Hi all

How can I realize the following code in maple:

 EquCon := K[4]*(diff(W(x), x, x, x, x))-omega^2*W(x)

EquConFour := subs((1/2)*(int(W(kappa)*exp^(-J*kappa*x), kappa = -infinity .. infinity))/Pi, EquControl)

Thanks~

if you want a random interger between 0 and 100

what will be the command?

For implicitplot of say (cos(\theta))^2, I had to use 'factor' in the options for the plot so that it considers cos(theta) also while plotting. But I couldn't do the same in implicitplot3d. How can I achieve this plotting of all factors of a function for implicitplot3d?

this is the matlab is it possible to rewrite it in simple maple code

J = rand()+1e-10;

function [M, num, E] = ising(N,J)

B = 0;

M = []; % The total magnetic field of the system

E = []; % The total energy of the system

randTol = 0.1; % The tolerance, dampens the spin flip process

% First we generate a random initial configuration

spin = (-1).^(round(rand(N)));

% Then we let the system evolve for a fixed number of steps

for i=1:1000,

% Calculating the total spin of neighbouring cells

neighbours = circshift(spin, [ 0 1]) + ...

circshift(spin, [ 0 -1]) + ...

circshift(spin, [ 1 0]) + ...

circshift(spin, [-1 0]);

% Calculate the change in energy of flipping a spin

DeltaE = 2 * (J*(spin .* neighbours) + B*spin);

% Calculate the transition probabilities

p_trans = exp(-DeltaE);

% Decide which transitions will occur

transitions = (rand(N) < p_trans ).*(rand(N) < randTol) * -2 + 1;

% Perform the transitions

spin = spin .* transitions;

% Sum up our variables of interest

M = sum(sum(spin));

E = -sum(sum(DeltaE))/2; % Divide by two because of double counting

% Display the current state of the system (optional)

image((spin+1)*128);

xlabel(sprintf('J = %0.2f, M = %0.2f, E = %0.2f', J, M/N^2, E/N^2));

set(gca,'YTickLabel',[],'XTickLabel',[]);

axis square; colormap bone; drawnow;

end

% Count the number of clusters of 'spin up' states

[L, num] = bwlabel(spin == 1, 4);

############################# 

For people new to Maple, an easy way to learn how to code may be Tutor Syntax, that is the technique of generating code by selecting everything in a Tutor dialog Maple Command window and then copying it to a current session.

The code can then be edited to tailor it to user’s needs. A problem with this technique is the copied syntax contains many single quotes (‘ ‘). The single quotes, which are usually not needed if the program in current session is short and specific, increase the difficulty when editing copied syntax. The attached file (mby2.mw) shows a method which removes the single quotes by using the SubstitueAll command in the StringTools package. One drawback: any strings inside the original syntax (e.g., “#78000E”) must be removed before the syntax can be converted to a string.

Is there a better way to generate code from Tutor dialog so it can be edited (without single quotes) in user’s current session?

mby2.mw

hi.please help me for remove error'' 

Error, illegal use of an object as a name''

thanks

PLATE.mw

Download PLATE.mw

When the Physics package is loaded, Maple returns the following error in connection with the simple statement 2*D[1]:

Error, (in TypeTools/ac_var_local) unable to determine the anticommutative character of D[1]

Why that? Although to no avail, for D[1] there is no problem. Note that the above error results even without having set up any anticommutative prefixes or the likes in Physics Setup.

PS: I am using Maple 17.

Hi,
I would like to present you a recurring problem of mine.

Context:

It is very common, in Modeling and Simulation activities, to account for Uncertainties.

In order to set these ideas down, consider a computational code F (typically a code that solves a set of PDEs in space (M) and time (t) ) and its response Y = F(M,t) (here Y is a short for Y(M,t)).

This response Y usually depends also on some set P of parameters (each of them considered as a scalar quantity) .
A more convenient way to note Y  is Y(M, t | P) where the "|" character is used here to express that Y is considered as a function of M and t for each given value of P.
Generally one does not consider Y as a whole but more often one focuses on some quantity of interest (Q) derived from Y through applying it some operator G (for example the operator max(Y) over some space and time domain).

