## Error in rootfinding...

Hello,

Error, (in RootFinding:-Analytic) Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc

What should I to do to overcome this error?

## Fitting variables to matrix eigenvalue solutions...

Hi guys,

I'm fairly new to programming as a whole, but I've currently set up a script which creates a matrix and then fills it in given a  condition. i.e if the x and y indices of the matrix are the same it has been told to add m^2F. If the y and x index differs by 3 is has been asked to fill in V3/4 and if they differ by 6 it has been asked to fill in V6/4. After the matrix is created it will then calculate the eigenvalues.

My question is as follows:

m^F is a constant and V3 and V6 are variables. I currently, manually, set a value of V3 and V6 at the top of the script and then calculate the eigenvalues. How would one go about reversing this process - i.e provide a set of eigenvalues and then perform a fit to find the best values of V3 and V6. Is this 'doable' in Maple or would it be best to use something else.

I have attached a copy of the script for viewing purposes in case what I have written is not very clear - Hindered_rotor.mw

David

## how to handled mixed conditions ?...

How 2 solve summation when M,  Z,  X are given with mixed conditions?

## Error, unable to convert to an explicit first-orde...

Hello everyone, I'm trying to run a simple calculation (Water flowing out of a pressurised container) using a combination of conservation of energy and conservation of mass. I have working models of the same system without pressurisation (purely gravity working) which work fine in Maple, but when re-writing the pressure as a function of the height of the water I receive the error:

"Error, (in DEtools/convertsys) unable to convert to an explicit first-order system".

The formula used is:

"Eq1:= -Rho_Water * A_Barrell * v_Barrel = Rho_Water * A_Nozzle * v_Nozzle"

Which returns:

"Eq1:= -25.23733555 * d/dt h_Water(t) = 0.5982 * (-190.1309944 - 13.64385474 * h_Water(t) + (d/dt h_Water(t))2)1/2"

With initial condition:

"ics1:= h_Water(0) = 0.2"

After giving the command:

"Sol1:= dsolve({Eq1, ics1}, numeric)"

Maple returns the aforementioned error. When trying to solve non-numerically the output is a list filled with "RootOf" and "_Z". Instinctively I would say the square root in the second part of the equation is the problem here, but I would not know how to fix this. Does anybody have a quick fix for this problem? Or is there a fundamental issue with the equation? Thank you in advance!

## Get rhs of equation in matrix...

I have matrix:

`m1 := Matrix([[x[0,0]=1,x[0,1]=1,x[0,2]=0,x[0,3]=0,x[0,4]=0,x[0,5]=0],[x[1,0]=0,x[1,1]=0,x[1,2]=1,x[1,3]=1,x[1,4]=0,x[1,5]=0],[x[2,0]=0,x[2,1]=0,x[2,2]=0,x[2,3]=0,x[2,4]=1,x[2,5]=1]]);`

How to get values on the rhs of x without using for loops and create a matrix using these values?.

Results should be:

