to control them.

The following equation should be solved:

diff(u(x, t), t, t)-c^2*(diff(u(x, t), x, x))

The approach function would be for example:

u := a(x)*sin(k1*(-c*t+x))

It would be great if maple could give me the solution again in this example:

solution = -c^2*(d^2*a*sin(k1*(-c*t+x))/dx^2+2*d*a*k1*cos(k1*(-c*t+x))/dx)

How exactly do I do this best?
Thanks a lot!
Frank

Hi,

How to simulate 1000 times the Dice1 experiment and put the results in a list to search for the percentils of A=[A1,..,A1000]

( See attachment)

Thanks

QuestionSimulation.mw

how can solve ordinary differenatial equation in maple?

how can use laplce transformation for this equation in maple?

U0 := proc (x) options operator, arrow; cosh(sqrt(2)*x)-1 end proc;
sys_ode := diff(Uc(x), x, x)-(2*(1+U0(x)))*Uc(x) = 0;

Download a.mw

Hi,

Persay I have a sinusodal function or dampened sinusodial; it is understand that the domain is from negative infinity to infinity.  Say I wish to find the zeros or a certain y value of a sinusodial on a restricted domain - say from A to B. How would I tell maple -syntax wise- to solve on that restricted domain? Using the solve feature on maple, it only yields 1 value that satisfies the condition I give it .

Thank you all for the support; you al l are allowing to me develop a better understanding for maple.

say I have the functions:

y=e^x*sin(x)

y=e

i wish to find all the x values that satisfy that system on the x domain of 0 to 100

Download Physics-Updates.mw
 

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