Applying G generally makes  Q to appear as a function of P alone.
In Uncertainty Quantification activities, a major concern is to understand how uncertainties about P modify the values of Q ?
The classical framework is to consider P as a (multi-dimensionnal) random variable. 
One of the most common problems is then to assess some basic characteristics of Q, where Q is considered as a function of P (a quick and notional notation is Q = H(P) = (G°F)(X, t | P)).

The simpler and faster method to do this is based on a Taylor expansion of H (provided some conditions hold) arround some particular point p* (p* could be the mean of the multi-dimensional distribution of P)
One writes, for every value p of P :

Q = H(p) = H(p*) + (H')^t (p-p*) + 1/2 (p-p*)^t H" (p-p*) ...

where
  H'  is the gradient vector of H according to P at point P = p*
  H" is the hessian matrix of H according to P at point P = p*
  (p-p*) is the vector of differences, assumed to be "small"

Let E the usual "mathematical expectation" operator.
Let us assume  p* denotes the mean of P.
Then, applying E to  the previous formula gives :

E(Q) = E(H(p*)) + E(...) + ....

Assuming some conditions hold, the first order mathematical expectation E(Q) of Q is simply E(H(p*)) = H(p*) = H(E(P))

Some little algebra gives the first order approximation of the variance V(Q) = E(Q^2)-(E(Q))^2 of Q : 

V(Q) = (H')^t V(P) H'  where V(P) is the variance matrix of P

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

Problem

I would like to define the operator E so that I could derive automatically approximations of the first 4 moments of Q, up to any desired order.
In particular, order 2 is often necessary as soon as (G°F) is highly non linear regarding P ; and estimations of the 3rd and 4th moments is of great help to determine how much symetric or flat is the distribution of Q.

The idea is to define an operator E with suitable properties and to apply it to a multivariate taylor expansion of Q^n where n is any positive integer

I tried to do this by my own (look to the supplied .mw file) but I do not have sufficient skill in Maple to complete the job.

Could someone help me ?

Even if I am not qualified in saying this, I believe that this type of approximation of the different moments of Q could be included in a future release of Maple ?


Thanks in advance 

Download MathematicalExpectation.mw

The expression (D[1]@D[2])(f) is equivalent to D[1,2](f). On grounds of that, I would naively have expected that (D[1]@D[1])(f) was equivalent to D[1,1](f). But it seems not to be, their lprint-versions being different:

expr1 := (D[1]@D[1])(f):
expr2 := D[1,1](f):
simplify(expr1 - expr2);
simplify(expr1 - expr2,`@`);
lprint(expr1);
lprint(expr2);

(D[1]@@2)(f)
D[1, 1](f)

I am curious to know why it has been implemented this way? Have I fundamentally misunderstood something?

I'm working in a tridimensional euclidean space, with vectorial functions of the type:

Fi(t)=<fix(t),fiy(t),fiz(t)>

Fi'(t)=<fix'(t),fiy'(t),fiz'(t)>

The two odes are of the type:

ode1:=K1*F1''(t)=K2*F2(t)&xF3(t)+...

While there are other non-differential vectorial equations like:

eq1:=K4*F4''(t)=(K5*F5(t)&x<0,1,0>)/Norm(F6(t))+..., etc

Is there a way i can input this system in dsolve with vectors instead of scalars? And without splitting everything into its 3 vectorial components? I can't make maple realize some of the Fi(t) functions are vectors, it counts them as scalars and says the number of functions and equations are not the same.

Thank you!

Hi

Hope a nice day for all

restart;

#  *%   define the product of between two operators, and q real number
a*%b = q*b*%a+1;

# First I would like to give a simple for

 a^n*%b;
# and                                    
a*%b^n;

them deduce a general for                                      

b^n*%a^k*%b^N*%a^K-q^(k*N-n*K)*b^N*%a^K*%b^n*%a^k;

 where n, k and k greater than 1 and  n geater than k

Simplification.mw

Thanks for your help

If I am in the Maple debugger, stopped in a routine, how can I navigate between stack frames, such as looking at the variables of the calling function?

"outfrom" is not sufficient for this purpose as that continues execution until return, which would change the variables of the routine I am in, and could potentially take a long time. And more importantly for my particular purpose, the routine I am stopped in is a package's "I found an error" routine which is (deliberately) throwing an exception, so there will not be any return.

