## Firewall blocking Maple 2018 after upgrading comp...

I have just upgraded my laptop from Windows 7 to Windows 10.  On starting up Maple 2018,  I receive the attached message on screen.  This is after previously loading the worksheet successfully.   Today,  I am not able to do so.  I need to permanently register my firewall to allow Maple to run; can anyone help?

Melvin

## Maple 2018.2 is not compatible with macOS Catalina...

Hi everybody

l I tried to install Maple 2018.2 on the golden master of Catalina and it didn't work : the installation process ended after the entering of the password to authorize the installation. In fact Maple 2018.2 still contains 32 bit elements. Is there a solution ? Thank you

David

## Chebyshev series in different intervals...

Hello,

My question is mathematical in nature, so it might be a little out of place but I though I would give it a shot.

You have a series of chebyshev coefficients in two connecting subdomains lets say S1 = [0,0.5] and S2=[0.5,1]. So far you are still in the spectral space. If you want to compute the solution in real space you can sum the coefficients with the Chebyshev polynomials.

Now imagine you change the interval to S1 = [0,0.6] and S2 = [0.6,1]. Is there a way to manipulate the Chebyshev coefficients from both initial subdomains to create a new set of Chebyshev coefficients that fit the solution in the new subdomains.

The brute force method would be to create the real solution of Chebyshev polynomials and then use that to form a new set of Chebyshev coefficients. Or you can use Clenshaw to compute the solution at several points, and then use the points to create new Chebyshev coefficients.

But what if we can stay in spectral space and create the new chebyshev coefficients. Is that possible? If so, how?

## 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

## 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)
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

## Visualising solutions to sums of polynomials...

I'm working towards creating a way to visualise real polynomial ideals! (or at least the solutions of the polynomials in the ideals) this code creates a plot showing the solutions to all the polynomials in the ideal generated by P1 and P2 (these are specified in the code)

with(plots);
P1 := x^2+2*y^2-3;
solve(P1, y);
Plot1 := plot([%], x = -2 .. 2);

P2 := -2*x^2+2*x*y+3*y^2+x-4;
solve(%, y);
Plot2 := plot([%], x = -4 .. 2);

P2*a+P1;
solve(%, y);
seq(plot([%], x = -4 .. 2), a = 0 .. 10, .1);
display(%, Plot1, Plot2)

This is because when you multiply two polynomials their set of solution curves is just the union of the sets of curves associated with the previous polynomials.

For the next step I'd like to create a graph of the solutions associated with an ideal with three generators. To stop this from being excessively messy I'd like to do it with the RGB value of the colour of a curve is determined by  a and b where the formula for a generic polynomial that we are solving and graphing is given by:

P1+a*P2+b*P3;

where P3 is given by

P3 := x*y-3

I've tried various ways to use cury to make this work (my intuition is cury is the right function to use here)  but got no where. Any ideas how to procede?

## pdsolve 2D equations with unknown parameter...

possible to solve following equation with unknown parameter omega.

parameter constant.

I see before for one dimension ode this type equation was solved.

Now for 2d equation is possible?

can consider or I can send again.

Best

2d-2

## Maple error pls help!!!...

maple does not work at all

it displays this error

Error, (in StringTools:-FormatMessage) unknown option MAPLE

## replace function u__0(r, theta, t) with f[1, 1](r,...

How I can replace  u__0r, theta, t) with f1, 1(r, theta) in attached file.

I want in I have only f1,1] function.

Thanks

 >
 (1)
 >
 (2)

## How do I sovle Double integration of function cont...

restart;

##########  omega and theta are variables,where J[3],F[2],H[2],etc are constants.

t1:=-1/(-16.*omega^2+exp(-4*omega)+exp(4*omega)-2.)*(-(0.5817764173e-1*I)*exp((2/9)*omega*cos(theta))*omega^5*cos(theta)*J[3]-(.6981317009*I)*exp((2/9)*omega*cos(theta))*omega^4*cos(theta)*H[3]-0.4524927691e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^3*G[3]-.6205615118*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*H[2]+.6205615118*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*F[2]+.9308422676*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*H[3]-.1034269187*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^3*G[2]-0.7757018900e-1*exp(.1111111111*omega*(2.*cos(theta)-9.))*cos(theta)*omega^2*G[2]-0.7757018898e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*J[3]-0.9696273622e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^3*J[3]-0.4524927691e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^2*J[3]-.2714956613*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^2*H[3]-0.7757018898e-1*exp(.2222222222*omega*(cos(theta)-9.))*cos(theta)*omega^4*G[3]+0.8726646261e-1*exp((2/9)*omega*cos(theta))*omega^3*J[3])*cos((2/9)*omega*sin(theta));

t2:=int(int(t1,omega=0..infinity),theta=0..2*Pi);

## use factor or using rule for simplify...

How I can simplify result? For factor or using rule.

Thanks

## plot toroidal and bipolar...

How can plot two  and bipolar figures as attached and extract their data.

Thank You.

## determination of Laplacian in a new form...

Hello,

How I can write a code for the determination of Laplacian in a new form that is introduced in the maple code (First line).

Thank you.

FOR

Maple Worksheet - Error

Failed to load the worksheet //convert/FOR

## Maple 2018 won't open...

Hello, i am experiencing some problems when trying to open the maple 2018 software*
I have tried to search for sollution but there is very ittle intel
When i open Maple 2018 it just lingeres on the start up (pic below) and just disappears after 10 seconds