## Complex ODE solutions using dsolve and fsolve....

I am currently trying to solve the following ODE using numerical methods:

+ [(z+ I*y)2/k12 -k22 +

Where the complex value (in this case, , has been written as z+Iy). I believe dsolve has capabilities for solving this as an initial value problem with complex values and thus to solve this as a boundary value problem I aim to use fsolve to find a zero other a function which is the (IVP solution) - (the non-initial boundary). This has worked very well for the case where y=0 however does not work for values of y>0, and it seems the problem is with fsolve. Any advice on how to deal with this problem, perhaps alternatives to fsolve?

## How to "remove output from worksheet" while it is ...

One of the known issues with Maple GUI (written in Java) is that it is slow.

When I run a long script, which prints few lines to the screen for each step (to help tell where it is during a long run), and if there are 20,000 steps to run which takes 2 days to finish), then the worksheet and I think all of Maple seem to slow down. May be due to GUI trying to flush output to worksheet which now has lots of output.

I noticed when I terminate the loop in the middle and then clear the worksheet from the output and start it again from where it stopped, then it runs/scrolls much faster initially untill the worksheet starts to fill up.

The problem is that one can no longer do Evaluate->Remove output from worksheet as worksheet is busy. This option becomes grayed out.

Is there a trick to bypass this limitation? It will be really nice to be able to clear output from worksheet while it is running.  I do not understand why a user can not do this now even if worksheet is running. In Mathematica for example, this is possible to clear the output while notebook is busy running. Not in Maple.

ps. I want to try to change my program to print output to external file instead to the worksheet and then can monitor the output progress using that file outside of Maple to see if this helps with performance.

This is until Maplesoft adds support to allow one to clear worksheet while it is busy.

Using Maple 2020.1 on windows. Using worksheet mode, not document mode.

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## Logaritmic curve to determine Eigenvalues...

Hello friends

I am a PhD student at the University of Miskolc (Hungary). I am writing to asking for help.

considering that my matrix is correct (based on Article 1) and I have all the values needed:

-  From Article 2, How can I plot the graph of Figure 2 and Figure 3 in a logarithmic scale (X-axis) and linear scale (Y-axis). Also, how can I plot the mode shapes of Figure 7 and Figure 8?

I tried to do it (below) but I am not sure it is correct.

Graphs_Article_2.mw

Reference:
Article 1 - Doyle, Paul F., and Milija N. Pavlovic. "Vibration of beams on partial elastic foundations." Earthquake Engineering & Structural Dynamics 10, no. 5 (1982): 663-674.

Article 2 - Cazzani, Antonio. "On the dynamics of a beam partially supported by an elastic foundation: an exact solution-set." International Journal of structural stability and dynamics 13, no. 08 (2013): 1350045.

## Why does Grid:-Map return set(...) in this exampl...

Hello

I have no choice but use Grid:-Map and Grid:-Seq in my calculations due to the size of them.  Here is a very small example that is puzzling me (Perhaps I did something really silly and did not realize).

ansa:=CodeTools:-Usage(Grid:-Map(w->CondswithOnesolutionTest(w,eqns,vars,newvars,tlim),conds5s)):


with the following result:

ansa:=set([{alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}, {}, {}, {}, {}, {}], [{}, {}, {}, {}, {}, {alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}], [{alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}, {}, {}, {}, {}, {}], [{}, {}, {}, {}, {}, {alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}])

The same thing but now using only map

ansb:=CodeTools:-Usage(map(w->CondswithOnesolutionTest(w,eqns,vars,newvars,tlim),conds5s)):

ansb:={[{}, {}, {}, {}, {}, {alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}], [{}, {}, {}, {}, {}, {alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}], [{alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 2] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}, {}, {}, {}, {}, {}], [{alpha[1, 1] = 0, alpha[1, 2] = 0, alpha[1, 3] = 0, alpha[1, 4] = 0, alpha[1, 5] = 0, alpha[1, 6] = 0, alpha[1, 8] = 0, alpha[1, 9] = 0, alpha[2, 0] = 0, alpha[2, 1] = 0, alpha[2, 2] = 0, alpha[2, 4] = 0, alpha[2, 5] = 0, alpha[2, 7] = 0, alpha[2, 8] = 0, alpha[2, 9] = 0, alpha[3, 0] = 0, alpha[3, 1] = 0, alpha[3, 3] = 0, alpha[3, 4] = 0, alpha[3, 5] = 0, alpha[3, 6] = 0, alpha[3, 7] = 0, alpha[3, 8] = 0, alpha[3, 9] = 0}, {}, {}, {}, {}, {}]}

(This is what I expected as the result).

Why did Grid:-Map add set to the answer?  What am I missing?