`m2 := Matrix([[1,1,0,0,0],[0,0,1,1,0,0],[0,0,0,0,1,1]]);`

## How to write a code to get following Matrix D?...

```How to write a code to get following Matrix D?

```

MY TRY: (But it' s not completely what I seek)

```restart:

k:=1:
M:=2:
N:=2^k*(M+1):

U:=Matrix(M+1,M+1):
for r from 2 to M+1 do
for s from 1 to r-1 do
if type(r+s,odd) then
U(r,s):=2^(k+1)*sqrt((2*r-1)*(2*s-1)):
else 0 end if:
end do:
end do:

#Let's find Matrix D, In here it' s shown matrix DD
DD:=Matrix(N,N,shape=diagonal,fill=U);```

## How to transform a permutation into numbers and vi...

Dear all,

I hope everyone helps me about the problem of converting a permutation into numbers and vice versa on maple

Let Sn denote the set of all permutations of the set {0, 1, ..., n − 1}

Lehmer code is a bijective function l : Sn ->{0, 1, 2, ..., n! − 1}.

Define function l(S)=Sum(ci x (n − 1 − i)! ) where S in Sn and ci is the number of elements of the set { j > i | sj < si }

Inverse Lehmer code is a bijective function l−1 : {0, 1, 2, ..., n! − 1} -> Sn

For example: n=4 -->{0, 1, 2, 3}, for S = (0, 2, 1, 3) , so c0 = 0, c1 = 1 ( j=2 > i=1 and sj = 1 < si = 2), c2 = 0, c3 = 0 -->

I(S) = 0 x (3-0)! + 1 x (3 - 1)! + 0 x (3-2)! + 0 x (3 - 3)! = 2! = 2. So I((0, 2, 1, 3)) =2  and I-1(2) = (0, 2, 1, 3).

## 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);

## Is there any Maple command to detect whether the d...

Is there any Maple command to detect whether the degree of a polynomial w.r.t. all variables is less or equal 1?

For example, if \$f=ax+by-1\$ when \$x\$ and \$y\$ are variables then the output is true and if \$g=a*x^2+b*y-c\$ then it returns false.

## Maple Cloud problem...

Problem copying a document to Maple Cloud (Public domain)

• Verified email is correct

• Chose File → Save to Cloud... (or clicked Send Document to Cloud on Maple Cloud palette) either way opend Login dialog

• Entered  Account = Maplesoft account, my Email and password then clicked Log in.  The following message appears: "The account type or email address or password is incorrect"

I've saved .mw files to Maple Cloud before with no problems.  Any help appreciated.

Thanks, Les

## Phase portrait ...

I have the equation (𝑑𝑥/𝑑𝑡)^2=𝑎𝑥^3+𝑏𝑥^2+𝑐𝑥+𝑑.

How do I plot 𝑑𝑥/𝑑𝑡 against x? (as the coefficients a, b, c and d vary)

I expect it looks like the following graph:

## Geodesics on cube...

Hello everybody! I want to build closed geodesic on a cube. I know how to determine the next face, but I do not know how to determine which edge and in what proportion the geodesic will cross.

Here is NET for geodesic on cube. Geodesic type (3,9). Yes, 3 and 9 is not relative prime, but geodesic (1,3) not closed.

Or did I choose the wrong way to solve the problem? Help pls. Thanks.

## Is there a riemann sum to integral converter?...

Is there a riemann sum to integral converter?

If not then,

So I thought I could make some progress using the maple limit command in the this problem:

limit(Sum(csc(Pi*x/i)^3*sin(Pi*x)^3/i^3, i = 1 .. n), n = infinity)

which gives signum(sin(Pi*x)^3/x^3)*infinity

but what does this mean?

How do I convert Sum(csc(Pi*x/i)^3*sin(Pi*x)^3/i^3, i = 1 .. n), n = infinity to an integral or from this result?

## Error, invalid input: subs received fsolve...

I'm trying to solve this set of two equations forn where (EQ1 and EQ2 are already défined in fontions of the followings variables (k, wr ,R,Pi), and i'm using the following loop

eqns:={EQ1,EQ2}:

for i from 1 by 1 to 101 do R:=(i-1):S:=fsolve((eqns), {k, wr},{k=0..10,wr=0..10} ):v(i):=(subs(S,(wr))):w(i):=(subs(S,(k)))end do:
Error, invalid input: subs received fsolve({-0.6391108652e160*k+0.2384499927e160*wr+0.714075224e160*k^3-0.4729440685e160*wr^3-0.4025871558e160*k^5+0.1700629083e159*wr^5-0.4813673552e156*k^9+0.1033594302e160*k^7-0.1044324938e156*wr^7-0.1017755535e159*k^3*wr^4+0.2163976160e160*k^5*wr^2-0.7986601863e160*k^4*wr-0.2729449277e160*k^6*wr+0.8693579523e154*k^3*wr^6+0.4453377949e156*k^4*wr^5-0.2636332727e157*k^5*wr^4-0.5817233940e157*k^7*wr^2+0.5719400327e157*k^6*wr^3-0.2875232976e161*k^2*wr+0.2294793648e161*k*wr^2+0.1483050053e158*k^2*wr^5-0.3944893217e159*k^4*wr^3-0.464413477e159*k^2*wr^3+0.2760407324e157*k^8*wr+0.8238787577e156*k*wr^6-0.1081920595e...

i do get a solution for Pi/2 and Pi/3 but beyond this value i get the above error

## Zeros of analytic function...

Dear Sir,

I have a question: I have an analytic function depending on a real parameter that is of the form  F_y (z) with y>0 and z is complex.

I search the zeros  of F_y(z), that is the complex z staisfying F_y(z)=0. I used  the Maple function

RootFinding:-Analytic(F, z, re = -5 .. 0, im = -100 .. 100, );

but he displays me an error message  "Error, (in RootFinding:-Analytic) the function, -(100+I*z)^(1/2)*(80-I*z)^2*cosh((1/150)*(100-I*z)^(1/2)*Pi)*sinh((1/150)*(100+I*z)^(1/2)*Pi)+(100-I*z)^(1/2)*(80+I*z)^2*cosh((1/150)*(100+I*z)^(1/2)*Pi)*sinh((1/150)*(100-I*z)^(1/2)*Pi)+(2*I)*y*z^2*cosh((1/150)*(100-I*z)^(1/2)*Pi)*cosh((1/150)*(100+I*z)^(1/2)*Pi), depends on more than one variable: {y, z}. "

Can you help me to resolve my problem?

Best regards,

Zayd.

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