MaplePrimes Questions

I'm perplexed by the fact that this bug is not fixed in Maple 2018:

seq(alias(a[i] = RootOf(_Z1^6-3*_Z1^2-2*_Z1+11, index = i)), i = 1 .. 6);
ee := a[1]*a[5]+a[2]*a[6]+a[3]*a[4];
evala(ee); # wrong
     -320/449*a[1]-(16/449*(a[2]^2))*a[1]^4*a[3]-(16/449*(a[2]^3))*a[3]*a[1]^2-
     (56/449*(a[2]^2))*a[1]^3*a[3]-(16/449*(a[2]^2))*a[1]^5*a[3]+(32/449*a[2])*
     a[3]*a[1]^5-(60/449*(a[2]^2))*a[1]^2*a[3]-(256/449*a[2])*a[1]*a[3]+(64/449*
     a[2])*a[3]*a[1]^2+(128/449*(a[2]^2))*a[3]*a[1]-(32/449*(a[2]^3))*a[3]*a[1]^3-
     (16/449*(a[2]^3))*a[3]*a[1]^4-(24/449*a[2])*a[3]*a[1]^4+(256/449*a[1])*a[2]+
     (88/449*(a[1]^4))*a[2]-220/449*a[3]-680/449*a[2]-128/449*(a[1]^4)-(48/449*
     (a[2]^2))*a[1]^4-(32/449*(a[1]^5))*a[2]-(48/449*(a[2]^2))*a[1]^3+(128/449*
     a[2])*a[1]^3-(48/449*(a[2]^3))*a[1]^3+(256/449*(a[2]^3))*a[1]-(32/449*
     (a[2]^3))*a[1]^5-(88/449*(a[2]^3))*a[1]^2-(232/449*a[3])*a[2]+(66/449*
     (a[2]^2))*a[3]+(130/449*(a[1]^2))*a[3]+(24/449*(a[1]^5))*a[3]+(64/449*
     (a[1]^4))*a[3]+(228/449*(a[2]^3))*a[3]+(164/449*a[3])*a[1]^3-(192/449*
     a[3])*a[1]-(256/449*(a[2]^2))*a[1]-196/449*(a[1]^3)+40/449*(a[1]^5)+110/449*
     (a[2]^2)-324/449*(a[2]^3)-18/449*(a[1]^2)+1780/449+(40/449*(a[2]^2))*a[1]^2+
     (32/449*(a[2]^2))*a[1]^5

(along with quite a few bugs that are less critical but seem trivial to fix, like INTERVAL(1..2, 3..4) being displayed as INTERVAL(1..2)).

Are the issues reported on MaplePrimes not being looked into by anyone?

EDIT: And now the original post (the first link above) is gone, for which I don't have any reasonable explanation. Here is the post: i.imgur.com/9kIhPz5.jpg. Here is what I'm seeing now: i.imgur.com/yC4cqE3.jpg.

I am trying to solve the equation

exp(2*sin(t))-1=0, over the interval 0 <= t <=  16

I tried entering this into Maple:

solve({exp(2*sin(t))-1=0, 0 <= t,t <= 16}, AllSolutions, Explicit)

When I enter it, Maple just says "Evaluating"... and then returns nothing.

I tried "solve" without AllSolutions/Explicit, and even fsolve.

Then Maple only gives me the trivial result t = 0.

Is there a way to approximate the roots, like a root solver.

Ideally I would like to get the exact roots over the interval [0,16].

Wolfram has no problem solving this exactly.https://www.wolframalpha.com/input/?i=solve(%5Bexp(2*sin(t))-1%3D0,+0+%3C%3D+t,t+%3C%3D+16%5D,+AllSolutions,+Explicit)

I posted the worksheet

solveroots.mw

Could some Maple expert help me understand why pdsolve gives me this error message from trying to solve this Schrödinger pde and if there is a work around?

restart;
pde:=I*diff(f(x,t),t)=-diff(f(x,t),x$2)+2*x^2*f(x,t);
bc:=f(-infinity,t)=0,f(infinity,t)=0;
sol:=pdsolve([pde,bc],f(x,t));

I must be doing something wrong, but do not see it.

Mathematica solves the above as follows

pde=I D[f[x,t],t]==-D[f[x,t],{x,2}] + 2 x^2 f[x,t];
bc={f[-Infinity,t]==0,f[Infinity,t]==0};
sol=DSolve[{pde,bc},f[x,t],{x,t}]

thank you

Have been using Maple on and off the last couple years, and am stuck on trying to get the output of a symbolic polynomial solution into MATLAB code.  

The original equation I am trying to solve (for lambda):

fl := t^2*lambda^4/pi+K*lambda^3/pi-4*pi/(3*(-nu^2+1)) = 0

And the way I am attempting to solve it in Maple: 

f1 := RootOf(fl = 0, lambda):

res := allvalues(f1):

 

I won't put the entire output of that last expression here :P.

