## How I can solve eigenvalue problem...

Hello,

How I can extract coefficients from and by calculating determinant for Eigenvalue problem, the value of omega.

For more details please see attached PDF file.

Thanks so much.

eign.pdf

## running in multiprocessor...

How to run the following calculation in multiple processor

## view matrix as 2-d image instead of 1-d text...

In Maply 2018, inputting (entering in red text)

A := <<1,2,3>|<6,7,8>>;

produces output (in blue text)

A := Matrix(3, 2, {(1, 1) = 1, (1, 2) = 6, (2, 1) = 2, (2, 2) = 7, (3, 1) = 3, (3, 2) = 8}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

What must I do to make the output appear appear instead as a standard 2-d array, with big brackets to the left and right, 1st column = <1,2,3>; 2nd column = <6,7,8>?

Thank you.

## Unexpected solution to PDE...

We solve Laplace's equation in the domain
in polar coordinates subject to prescribed Dirichlet data.

Maple produces a solution in the form of an infinite sum,
but that solution fails to satisfy the boundary condition
on the domain's outer arc.  Is this a bug or am I missing
something?

 > restart;
 > kernelopts(version);

 > with(plots):
 > pde := diff(u(r,t),r,r) + diff(u(r,t),r)/r + diff(u(r,t),t,t)/r^2 = 0;

 > a, b, c, d := 1, 2, Pi/6, Pi/2;

 > bc := u(r,c)=c, u(r,d)=0, u(a,t)=0, u(b,t)=t;

We plot the boundary data on the domain's outer arc:

 > p1 := plots:-spacecurve([b*cos(t), b*sin(t), t], t=c..d, color=red, thickness=5);

Solve the PDE:

 > pdsol := pdsolve({pde, bc});

Truncate the infinite sum at 20 terms, and plot the result:

 > eval(rhs(pdsol), infinity=20): value(%): p2 := plot3d([r*cos(t), r*sin(t), %], r=a..b, t=c..d);

Here is the combined plot of the solution and the boundary condition.
We see that the proposed solution completely misses the boundary condition.

 > plots:-display([p1,p2], orientation=[25,72,0]);

## I Have a problem in Do loop...

Dears, greeting for all

I have a problem, I try to explain it by a figure

This formula does not work.

I need to substitute n=0 to give G_n+1 as a function of the parameter s, then find the limit.

.where G_n is a function in s.

this is the result

## how to express eigenvector or eigenvalues in terms...

how to express eigenvector or eigenvalues in terms of fibonacci or lucas or golden ratio?

fibonacci ratio has many

f(n)/f(n-1) , all eigenvector can not divided by any one of them

## how to verify lambda calculus is computable and re...

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?

## Passing variable number of arguments...

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.

## Generation of numbers with Cauchy distribution in ...

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)?

## how to make diff(y(x),x) display as y'(x) in works...

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.

## Wrong values for Eigenvalues, depending on Digits ...

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_.

 >

Problems LinearAlgebra:-Eigenvalues, Digits, ':-datatype' = ':-sfloat', ':-datatype' = ':-complex'( ':-sfloat' )

 > restart;
 > interface( ':-displayprecision' = 5 ):
 > infolevel['LinearAlgebra'] := 5; myPlatform := kernelopts( ':-platform' ); myVersion := kernelopts( ':-version' );
 (1.1)

Example 1

 > A1 := Matrix( 5, 5, [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [-10201/1000, 30199/10000, -5049/250, 97/50, -48/5]] );
 (1.1.1)
 > LinearAlgebra:-Eigenvalues( A1 );
 CharacteristicPolynomial: working on determinant of minor 2 CharacteristicPolynomial: working on determinant of minor 3 CharacteristicPolynomial: working on determinant of minor 4 CharacteristicPolynomial: working on determinant of minor 5
 (1.1.2)
 > A11 := Matrix( op( 1, A1 ),( i,j ) -> evalf( A1[i,j] ), ':-datatype' = ':-sfloat' );
 (1.1.3)
 > Digits := 89; LinearAlgebra:-Eigenvalues( A11 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.1.4)
 > Digits := 90; LinearAlgebra:-Eigenvalues( A11 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.1.5)
 > A12 := Matrix( op( 1, A1 ),( i,j ) -> evalf( A1[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );
 (1.1.6)
 > Digits := 100; LinearAlgebra:-Eigenvalues( A12 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.1.7)
 > Digits := 250; LinearAlgebra:-Eigenvalues( A12 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.1.8)
 >
 >

