Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Here is an animation of a mass-spring system where the mass slides horizontally on a steadily moving conveyor belt.

The contact between the block of mass and the belt is of the dry friction kind (Coulomb's friction). Consequently the block periodically sticks to the belt and moves forward with it until the force of the stretching spring overcomes the force of friction and yanks it back, making it to slip against the belt. In the animation the block is shown in a dark color while slipping, and a light color while sticking.

The fully executed Maple worksheet can be slow to load and requires a good deal of memory. Therefore I have attached two versions which are identical in all respects except that in one of them I have removed the Maple output to make is easy to load if your computer has limitations.

Download worksheet (no Maple output) block-sliding-on-conveyor-belt-stripped.mw

Doiwnload worksheet (with Maple output) (sorry, exceeds MaplePrime's size limit)

Hello,

I have the following expression

Ve*k21*ke*x1+Ve*k21*x1^2+k12*ke^2*x1[t]+2*k12*ke*x1*x1[t]+k12*x1^2*x1[t]+k21*ke
^2*x1[t]+2*k21*ke*x1*x1[t]+k21*x1^2*x1[t]+Ve*ke*x1[t]+ke^2*x1[t,t]+2*ke*x1*x1[t
,t]+x1^2*x1[t,t]


and I want to convert it to

x1[t,t]*(x1+ke)^2+(k12+k21)*x1[t]*(x1+ke)^2+Ve*x1[t]*ke+(k21*Ve)*x1*(x1+ke)

 

How can I do this opperation? This is just a simple example of a more general problem I am facing. Thanks in advance for your help

In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. I'd like to use maple to compute crossing number of some graphs (any graphs is ok,  for example: cr(K5)=1 ). Someone can help me ? thanks. 

I know the problem of computing the crossing number is NP, but I guess we have some good  ways to compute in some small graphs.

Hello,

Since I installed Maple 2019 in my new iMac with Catalina, I can't make it work properly.

1. Once open, it's impossible to shut it down. I always have to force its exit.

2. The context panel doesn't seem to work properly. It never shows the actions that it sould do.

3. It doesn't flow as the old Maple I use to have in my old iMac.

I've been looking for this issue both in this forum and in the whole internet, as well as sending messages to technical support, and still can't find any answers. If someone knows something, plese let me know.

Kind regards,

Fermat66 

Sorry if this is stupid but How do I use the interactive debugger?   the button is greyed out for me and 
 

stopat(EAdd(x^3+2x+1,x, 13, 1, 2, 1, 2), 1);

Error, missing operator or `;`

 

stopat(EAdd, 1);

                             [EAdd]
 

debug button is still greyed out IDK what to do now


p.s. is there a way to set breakpoints in your code by clicking like in other programming?
 

I want to factor large numbers, for this purpose I want to utilize multi cores on my computer.

Anyone who can help me in solving this problem?

I am utilizing Lenovo Thinkpad T440s with specifications core i7-4600 CPU @ 2.19 GHz.

In addition I would like to ask if anyone can help me in integrating GPU's with Maplesoft 2019 for factorization.

 

I am having a cluster of 64 GPU's i.e. AMD RX-460.

 

Any help in this regard will be appreciated.

 

Hello people in Mapleprimes,

A long time has passed since I came here before.
I have forgotten a lot of what I remembered about maple.

I want to incert gamma from e_nsp1 and (1-gamma) from e_nsp2 into set_3, so deleting gamma and (1-gamma) from set_3.
How can I do this?

Thank you in advance.

Take care.

question_1.mw

 

taro 
 

Dear maple users,

How to plot a figure for different values of rk?

like rk=5,10,15,20:

jb.mw

Thanking you,

Waiting for replay.

 

 

How would I turn this set into matrix form?

would it be possible to seperate the matrix form into:

v1e^(lamba*t) + v2e^(lambda2*t) .... + v^ne^(lambdan*t) where v1, v2, and vn are the eigenvectors and lamba1, lambda2, and lamban are their respective eigenvectors.

