MaplePrimes Questions

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

 

How to run the following calculation in multiple processor

 

ADD.mw

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.

 

We solve Laplace's equation in the domain a < r and r < b, c < t and t < d
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);

`Maple 2019.1, X86 64 LINUX, May 21 2019, Build ID 1399874`

with(plots):

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

diff(diff(u(r, t), r), r)+(diff(u(r, t), r))/r+(diff(diff(u(r, t), t), t))/r^2 = 0

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

1, 2, (1/6)*Pi, (1/2)*Pi

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

u(r, (1/6)*Pi) = (1/6)*Pi, u(r, (1/2)*Pi) = 0, u(1, t) = 0, u(2, 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});

u(r, t) = Sum((1/6)*cos(3*signum(n1-1/4)*(-1+4*n1)*t)*(2*Pi*sin((1/2)*signum(n1-1/4)*Pi)*abs(n1-1/4)-6*Pi*sin((3/2)*signum(n1-1/4)*Pi)*abs(n1-1/4)+cos((3/2)*signum(n1-1/4)*Pi)-cos((1/2)*signum(n1-1/4)*Pi))*signum(n1-1/4)*8^(signum(n1-1/4)*(4*n1+1))*(r^((-3+12*n1)*signum(n1-1/4))-r^((3-12*n1)*signum(n1-1/4)))/(abs(n1-1/4)*Pi*(-1+4*n1)*(16777216^(signum(n1-1/4)*n1)-64^signum(n1-1/4))), n1 = 0 .. infinity)+Sum(-(1/3)*((-1)^n-1)*sin(n*Pi*ln(r)/ln(2))*(exp((1/6)*Pi*n*(Pi+6*t)/ln(2))-exp((1/6)*Pi*n*(7*Pi-6*t)/ln(2)))/(n*(exp((1/3)*n*Pi^2/ln(2))-exp(n*Pi^2/ln(2)))), n = 1 .. infinity)

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]);


 

Download mw.mw

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 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 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!
 

``

 

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

 

restart;

interface( ':-displayprecision' = 5 ):
 

infolevel['LinearAlgebra'] := 5;
myPlatform := kernelopts( ':-platform' );
myVersion := kernelopts( ':-version' );

5

 

"windows"

 

`Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973`

(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]] );

Matrix(5, 5, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 1, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 1, (5, 1) = -10201/1000, (5, 2) = 30199/10000, (5, 3) = -5049/250, (5, 4) = 97/50, (5, 5) = -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

 

Vector(5, {(1) = -10, (2) = 1/10+I, (3) = 1/10-I, (4) = 1/10+I, (5) = 1/10-I})

(1.1.2)

A11 := Matrix( op( 1, A1 ),( i,j ) -> evalf( A1[i,j] ), ':-datatype' = ':-sfloat' );

Matrix(5, 5, {(1, 1) = 0., (1, 2) = 1.00000, (1, 3) = 0., (1, 4) = 0., (1, 5) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 1.00000, (2, 4) = 0., (2, 5) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 1.00000, (3, 5) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0., (4, 5) = 1.00000, (5, 1) = -10.20100, (5, 2) = 3.01990, (5, 3) = -20.19600, (5, 4) = 1.94000, (5, 5) = -9.60000})

(1.1.3)

Digits := 89;
LinearAlgebra:-Eigenvalues( A11 );

Digits := 89

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881249354686)

(1.1.4)

Digits := 90;
LinearAlgebra:-Eigenvalues( A11 );

Digits := 90

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881249352150)

(1.1.5)

A12 := Matrix( op( 1, A1 ),( i,j ) -> evalf( A1[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );

Matrix(5, 5, {(1, 1) = 0.+0.*I, (1, 2) = 1.00000+0.*I, (1, 3) = 0.+0.*I, (1, 4) = 0.+0.*I, (1, 5) = 0.+0.*I, (2, 1) = 0.+0.*I, (2, 2) = 0.+0.*I, (2, 3) = 1.00000+0.*I, (2, 4) = 0.+0.*I, (2, 5) = 0.+0.*I, (3, 1) = 0.+0.*I, (3, 2) = 0.+0.*I, (3, 3) = 0.+0.*I, (3, 4) = 1.00000+0.*I, (3, 5) = 0.+0.*I, (4, 1) = 0.+0.*I, (4, 2) = 0.+0.*I, (4, 3) = 0.+0.*I, (4, 4) = 0.+0.*I, (4, 5) = 1.00000+0.*I, (5, 1) = -10.20100+0.*I, (5, 2) = 3.01990+0.*I, (5, 3) = -20.19600+0.*I, (5, 4) = 1.94000+0.*I, (5, 5) = -9.60000+0.*I})

(1.1.6)

Digits := 100;
LinearAlgebra:-Eigenvalues( A12 );

Digits := 100

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881249345038)

(1.1.7)

Digits := 250;
LinearAlgebra:-Eigenvalues( A12 );

Digits := 250

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881342643606)

(1.1.8)

 

 

Example 2

 

A2 := Matrix(3, 3, [[0, 1, 0], [0, 0, 1], [3375, -675, 45]]);