 

However upon attempting to convert to MATLAB code, I get an error:

> Matlab(res);
Error, (in Translate) options [-(1/4)*(-3*K+3*K*nu^2)/(3*t^2*nu^2-3*t^2)+(1/12)*3^(1/2)*((-3*K^2*(pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(1/3)+3*K^2*(pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(1/3)*nu^2+4*2^(1/3)*(pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(2/3)*t^2-32*pi^2*2^(2/3)*t^4+32*pi^2*2^(2/3)*t^4*nu^2)/((pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(1/3)*(-1+nu^2)))^(1/2)/t^2-(1/12)*(-(18*K^2*(pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(1/3)*((-3*K...
 

 

I'm guessing it's something to do with the fact that the allvalues() funciton spits out four answers (and I want to examine them one at a time in MATLAB to know which one is right for me).

 

Any thoughts?

 

B

> S:=-1/2*((-30*sqrt(3)+81*I)^(2/3)+21+2*sqrt(3)*(-30*sqrt(3)+81*I)^(1/3)-6*(-30*sqrt(3)+81*I)^(1/3)+I*sqrt(3)*(-30*sqrt(3)+81*I)^(2/3)-21*I*sqrt(3))/(-30*sqrt(3)+81*I)^(1/3);

When I enter

simplify(S);

a not much simpler expression involving arctan is output
but when I enter

factor(S);

the expected simplification to the number

3

is output.

This is not a but report, just a report of curious behavior.

I am using Maple 2016 on a Windows 10 PC.

 

             

I just installed Maple 2018.   There are long delays when typing imput into a worksheet.  Never had this problem with Maple 2017. I assume that there is some new debugging going on during my input.  But, whatever it is, is there a way to turn it off?

Hello. I have the system of inequalities -x / 2> 0, -x> 0, (-x-y) / 2> 0, (-x-z) / 2> 0, -y> 0, -z> 0. Tell me, please, how to build a graph on it?

Error, (in is/internal) too many levels of recursion

I get the error above when attempting to solve for the roots of partial derivative.  My results are below:


 

S3 := -(1/2*I)*(-(2*I)*exp(I*Pi*k*tau/T)*Pi*k-exp(I*Pi*k*tau/T)*T+I*exp(I*Pi*k*tau/T)*Pi*k*tau+(4*I)*Pi*k-(2*I)*exp(-I*Pi*k*tau/T)*Pi*k+exp(-I*Pi*k*tau/T)*T+I*exp(-I*Pi*k*tau/T)*Pi*k*tau)*sin(2*Pi*k*x/T)/(Pi^2*k^2)

S3 = ((-I)*(1/2))*((I*Pi*k*tau-(2*I)*Pi*k)*(exp(I*Pi*k*tau/T)+exp(-I*Pi*k*tau/T))-T*(exp(I*Pi*k*tau/T)-exp(-I*Pi*k*tau/T))+(4*I)*Pi*k)*sin(2*Pi*k*x/T)/(Pi^2*k^2)
"(->)"true"(->)"true

Despite the the simplifications MAPLE generated above MAPLE does not recognize the expressions as being equivalent.  So set the following for the Fourier coeffs:NULL

Ck := (-I*((2*(I*Pi*k*tau-(2*I)*Pi*k))*cos(Pi*k*tau/T)-(2*I)*T*sin(Pi*k*tau/T)+(4*I)*Pi*k))*(1/(2*Pi^2*k^2))

-((1/2)*I)*(2*(I*Pi*k*tau-(2*I)*Pi*k)*cos(Pi*k*tau/T)-(2*I)*T*sin(Pi*k*tau/T)+(4*I)*Pi*k)/(Pi^2*k^2)

(1)

The Fourier series can now be expressed as a 1 sided series employing both the Sum vs sum vs add commands for comparison:``

T0 := kernelopts(cputime), time(), time[real]();

204175839, 9435456, 8.998352053

(2)

S7 := a[0]+Sum(Ck*sin(2*Pi*k*x/T), k = 1 .. m):

1600991, 0, 0.

(3)

solve([diff(S5, x) = 0, 0 < x, x < 10*T/(2*Pi*m)], x)

Error, (in is/internal) too many levels of recursion

 

solve([diff(S5, x) = 0, 0 < x, x < 1/8], x)

Error, (in is/internal) too many levels of recursion

 

``


 

Download 2_many_levels_of_recursion.mw

How I can pdsolve this partial fractional  equation?

