Can Maple perform huge calculations via parallel-pooling (i.e working on multiple or all CPUs) similar to Matlab?

verify(2*cos(phi)^2-1, cos(2*phi), equal); returns FAIL even though is a trig identify. Any ideas why?
 

Maple currently can't integrate things like sin(x)^n or cos(x)^n. These have antiderivative in terms of  hypergeometric functions.

Is there a technical reason why Maple at version 18 still can't integrate these? Will it be able to in next version?

int(cos(x)^k, x) 
int(sin(x)^k, x) 

fyi, These are the antiderivatives

Same problem for tan(x)^n....  I am asking because Maple is able to solve many ODE's but some results contains unevaluated integrals such as the above. 

When making this call to dsolve

restart;
ode:=diff(y(x),x)=1:
stopat(dsolve);
dsolve(ode,y(x));

Then in the debugger, I see that dsolve signature is

dsolve := proc(ODEs::{anything} := NULL, 
                {atomizenames::truefalse := true, build::truefalse := false, type::name := 'none'})

When typing print(ODEs) inside the debugger, it gives "diff(y(x),x)=1" which is correct.

But where is the second argument I passed to dsolve in the above call, which is "y(x)" gone?  I also do print(_nparams) inside the debugger and Maple returns 1 and not 2.

I expected to see 2 since I passed in two arguments to dsolve.

dsolve actually works without passing y(x), as follows

dsolve(ode);

And it seems Maple figure inside what is the dependent variable.

But my question is, is the second argument being thrown away before calling dsolve? If not, why it does not show in the debugger?   Is there some other pre-processing being done between the time the user calls dsolve() and the time the debugger is called?

So i have beeing working with finite elements and i have the stifness matrix that i came with Maple as you can see here:

Ke := Matrix(4, 4, {(1, 1) = (12*I)*E/l^3, (1, 2) = (6*I)*E/l^2, (1, 3) = -(12*I)*E/l^3, (1, 4) = (6*I)*E/l^2, (2, 1) = (6*I)*E/l^2, (2, 2) = (4*I)*E/l, (2, 3) = -(6*I)*E/l^2, (2, 4) = (2*I)*E/l, (3, 1) = -(12*I)*E/l^3, (3, 2) = -(6*I)*E/l^2, (3, 3) = (12*I)*E/l^3, (3, 4) = -(6*I)*E/l^2, (4, 1) = (6*I)*E/l^2, (4, 2) = (2*I)*E/l, (4, 3) = -(6*I)*E/l^2, (4, 4) = (4*I)*E/l})

How can i re-write this matrix to put in this form:


Thanks

Hi, everybody.

Is there a command or a way to assign an initial value to animate plot?

Trivial example:

animate(plot,[m*x,x=-10..10],m=-10..10)

but initial value for m would be m=1 so the initial render will present the line with slope 1.

As always, thank you all in advanced.

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?