Matrix(3, 3, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (3, 1) = 3375, (3, 2) = -675, (3, 3) = 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)

 

Vector(3, {(1) = 15, (2) = 15, (3) = 15})

(1.2.2)

A21 := Matrix( op( 1, A2 ),( i,j ) -> evalf( A2[i,j] ), ':-datatype' = ':-sfloat' );

Matrix(3, 3, {(1, 1) = 0., (1, 2) = 1.00000, (1, 3) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 1.00000, (3, 1) = 3375.00000, (3, 2) = -675.00000, (3, 3) = 45.00000})

(1.2.3)

Digits := 77;
LinearAlgebra:-Eigenvalues( A21 );

Digits := 77

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881342621686)

(1.2.4)

Digits := 78;
LinearAlgebra:-Eigenvalues( A21 );

Digits := 78

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881342617230)

(1.2.5)

A22 := Matrix( op( 1, A2 ),( i,j ) -> evalf( A2[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );

Matrix(3, 3, {(1, 1) = 0.+0.*I, (1, 2) = 1.00000+0.*I, (1, 3) = 0.+0.*I, (2, 1) = 0.+0.*I, (2, 2) = 0.+0.*I, (2, 3) = 1.00000+0.*I, (3, 1) = 3375.00000+0.*I, (3, 2) = -675.00000+0.*I, (3, 3) = 45.00000+0.*I})

(1.2.6)

Digits := 58;
LinearAlgebra:-Eigenvalues( A22 );

Digits := 58

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881342614934)

(1.2.7)

Digits := 59;
LinearAlgebra:-Eigenvalues( A22 );

Digits := 59

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881325525942)

(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]]);

Matrix(4, 4, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 1, (4, 1) = -48841, (4, 2) = 8840, (4, 3) = -842, (4, 4) = 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)

 

Vector(4, {(1) = 10+11*I, (2) = 10-11*I, (3) = 10+11*I, (4) = 10-11*I})

(1.3.2)

A31 := Matrix( op( 1, A3 ),( i,j ) -> evalf( A3[i,j] ), ':-datatype' = ':-sfloat' );

Matrix(4, 4, {(1, 1) = 0., (1, 2) = 1.00000, (1, 3) = 0., (1, 4) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 1.00000, (2, 4) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 1.00000, (4, 1) = -48841.00000, (4, 2) = 8840.00000, (4, 3) = -842.00000, (4, 4) = 40.00000})

(1.3.3)

Digits := 75;
LinearAlgebra:-Eigenvalues( A31 );

Digits := 75

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881324662046)

(1.3.4)

Digits := 76;
LinearAlgebra:-Eigenvalues( A31 );

Digits := 76

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881324657710)

(1.3.5)

A32 := Matrix( op( 1, A3 ),( i,j ) -> evalf( A3[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );

Matrix(4, 4, {(1, 1) = 0.+0.*I, (1, 2) = 1.00000+0.*I, (1, 3) = 0.+0.*I, (1, 4) = 0.+0.*I, (2, 1) = 0.+0.*I, (2, 2) = 0.+0.*I, (2, 3) = 1.00000+0.*I, (2, 4) = 0.+0.*I, (3, 1) = 0.+0.*I, (3, 2) = 0.+0.*I, (3, 3) = 0.+0.*I, (3, 4) = 1.00000+0.*I, (4, 1) = -48841.00000+0.*I, (4, 2) = 8840.00000+0.*I, (4, 3) = -842.00000+0.*I, (4, 4) = 40.00000+0.*I})

(1.3.6)

Digits := 100;
LinearAlgebra:-Eigenvalues( A32 );

Digits := 100

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881324648198)

(1.3.7)

Digits := 250;
LinearAlgebra:-Eigenvalues( A32 );

Digits := 250

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881327288182)

(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]]);

Matrix(8, 8, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 1, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 1, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 1, (5, 7) = 0, (5, 8) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 1, (6, 8) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 1, (8, 1) = -1050625/20736, (8, 2) = 529925/1296, (8, 3) = -15417673/10368, (8, 4) = 3622249/1296, (8, 5) = -55468465/20736, (8, 6) = 93265/108, (8, 7) = -1345/8, (8, 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

 

Vector(8, {(1) = 1/3-(1/4)*I, (2) = 1/3+(1/4)*I, (3) = 4-5*I, (4) = 4+5*I, (5) = 1/3-(1/4)*I, (6) = 1/3+(1/4)*I, (7) = 4-5*I, (8) = 4+5*I})

(1.4.2)

A41 := Matrix( op( 1, A4 ),( i,j ) -> evalf( A4[i,j] ), ':-datatype' = ':-sfloat' );

