how to verify lambda calculus is computable and realizable in maple?

is it possible to realize lambda calculus into algebra ?

how to use β-reduction to convert algebra function into lambda calculus?

is there a way to convert back ?

how to combine multiple lambda calculus into one lambda calculus and check computable and then convert back to algebra function?

I'm starting to use procs a lot just because they are more general and can more easily handle complex functionality.

I usually have to pass a function to them and that function may or may not take a series of arguments.

e.g.,

f := (x,y,a)->a*x*y;

g := proc(q, ...)

    q(x,y,...)

end proc;

g(f, 3);

Here 3 should be passed for a(using ... to represent it).

If I pass a function

h := (x,y)->x*y

then it would be g(f)

I could possibly use nops, ops, arrays, etc... but looking for the right solution.

Hello. To generate nine numbers with Cauchy distribution C(0,1) I use Sample(Random Variable(Cauchy(0, 1)), 9). Is there a way to make all generated numbers belong to the interval (-1,1)?

I spend some time searching and reading help. But not able to find if this is possible.

I use worksheet only (i.e. not 2D document). I have my display set as

I'd like diff(y(x),x) to display as y'(x) in output.

I know I can do this 

PDEtools:-declare(y(x), prime = x);

And that will make diff(y(x),x) display as y'  but I want y'(x). And the same for diff(y(x),x$2) to display as y''(x). And to be clear, y(x) will still display as y(x).  I am mainly interested in making the derivative display a little nicer if possible.

Is there a way to do this?

I am using 2019.1 on windows 10.

Hello!

I want to calculate Eigenvalues. Depending on values for digits and which datatype I choose Maple sometimes returns zero as Eigenvalues. Maybe there is a problem with the used routines: CLAPACK sw_dgeevx_, CLAPACK sw_zgeevx_.

Thank you for your suggestions!
 

Download Problems_LinearAlgebra_Eigenvalues.mw

has anyone tried to use Peter Fritzone's book with maplesim helloworld modelica??

The simple approach from Peter (creating a custom modelica component) is to getting started by running a simple simulation where x_dot(t) = - a*x,  where the normal form is x(t) = x^-a for logarithmic type decay.

plot of x(t) should be a decay curve.  

Maple Code

A:-LinkModel = fine, connects

SimData := A:-Simulate(outputs = x, returntype = datapoints, tf = 2);

Error, invalid input: Simulate expects value for keyword parameter [outputs, output] to be of type {list(algebraic), list(anyfunc(identical(t)))}, but received x
 

***********

Simcode

Model Main;

Imports

public HelloWorld HelloWorld1 annotation(Placement(transformation(origin={100.0,200.0},extent={{-20.0,-20.0},{20.0,20.0}},rotation=0)));
    annotation(
            Diagram(coordinateSystem(preserveAspectRatio=true, extent={{0,0},{200.0,200.0}}),graphics),
            Icon(coordinateSystem(preserveAspectRatio=true, extent={{0,0},{200.0,200.0}}),graphics={Rectangle(extent={{0,0},{200.0,200.0}}, lineColor={0,0,0})}),
            uses(Modelica(version="3.2.3")),
            experiment(
              StartTime = 0,
              StopTime = 2.0,
              __Maplesoft_solver = "ck45",
              __Maplesoft_adaptive = true,
              Tolerance = 0.1e-4,
              __Maplesoft_tolerance_abs = 0.1e-4,
              __Maplesoft_step_size = 0.1e-2,
              __Maplesoft_min_step_size = 0,
              __Maplesoft_max_step_size = 0,
              __Maplesoft_plot_points = 2000,
              __Maplesoft_numeric_jacobian = false,
              __Maplesoft_constraint_iterations = 50,
              __Maplesoft_event_iterations = 100,
              __Maplesoft_algebraic_error_control = false,
              __Maplesoft_algebraic_error_relaxation_factor = 1,
              __Maplesoft_rate_hysteresis = 0.1e-9,
              __Maplesoft_reduce_events = false,
              __Maplesoft_integration_diagnostics = false,
              __Maplesoft_compiler = true,
              __Maplesoft_compiler_optimize = true,
              __Maplesoft_scale_method = "none",
              __Maplesoft_plot_event_points = true
            )
    );

end Main;

class HelloWorld
    Real x (start =1);
    parameter Real a = 1;
equation
    der(x) = -a*x;
end HelloWorld;

Dear Maple users,

I want to find an expression for the Fourier Transform (FT) of an expression like  f(t)=exp(-t^2)/t^a, where a>0 is a constant.