Example 2

 > A2 := Matrix(3, 3, [[0, 1, 0], [0, 0, 1], [3375, -675, 45]]);
 (1.2.1)
 > LinearAlgebra:-Eigenvalues( A2 );
 IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 3 x 3 matrix IntegerCharacteristicPolynomial: Using prime 33554393 IntegerCharacteristicPolynomial: Using prime 33554383 IntegerCharacteristicPolynomial: Used total of  2  prime(s)
 (1.2.2)
 > A21 := Matrix( op( 1, A2 ),( i,j ) -> evalf( A2[i,j] ), ':-datatype' = ':-sfloat' );
 (1.2.3)
 > Digits := 77; LinearAlgebra:-Eigenvalues( A21 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.2.4)
 > Digits := 78; LinearAlgebra:-Eigenvalues( A21 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.2.5)
 > A22 := Matrix( op( 1, A2 ),( i,j ) -> evalf( A2[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );
 (1.2.6)
 > Digits := 58; LinearAlgebra:-Eigenvalues( A22 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.2.7)
 > Digits := 59; LinearAlgebra:-Eigenvalues( A22 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.2.8)
 >
 >

Example 3

 > A3 := Matrix(4, 4, [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-48841, 8840, -842, 40]]);
 (1.3.1)
 > LinearAlgebra:-Eigenvalues( A3 );
 IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix IntegerCharacteristicPolynomial: Using prime 33554393 IntegerCharacteristicPolynomial: Using prime 33554383 IntegerCharacteristicPolynomial: Used total of  2  prime(s)
 (1.3.2)
 > A31 := Matrix( op( 1, A3 ),( i,j ) -> evalf( A3[i,j] ), ':-datatype' = ':-sfloat' );
 (1.3.3)
 > Digits := 75; LinearAlgebra:-Eigenvalues( A31 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.3.4)
 > Digits := 76; LinearAlgebra:-Eigenvalues( A31 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.3.5)
 > A32 := Matrix( op( 1, A3 ),( i,j ) -> evalf( A3[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );
 (1.3.6)
 > Digits := 100; LinearAlgebra:-Eigenvalues( A32 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.3.7)
 > Digits := 250; LinearAlgebra:-Eigenvalues( A32 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.3.8)
 >
 >

Example 4

 > A4 := Matrix(8, 8, [[0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1], [-1050625/20736, 529925/1296, -15417673/10368, 3622249/1296, -55468465/20736, 93265/108, -1345/8, 52/3]]);
 (1.4.1)
 > LinearAlgebra:-Eigenvalues( A4 );
 CharacteristicPolynomial: working on determinant of minor 2 CharacteristicPolynomial: working on determinant of minor 3 CharacteristicPolynomial: working on determinant of minor 4 CharacteristicPolynomial: working on determinant of minor 5 CharacteristicPolynomial: working on determinant of minor 6 CharacteristicPolynomial: working on determinant of minor 7 CharacteristicPolynomial: working on determinant of minor 8
 (1.4.2)
 > A41 := Matrix( op( 1, A4 ),( i,j ) -> evalf( A4[i,j] ), ':-datatype' = ':-sfloat' );
 (1.4.3)
 > Digits := 74; LinearAlgebra:-Eigenvalues( A41 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.4.4)
 > Digits := 75; LinearAlgebra:-Eigenvalues( A41 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.4.5)
 > A42 := Matrix( op( 1, A4 ),( i,j ) -> evalf( A4[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );
 (1.4.6)
 > Digits := 100; LinearAlgebra:-Eigenvalues( A42 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.4.7)
 > Digits := 250; LinearAlgebra:-Eigenvalues( A42 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.4.8)
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

## has anyone tried to use Peter Fritzone's book with...

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

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",
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;

## How do you find Fourier Transform of non-integer p...

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

 (1)

 (2)

 (3)

 (4)

 (5)

## i want to plot a few equation with animate plot or...

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)]);

## Elliptical PDEs...

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.

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