Matrix(8, 8, {(1, 1) = 0., (1, 2) = 1.00000, (1, 3) = 0., (1, 4) = 0., (1, 5) = 0., (1, 6) = 0., (1, 7) = 0., (1, 8) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 1.00000, (2, 4) = 0., (2, 5) = 0., (2, 6) = 0., (2, 7) = 0., (2, 8) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 1.00000, (3, 5) = 0., (3, 6) = 0., (3, 7) = 0., (3, 8) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0., (4, 5) = 1.00000, (4, 6) = 0., (4, 7) = 0., (4, 8) = 0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 0., (5, 6) = 1.00000, (5, 7) = 0., (5, 8) = 0., (6, 1) = 0., (6, 2) = 0., (6, 3) = 0., (6, 4) = 0., (6, 5) = 0., (6, 6) = 0., (6, 7) = 1.00000, (6, 8) = 0., (7, 1) = 0., (7, 2) = 0., (7, 3) = 0., (7, 4) = 0., (7, 5) = 0., (7, 6) = 0., (7, 7) = 0., (7, 8) = 1.00000, (8, 1) = -50.66671, (8, 2) = 408.89275, (8, 3) = -1487.04408, (8, 4) = 2794.94522, (8, 5) = -2674.98384, (8, 6) = 863.56481, (8, 7) = -168.12500, (8, 8) = 17.33333})

(1.4.3)

Digits := 74;
LinearAlgebra:-Eigenvalues( A41 );

Digits := 74

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881317242630)

(1.4.4)

Digits := 75;
LinearAlgebra:-Eigenvalues( A41 );

Digits := 75

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881317239134)

(1.4.5)

A42 := Matrix( op( 1, A4 ),( i,j ) -> evalf( A4[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );

Matrix(8, 8, {(1, 1) = 0.+0.*I, (1, 2) = 1.00000+0.*I, (1, 3) = 0.+0.*I, (1, 4) = 0.+0.*I, (1, 5) = 0.+0.*I, (1, 6) = 0.+0.*I, (1, 7) = 0.+0.*I, (1, 8) = 0.+0.*I, (2, 1) = 0.+0.*I, (2, 2) = 0.+0.*I, (2, 3) = 1.00000+0.*I, (2, 4) = 0.+0.*I, (2, 5) = 0.+0.*I, (2, 6) = 0.+0.*I, (2, 7) = 0.+0.*I, (2, 8) = 0.+0.*I, (3, 1) = 0.+0.*I, (3, 2) = 0.+0.*I, (3, 3) = 0.+0.*I, (3, 4) = 1.00000+0.*I, (3, 5) = 0.+0.*I, (3, 6) = 0.+0.*I, (3, 7) = 0.+0.*I, (3, 8) = 0.+0.*I, (4, 1) = 0.+0.*I, (4, 2) = 0.+0.*I, (4, 3) = 0.+0.*I, (4, 4) = 0.+0.*I, (4, 5) = 1.00000+0.*I, (4, 6) = 0.+0.*I, (4, 7) = 0.+0.*I, (4, 8) = 0.+0.*I, (5, 1) = 0.+0.*I, (5, 2) = 0.+0.*I, (5, 3) = 0.+0.*I, (5, 4) = 0.+0.*I, (5, 5) = 0.+0.*I, (5, 6) = 1.00000+0.*I, (5, 7) = 0.+0.*I, (5, 8) = 0.+0.*I, (6, 1) = 0.+0.*I, (6, 2) = 0.+0.*I, (6, 3) = 0.+0.*I, (6, 4) = 0.+0.*I, (6, 5) = 0.+0.*I, (6, 6) = 0.+0.*I, (6, 7) = 1.00000+0.*I, (6, 8) = 0.+0.*I, (7, 1) = 0.+0.*I, (7, 2) = 0.+0.*I, (7, 3) = 0.+0.*I, (7, 4) = 0.+0.*I, (7, 5) = 0.+0.*I, (7, 6) = 0.+0.*I, (7, 7) = 0.+0.*I, (7, 8) = 1.00000+0.*I, (8, 1) = -50.66671+0.*I, (8, 2) = 408.89275+0.*I, (8, 3) = -1487.04408+0.*I, (8, 4) = 2794.94522+0.*I, (8, 5) = -2674.98384+0.*I, (8, 6) = 863.56481+0.*I, (8, 7) = -168.12500+0.*I, (8, 8) = 17.33333+0.*I})

(1.4.6)

Digits := 100;
LinearAlgebra:-Eigenvalues( A42 );

Digits := 100

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881317227806)

(1.4.7)

Digits := 250;
LinearAlgebra:-Eigenvalues( A42 );

Digits := 250

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881356880102)

(1.4.8)

 

 

 

 

 

 

 

 

 

 

``


 

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


 

with(inttrans)

fourier(exp(-t^2), t, w)

exp(-(1/4)*w^2)*Pi^(1/2)

(1)

fourier(t*exp(-t^2), t, w)

-((1/2)*I)*w*exp(-(1/4)*w^2)*Pi^(1/2)

(2)

fourier(exp(-t^2)/t, t, w)

-I*Pi*erf((1/2)*w)

(3)

fourier(t^.3*exp(-t^2), t, w)

fourier(t^(3/10)*exp(-t^2), t, w)

(4)

fourier(exp(-t^2)/t^.3, t, w)

fourier(exp(-t^2)/t^(3/10), t, w)

(5)

``


 

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.

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