I have problem on RKF45 with result on 

"unable to convert to an explicit first order system"


 

``

restart

with(plots):

vf := .3:

kf := .2:

c := .2:

`Τt` := .3:

N := .1:

`φd` := .2:

`ρs` := 8933:

`ρf` := 997.1:

y := .1:

alpha := .5:

Pr := 6.2:

beta := .5:

`βT` := .2:

`ε` := .1:

ks := 400:

kf := .613:

cps := 385:

cpf := 4179:

delta := .5:

Ec := .2:

`Τv` := 1:

A := .5:

B := .5:

omega := 1.5:

K := (ks+2*kf-2*phi*(kf-ks))/(ks+2*kf+phi*(kf-ks))

(401.226+798.774*phi)/(401.226-399.387*phi)

(1)

Eq1 := (1-`φd`)*(diff(f(eta), eta, eta, eta))/(1-phi)^2.5-(1-`φd`)*(1-phi+phi*`ρs`/`ρf`)*((diff(f(eta), eta))^2-f(eta)*(diff(f(eta), eta, eta)))+alpha*beta*(diff(G(eta), eta)-(diff(f(eta), eta))) = 0

.8*(diff(diff(diff(f(eta), eta), eta), eta))/(1-phi)^2.5-.8*(1+7.958981045*phi)*((diff(f(eta), eta))^2-f(eta)*(diff(diff(f(eta), eta), eta)))+.25*(diff(G(eta), eta))-.25*(diff(f(eta), eta)) = 0

(2)

Eq2 := (diff(G(eta), eta))^2-G(eta)*(diff(G(eta), eta, eta))-beta*(diff(f(eta), eta)-(diff(G(eta), eta))) = 0

(diff(G(eta), eta))^2-G(eta)*(diff(diff(G(eta), eta), eta))-.5*(diff(f(eta), eta))+.5*(diff(G(eta), eta)) = 0

(3)

Eq3 := G(eta)*(diff(G(eta), eta))+beta*(f(eta)-G(eta)) = 0

G(eta)*(diff(G(eta), eta))+.5*f(eta)-.5*G(eta) = 0

(4)

Eq4 := K*(diff(theta(eta), eta, eta))/Pr+(1-phi+phi*`ρs`*cps/(`ρf`*cpf))*(f(eta)*(diff(theta(eta), eta))-2*(diff(f(eta), eta))*theta(eta))+alpha*`βT`*(H(eta)-theta(eta))+Ec*alpha*(diff(G(eta), eta)-(diff(f(eta), eta)))^2/`Τv`+(A*(diff(f(eta), eta))+B*theta(eta))/Pr = 0

.1612903226*(401.226+798.774*phi)*(diff(diff(theta(eta), eta), eta))/(401.226-399.387*phi)+(1-.1746332371*phi)*(f(eta)*(diff(theta(eta), eta))-2*(diff(f(eta), eta))*theta(eta))+.10*H(eta)-0.1935483870e-1*theta(eta)+.10*(diff(G(eta), eta)-(diff(f(eta), eta)))^2+0.8064516130e-1*(diff(f(eta), eta)) = 0

(5)

Eq5 := 2*(diff(G(eta), eta))*H(eta)-G(eta)*(diff(H(eta), eta))+y*`βT`*(H(eta)-theta(eta)) = 0

2*(diff(G(eta), eta))*H(eta)-G(eta)*(diff(H(eta), eta))+0.2e-1*H(eta)-0.2e-1*theta(eta) = 0

(6)

bcs1 := (D(f))(0) = `ε`+delta*((D@@2)(f))(0), f(0) = 0, (D(f))(10) = 0;

(D(f))(0) = .1+.5*((D@@2)(f))(0), f(0) = 0, (D(f))(10) = 0

(7)

bcs2 := (D(G))(10) = 0, G(10) = f(10);

(D(G))(10) = 0, G(10) = f(10)

(8)

bcs3 := theta(0) = 1+omega*(D(theta))(0), theta(10) = 0;

theta(0) = 1+1.5*(D(theta))(0), theta(10) = 0

(9)

bcs4 := H(10) = 0;

H(10) = 0

(10)

L := [0., 0.5e-1, .1, .15, .2]:

for k to 5 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, bcs1, bcs2, bcs3, bcs4}, phi = L[k]), [f(eta), G(eta), theta(eta), H(eta)], numeric, output = listprocedure); Y || k := rhs(R[3]) end do

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

plot([Y || (1 .. 5)], 0 .. 10)

Error, (in plot) procedure expected, as range contains no plotting variable

 

``

``

``


 

Download RKF45_A.mw

 

thank you in advance for your help and kindness.