Many thanks

## how to start new instance of Maple 2020 while anot...

Here is the problem. I start Maple 2020 on windows 10. Run a script which takes 1-2 days to complete.

During this time, I can't use that Maple at all, since it is busy.

I could start Maple 2019, and that runs as completely separate process. But I want to use Maple 2020 since some things in my scripts do not work on Maple 2019 that work on Maple 2020.

If I start a new instance of Maple 2020, by doing Start->Maple 2020. it does seem to start it OK, but I noticed it seems to be somehow still connected to the one running somehow.  May be they are sharing the same interface?

I can use the new instance now and open new worksheet and use it. But it seems to become very slow, as if it is sharing something with the other Maple 2020 running the long script which uses lots of resources. It is not RAM issue, I have 64 GB RAM, and there is plenty of free RAM left.

When I close the new Maple 2020 workseet I started, I get a message asking if I want to save the worksheet that I have open from the earlier instance which is still running !

I say no ofcourse, as I do not want to terminate that instance, I want to keep it running until the script is completed.

My question is: Could someone may be explain exactly what happens when one starts new Maple 2020, while one is allready running? Why it seems they are sharing either the interface or something else.  How to start completely separate Maple 2020 instance on same PC while one is allready running?

With Mathematica, this issue does not happen. I can start two instances of same version on same PC, and there is nothing shared between them at all.  This does not seem to be the case with Maple.

Maple 2020.1 on windows 10.

## Solving a Pair of Differential Equations with Asym...

Is it possible to determine an analytic solution to the following system of two differential equations for $A$ and $B$ using Maple.  My suspicion is that trial and error would find an analytic solution in theory and so that Maple could find the solution.  M is a constant and \sigma is some arbitrary function of t and the spatial coordinates.

$\Bigg( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} + \frac{1}{2} \Bigg( 1 + \frac{M}{2 \sqrt{x^2 + y^2 + z^2}} \Bigg) \Bigg( \frac{\partial \sigma}{\partial x }\frac{\partial}{\partial x} +\frac{\partial \sigma}{\partial y}\frac{\partial}{\partial y} +\frac{\partial \sigma}{\partial z}\frac{\partial}{\partial z} \Bigg) \Bigg)B=0,$

$\frac{d A}{dt} = AB.$

Furthermore, the boundary conditions are

$B \rightarrow -1 \: \text{as} \: \sqrt{x^2 + y^2 + z^2} \rightarrow \infty,$

$A \rightarrow e^{-t} \: \text{as} \: \sqrt{x^2 + y^2 + z^2} \rightarrow \infty$

System_of_Equations.pdf

## Maple difference between "text" and "2d input" in ...

I do not quite understand why prof asks this question. Or I am doing right? Where can I improve? Or I understand this question completely wrong. To be honest, I did not get the point

## improvements in Latex for trig(x)^n expressions...

When Maple converts sin(x)^n to Latex, the result remain  sin(x)^n.  But in Mathematical typesetting, this is normally written as sin^n(x).   Ofcourse this is only for Latex. In Maple code this not valid.

Is it possible to change Maple's Latex to make it do this automatically? Mathematica does this automatically. Here is an example

restart;
expr:=sin(x)^3+cos(3*x)^5;
Physics:-Latex(expr)

\sin \left(x \right)^{3}+\cos \left(3 x \right)^{5}

Which when compiled gives

Compare to Latex generated by Mathematica

Which compiles to

Which is more standard in books and papers, than Maple's version.

Both Maple's Physics:-Latex and latex() command do the same thing.

Is there a way to make it generate the improved version for latex?

Maple 2020.1

## modp1(('Multiply')(...))...

Hi there.

As we all know if we multiply two polynomials f(x) and g(x) of degrees m and n respectively we get polynomial h(x)= f(x)*g(x) of degree m+n and with m+n+1 coefficients in general. Function modp1(('Multiply')(...)) doing this very well. But sometimes we don't need full resulting h(x) - just subset of monomials and subset of coefficients of h(x) - so we don't need to calculate all m+n+1 coefficients of h(x) and waste time and resources for that.

I would request some additional rework of modp1 package: by adding to modp1(('Multiply')(...)) two optional parameters - degrees of first and last calculating coefficients of h(x).

For example:

h:=modp1(Multiply(f, g,n-1,n+1), p) could calculate only monomials with n-1, n and n+1 degrees and set other monomials to zero.

Or maybe it should be new function:

h:=modp1(Multiply_Truncate(f, g,n-1,n+1), p)

Is it possible?

It would be great and very efficient in many tasks.

Thank you.

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## why PDEtools:-Solve hangs, but solve does not on ...

These are 4 equations in 4 unknowns. the equations are kinda long. But the issue is that PDEtools:-Solve hangs, while solve finishes instantly.