I note that integer values of a (postive or negative) is ok; but non-integer fails. See sheet attached where I have tried 1 or 2 cases, a=0, 1, 0.3, etc.

So the questions are:

(1) how can I find the FT of the above for typical non-integer values of a>0 ?

(2) how can I find the FT of the above for general a -- i.e. declare a as a parameter?

Thanks

Nadeem

Download Sheet_fourier_1.mw

hi 

i want to plot this equations , i want to show that step by step and remind previous . i plot with animte plot but it do not show the previous

restart;
with(plottools);
co := blue;
with(plots);

t := 1;
for i from 20 by -1 to 0 do t := t+1; a[i] := -i*x/t+i; p[i] := plot(a[i], x = 0 .. 20, y = 0 .. 20, color = co, thickness = 3) end do;

plots[animate](plot, [a[k], x = 0 .. 20, y = 0 .. 20], k = [seq(i, i = 1 .. 20)]);

pde := (diff(u(r, theta), r) + r * diff(u(r, theta), r, r) + diff(u(r, theta), theta, theta) / r ) / r:
iv := u( 1, theta) = 0, u( 3, theta) = theta, u( r, 0) = 10, u( r, Pi/2) = 0:
           Maple 2019 returns a symbolic solution for PDE:
pdsolve([pde, iv], u(r, theta));
   But for the numeric option, it returns a message saying that Maple is unable to handle elliptical PDEs.
pdsolve(pde, {iv}, numeric, time = t, range = 1 .. 3);

Error, (in pdsolve/numeric) unable to handle elliptic PDEs
I found it strange.

Oliveira.

How to get the functional form of interpolation in the given example below

GP.mw

Hi

please help me, how could I write this? 

Hi, 

The procedure Statistics:-ChiSquareSuitableModelTest returns wrong or stupid results in some situations.
The stupid answer can easily be avoided if the user is careful enough.
The wrong answer is more serious: the standard deviation (in the second case below) is not correctly estimated.

PS: the expression "CORRECT ANSWER" is a short for "POTENTIALLY CORRECT ANSWER" given that what ChiSquareSuitableModelTest really does is not documented
 

Download ChiSquareSuitableModelTest.mw

How to get the result of this limit? I don't get the result.
 

limit(sum(1/(i*sqrt(i+1)+(i+1)*sqrt(i)), i = 1 .. n), n = infinity);

With Mathematica, I got the output is 1.

Hello. Let's say I have a list of many items. Well, let's list A:=[1,1.732,1.23,4.42,9,6.45,3.45,8.428,9.1,12]. How to get three numbers from it randomly?

In answers given in 

In https://www.mapleprimes.com/questions/227546-How-To-Make-Odetest-Verify-Dsolve

It shows that odetest() did not verify a solution to ODE becuase solution was using hypergeom special functions. If the solution to the ODE was in integral form, then odetest() will verify it OK.

But what to do if the solution I want to verify is already in hypergoem? If I try odetest() it will fail to verify now. Then I can try to convert the solution to integral form and try again.

But when  using convert(sol,Int) followed by odetest() it did not work.

The solutions I try to verify are hand solutions or book solutions, and not coming from dsolve. 

But some of them are the same solution that comes from dsolve() when not using the useInt option. 

Also, I am doing this all inside a Maple program. It is not an interactive process. So I can't do plots and look at them to decide on anything. So verification must all be implemented in code.

The question is: Why did convert(hand_solution,Int) not give the same result as dsolve(ode,useInt)? Is there another way around this? (May be I am asking for too much in this one based on answers in the above link, So that is OK if not possible. But I really like the solution given when using "useInt" option. Much more clear than otherwise).
 

Maple 2019.1

Download 072619_2.mw