1.mw
 

restart; CK := .3; Z := 10; L := 1; alpha := .95

###The Riemann–Liouville fractional integral H^alpha  is written in a convolution-form as:

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

 

#where GAMMA(...) represents the Gamma function

 

 
PDE := diff(theta(xi, beta), beta, beta)+L*(diff(theta(xi, beta), xi, beta, beta))+diff(theta(xi, beta), beta, beta, beta)+(1/2)*(diff(theta(xi, beta), beta, beta, beta, beta)) = H^(alpha-1)*CK*(diff(theta(xi, beta), xi, xi))+H(CK*Z+1)^(alpha-1)*(diff(theta(xi, beta), xi, xi, beta))+H^(alpha-1)*Z*(diff(theta(xi, beta), xi, xi, beta, beta))

Init := {theta(xi, 0) = 0, (D[2](theta))(xi, 0) = 0}

{theta(xi, 0) = 0, (D[2](theta))(xi, 0) = 0}

(1)

Bdry := {theta(0, beta) = 1, theta(10, beta) = 0}

{theta(0, beta) = 1, theta(10, beta) = 0}

(2)

smod1 := pdsolve(PDE, Init, Bdry, numeric)

 

 

``


 

Download 1.mw

 

I have just begun to study Green's functions and made some initial progress on a problem, but now need Maple to make further progress.  Apologies, I have written up the equations in LaTeX form rather than Maple, as my Maple has gotten very rusty.

$\frac{d^4y}{dx^4}=f(x)

y(0)=y'(0)=0, y(1)=y'(1)=0$

I showed that the Green function $G(x,u)$ for this equation satisfies a condition

$\lim_{\epsilon\to0}\bigg[\frac{\partial^3G}{\partial x^3}\bigg]_{x=u-\epsilon}^{u+\epsilon}=1$

and showed that there is continuity of the Green's function and its first and second partial derivatives with respect to $x$ at $x=u$.  The next step is to show that this function has a piecewise definition such that

\[G=\frac{1}{6}x^2(1-u)^2(3u - 2ux -x\] for x between the range 0 and u and such that

\[G(x,u)=\frac{1}{6}u^2(1-x^2)(3x - 2xu - u) for x between u and 1

I am not entirely sure how to do this with pen and paper, so I have reason to believe that it could be a done a lot more easily with Maple, if someone could give some pointers that would be much appreciated.

Hi, i want to plot a function say R(t,n),

plot(R(t), t = 500 .. 50000) how can specify the t can only take intger value in the range of [500, 50000]?

I am looking for something like :plot(R(t), t = 500 .. 50000, assume=integer)

Hi all, I am having the follwing DE:

restart: 
(diff(z(x), x, x))-z(x) - cos(2*x)/(1+delta*z(x)) = 0:

With initial conditions: z(-pi/4)=z(pi/4)=0 and |delta|<<1

I showed by hand by using perturbation theory the second order approximation. The hint was: you can use Maple to check your answer. 

Is there somebody who can help me with this?

 

 

I have been attempting to resolve a particular problem to which I have posted a number of questions in the past.  In my attempts I have stumbled onto a number of command syntax issues & inconsistent result outputs.  Each time I try to post questions that appear to me to be separate questions even though it pertains to the same problem.  On numerous occasions a website moderator has deleted my questions unilaterally because the moderator has the opinion the question is identical to a previous question.

Deleting my questions instead of placing them into a previous thread without a response impedes my progress.  I am going to repost this inconsistent output, ONCE again!  If it is directly related to another thread then notify me of the response somehow instead of simply deleting the question.

The following inconsistency as far as I can tell is not explained in any of my previous questions.  I have a series that represents a particular waveform.  The series representation gives a definitive output.  However, when attempting generate the series of the derivative of this waveform (Q3 & Q4), which does exist (Q1 & Q2), MAPLE chokes on that representation & simply continues to evaluate for days & weeks without generating an output.  Why is this?  If anyone gets a definitive result please post it so that I might be able to reproduce the results.

Thanks in advance.

inconsistent_results.mw

Hi, 

I'm currently studying the Rossler Attractor, which is the following system:

diff(x(t), t) = -y(t)-z(t)

 diff(y(t), t) = x(t)+a*y(t)

diff(z(t), t) = b+x(t)*z(t)-c*z(t).

I have found the points of equilibrium of the system.

But now I need to draw bifurcation diagrams: one for varying a, one for varying b, and one for varying c.

 

Can someone please help me with a procedure of how to do this?

Thanks in advance.

 

I have a relatively complicated ODE that i am plotting. One of the variables in particular (B[2211], purple line in the graph) should under go an exponential-like decay to zero, but instead flies off into negative territory  (see graph below) despite having a very simple equation:

problem variable rate of change= -problem variable*constant +linear combination of variables that  are always posotive.

 

My intuition is that this is because i have somehow used the odeplot tool wrong - possibly due to a problem with stepsizes.

Here is a MWE i've made:

aa_problem_MWE.mw

 

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