I am using a maple workbook to develop, test, and install a package I am developing.  Several days ago, I noticed that the workbook was not updating the package to reflect the most recent versions of my source code (.mpl). I initially assumed the problem caused by some unintentional change I made to the file, but in the end I found there is a general problem with the URIs in the maple workbook. Everything worked in 2019.1 and I hadn't made any changes after I updated to 2019.2.1.

To confirm the problem, I created a new directory(in fully updated Windows 10 ) and copied my source file into the directory. Then I created a worksheet in maple and saved it into the directory as xx.mw. Using the Navigator panel I then saved the worksheet as a workbook creating xx.maple in the directory.  I then tried to attach the mpl file to the workbook.  In the Navigator menu, the item "attach a file" is unavailable( greyed out).  This is also the case in any of the other earlier workbooks I have created.  I have confirmed the problem is not affecting worksheets because I was able to read my mpl file into a worksheet and load the module using a with(modulename) command.

Please advise.


 

eqs := [II-(phi+mu)*DD+tau*D__g, phi*DD+lambda__2*D__a+lambda__3*D__H-(lambda__4+lambda__1*D__a/(S+D__g)+mu)*D__g, lambda__1*D__g*D__a/(S+D__g)-(lambda__2+beta+mu)*D__a, beta*D__a-(lambda__3+mu+gamma__t)*D__H+lambda__4*D__g, gamma__t*D__H-(delta+mu)*D__c];

[II-(phi+mu)*DD+tau*D__g, phi*DD+lambda__2*D__a+lambda__3*D__H-(lambda__4+lambda__1*D__a/(S+D__g)+mu)*D__g, lambda__1*D__g*D__a/(S+D__g)-(lambda__2+beta+mu)*D__a, beta*D__a-(lambda__3+mu+gamma__t)*D__H+lambda__4*D__g, gamma__t*D__H-(delta+mu)*D__c]

(1)

Sol := {DD = (II+B*tau)/(phi+mu), D__H = E/P, D__a = ((lambda__3+mu+gamma__t)*E/P-lambda__4*B)/beta, D__c = gamma__t*E/((delta+mu)*P), D__g = B};

{DD = (II+B*tau)/(phi+mu), D__H = E/P, D__a = ((lambda__3+mu+gamma__t)*E/P-lambda__4*B)/beta, D__c = gamma__t*E/((delta+mu)*P), D__g = B}

(2)

Inter := [B = S*(lambda[2]+beta+mu)/(lambda[1]-lambda[2]-beta-mu), C = 1/(S+B), E = lambda[2]*lambda[4]*B/beta+B*lambda[4]+mu*B-(lambda[4]*B/beta*B)*C-(phi*II+B*tau*phi)*P/(phi+mu) and lambda[2]*lambda[4]*B/beta+B*lambda[4]+mu*B-(lambda[4]*B/beta*B)*C-(phi*II+B*tau*phi)*P/(phi+mu) = lambda[2]*(lambda[3]+mu+gamma[t])/beta+lambda[3]-lambda[1]*(lambda[3]+mu+gamma[t])*C*B/beta];

[B = S*(lambda[2]+beta+mu)/(lambda[1]-lambda[2]-beta-mu), C = 1/(S+B), false]

(3)

simplify(eval(eqs, eval[recurse](Sol, Inter)))

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received Inter

 

``


 

Download tes.mwtes.mw

Dear experts

I have a complex equation (eq=0) which is a function of K, Q, p and s. K and Q can be complex variables and pa and s are parameters.

equation is

eq:= (K*( Q*sinh(K)*cosh(Q)-K*cosh(K)*sinh(Q))*(1+s*K^2)
   +p*(-4*K^2*Q*(K^2+Q^2)
       +Q*(Q^4+2*K^2*Q^2+5*K^4)*cosh(K)*cosh(Q)
       -K*(Q^4+6*K^2*Q^2+K^4)*sinh(K)*sinh(Q)))/(K^2*Q*cosh(Q)) =0 :

and we know that Q:= sqrt(K^2-I*omega); where omega is complex variable

i) How can I study and plot K vs p if Q is 1) real and 2) pure imaginary. 3) complex variable and vice versa

ii) How can I study and plot p vs s

 

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