I have though before that  PDEtools:-Solve is a higher level API which ends up using solve? So why does it hang on this?

restart;

eqs:=[2 = c1+c2+c4-1, 0 = ((c2+c4-2)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(1/12*c3*3^(1/2)+1/12*c2-1/6*c4)*(108+12*59^(1/2)*3^(1/2))^(2/3)+2*c3*3^(1/2)-2*c2+4*c4)/(108+12*59^(1/2)*3^(1/2))^(1/3), -1 = -1/6/(108+12*59^(1/2)*3^(1/2))^(2/3)*((((c2-2*c4)*3^(1/2)-3*c3)*59^(1/2)-33*c3*3^(1/2)+33*c2-66*c4)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(2*c2+2*c4+12)*(108+12*59^(1/2)*3^(1/2))^(2/3)+((-12*c2+24*c4)*3^(1/2)-36*c3)*59^(1/2)-60*c3*3^(1/2)-60*c2+120*c4), -5 = ((((2*c2-4*c4)*3^(1/2)+6*c3)*59^(1/2)-30*c3*3^(1/2)-30*c2+60*c4)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(((-c2+2*c4)*3^(1/2)+3*c3)*59^(1/2)+13*c3*3^(1/2)-13*c2+26*c4)*(108+12*59^(1/2)*3^(1/2))^(2/3)-96*(59^(1/2)*3^(1/2)+9)*(c2+c4))/(24*59^(1/2)*3^(1/2)+216)];

unknowns:=[c1, c2, c3, c4];

#han to put a timelimit, else it will never finish. I waited 20 minutes before.
timelimit(30,PDEtools:-Solve(eqs,unknowns));

#this completes right away
solve(eqs,unknowns);


Is this a known issue and to be expected sometimes?

 > restart;
 > interface(version);

 > Physics:-Version();

 > eqs:=[2 = c1+c2+c4-1, 0 = ((c2+c4-2)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(1/12*c3*3^(1/2)+1/12*c2-1/6*c4)*(108+12*59^(1/2)*3^(1/2))^(2/3)+2*c3*3^(1/2)-2*c2+4*c4)/(108+12*59^(1/2)*3^(1/2))^(1/3), -1 = -1/6/(108+12*59^(1/2)*3^(1/2))^(2/3)*((((c2-2*c4)*3^(1/2)-3*c3)*59^(1/2)-33*c3*3^(1/2)+33*c2-66*c4)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(2*c2+2*c4+12)*(108+12*59^(1/2)*3^(1/2))^(2/3)+((-12*c2+24*c4)*3^(1/2)-36*c3)*59^(1/2)-60*c3*3^(1/2)-60*c2+120*c4), -5 = ((((2*c2-4*c4)*3^(1/2)+6*c3)*59^(1/2)-30*c3*3^(1/2)-30*c2+60*c4)*(108+12*59^(1/2)*3^(1/2))^(1/3)+(((-c2+2*c4)*3^(1/2)+3*c3)*59^(1/2)+13*c3*3^(1/2)-13*c2+26*c4)*(108+12*59^(1/2)*3^(1/2))^(2/3)-96*(59^(1/2)*3^(1/2)+9)*(c2+c4))/(24*59^(1/2)*3^(1/2)+216)]; unknowns:=[c1, c2, c3, c4];

 > timelimit(30,PDEtools:-Solve(eqs,unknowns))

Error, (in expand/bigprod) time expired

 > solve(eqs,unknowns):
 >

## What is the best curve fit for Primes of the form ...

Hi all,

We want to find a curve fit for an integer sequence.

We have n such that n^2+n+17 is a prime number.

Use the Maple CurveFitting package.

I tried with(CurveFitting).

We do not know if this is best represented by a polynomial or exponential curve fit.

n2_and_n_and_17_in_OEIS_007635.mw

n2_and_n_and_17_in_OEIS_007635.pdf

Regards,

Matt

## How Does Maple Actually Solve an Identity, Say, fo...

Since I am a mathematician, I am wondering how Maple goes about solving an identity for 3 functions.
Let's say we have af1(t)+bf_2(t)+cf_3(t) = 0 for all t. How does maple actually find a triplet a,b,c that works for all real t?
It does with solve(identity( ),[a,b,c]). But what is the theory behind it?
We know, of course, a priori, that such a triplet exists.

Thank you!

mapleatha

## Computational Nash equilibrium...

Dear Colleagues,

Apologies for the generic question below.

I am trying to obtain the Nash equilibrium solutions for a two-person game. I am not sure of any in-built packages that can help me in obtaining the solutions computationally. The algorithms that I created do not seem to give good solutions that are meaningful in my application. Any suggestion would be much appreciated.

Regards,

Omkar

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