I can use where or where? to look at the name of the calling routines. Unfortunately, for the code I am debugging, the calling routine is being dynamically loaded so I do not have a file name for it and I cannot put a persistent breakpoint in it: I need to climb the tree of dynamic calls with their various parameters in order to figure out how the error occured.

This is the second of three blog posts about working with data sets in Maple.

In my previous post, I discussed how to use Maple to access a large number of data sets from Quandl, an online data aggregator. In this post, I’ll focus on exploring built-in data sets in Maple.

Data is being generated at an ever increasing rate. New data is generated every minute, adding to an expanding network of online information. Navigating through this information can be daunting. Simply preparing a tabular data set that collects information from several sources is often a difficult and time consuming effort. For example, even though the example in my previous post only required a couple of lines of Maple code to merge 540 different data sets from various sources, the effort to manually search for and select sources for data took significantly more time.

In an attempt to make the process of finding data easier, Maple’s built-in country data set collects information on country-specific variables including financial and economic data, as well as information on country codes, population, area, and more.

The built-in database for Country data can be accessed programmatically by creating a new DataSets Reference:

CountryData := DataSets:-Reference( "builtin", "country" );

This returns a Reference object, which can be further interrogated. There are several commands that are applicable to a DataSets Reference, including the following exports for the Reference object:

exports( CountryData, static );

The list of available countries in this data set is given using the following:

GetElementNames( CountryData );

The available data for each of these countries can be found using:

GetHeaders( CountryData );

There are many different data sets available for country data, 126 different variables to be exact. Similar to Maple’s DataFrame, the columns of information in the built-in data set can be accessed used the labelled name.

For example, the three-letter country codes for each country can be returned using:

CountryData[.., "3 Letter Country Code"];

The three-letter country code for Denmark is:

CountryData["Denmark", "3 Letter Country Code"];

Built-in data can also be queried in a similar manner to DataFrames. For example, to return the countries with a population density less than 3%:

pop_density := CountryData[ .., "Population Density" ]:

pop_density[ `Population Density` < 3 ];

At this time, Maple’s built-in country data collection contains 126 data sets for 185 countries. When I built the example from my first post, I knew exactly the data sets that I wanted to use and I built a script to collect these into a larger data container. Attempting a similar task using Maple’s built-in data left me with the difficult decision of choosing which data sets to use in my next example.

So rather than choose between these available options, I built a user interface that lets you quickly browse through all of Maple’s collection of built-in data.

Using a couple of tricks that I found in the pages for Programmatic Content Generation, I built the interface pictured above. (I’ll give more details on the method that I used to construct the interface in my next post.)

This interface allows you to select from a list of countries, and visualize up to three variables of the country data with a BubblePlot. Using the preassigned defaults, you can select several countries and then visualize how their overall number of internet users has changed along with their gross domestic product. The BubblePlot visualization also adds a third dimension of information by adjusting the bubble size according to the relative population compared with the other selected countries.

Now you may notice that the list of available data sets is longer than the list of available options in each of the selection boxes. In order to be able to generate BubblePlot animations, I made an arbitrary choice to filter out any of the built-in data sets that were not of type TimeSeries. This is something that could easily be changed in the code. The choice of a BubblePlot could also be updated to be any other type of Statistical visualization with some additional modifications.

You can download a copy of this application here: VisualizingCountryDataSets.mw

You can also interact with it via the MapleCloud: http://maplecloud.maplesoft.com/application.jsp?appId=5743882790764544

I’ll be following up this post with an in-depth post on how I authored the country selector interface using programmatic content generation.

Hi all

Is Ising a package?

for i = 1:12000

%while (1),

% Choose a random value between 0 and 1 for the interaction strength

J = rand()+1e-10;

% Perform a simulation

[M, N, E] = ising2(n_grid, J);

% Records the results

Ms = [Ms M/(n_grid^2)];

Es = [Es E/(n_grid^2)];

Ns = [Ns N];

Js = [Js J];

i = i+1;

Is there an elegant way to plot the region between the surfaces z=-y^2 and z=x^2, only on the domain of the XY-plane bounded by the triangle with vertices (0,0), (1,0) and (1,1)?