I think I just found one of the most serious problems in Maple I've seen (other than timelimit hanging).

This is using Maple 2024.2 on windows 10.

I'll explain in words the problem, then give worksheet below to reproduce this. I can reproduce this all the time.

I have implicit solution in y(x) to an ode.

If I first solve for y(x) from the solution, so solution is now explicit, then call odetest to check if this explicit solution is correct, and if I use assumptions on the odetest call, and then after that call odetest on the original implicit solution, then odetest fails to verify the implicit solution.

But, if I change the order, and first call odetest to verify the implicit solution first, it verifies it OK !  

So the problem ONLY happens if I change the order of calling odetest and if I use assumptions on the odetest call that was used before on the explicit solution.

This tells me that Maple remembers something from earlier call. Does it remember the assumptions used? If so, this is very risky. As some part of program might call odetest with some assumptions, and another part of the program can use no assumptions.  I thought assuming is only applied to the call it is used at only and will not affect future calls.

Is there a way then to clear all assumptions used on earlier call to Maple command before using the command again? Or to tell Maple not to remember assumptions used on a call?

This is a big problem. It took me 14 hrs of debuging to find it. Order of calls to odetest should not make it behave different.

I hope someone could find solution to this, since now I have no idea what to do as I need to use odetest on explicit and implicit solutions and I do not want the order of calling Maple command to make difference in results.

This worksheet shows the problem. 3 cases are given. Notice that when using assumptions on earlier call to odetest, how it fails to verify the implicit solution in later call.

Download order_of_ode_test_makes_difference_oct_31_2024.mw

update NOV 2, 2024 6 AM

I found the cause.

Removing PHYSICS from libname, then the problem goes away !

So this is caused by PHYSICS package. For some reason, having Physics package in the libname causes odetest to hang/fail compared to when the physics package is not in the libname path. Worksheet below.

Download order_of_ode_test_makes_difference_NOV_2_2024.mw

my question is: Is it safe to permanently remove Physics package from libname? Why is having physics package in libname (which is by default) causes this problem?

I do not use Physics package explicitly in my code. i.e. I do not do Physics:- calls. 

Any one knows what effect not having Physics on libname cause? Will Maple still work OK for everything if one is not calling Physics package explicitly?

When I export images as SVG the resulting file always has the image much larger than the viewbox resulting in only part of it showing. My normal workflow is to then load in Inkscape and correct the error, however, I would love to not have an extra step. Is there any other fix for this?

How do you convert this system of equations into matrix form? The decoupling process is performed.Convert the equations into photographs.fuxian1030.mw

Low power user (occasional) here! I would like to extract the parameters from a curve fit and assign to another variable?

What I do at the moment

u-> changecoords(u,[x,y,z],spherical_physics,[r,theta,phi]):
map(%,[x,y,z])
  [r cos(phi) sin(theta), r sin(phi) sin(theta), r cos(theta)]

Any other (preferably shorter) ways to look up transformations defined in ?coords

I am studying linear operators that have vanishing Nijenhuis Torsion, that is a (1-1) tensor L whose corresponding (1-2) tensor N given by a tensor equation of L (see attached) is identically zero.

I am new to maple, i have used it to plot vector fields and solve systems of equations in the past but i am unfamiliar with the DifferentialGeometry and Physics packages.

Attached is my best effort at solving this problem directly for a simple 2d case without the use of any packages and i am wondering if it is possible to do it all in one line without having to define tensor components one by one.

nijenhuis_torsion.mw

I just realized that voting for a deleted answer is possible. This does not make sense. Does an upvote also change the reputation?

You can try it in the answer to myself below, but please do not upvote permanetly for this question.
 

How can I use Maple to solve a system of nonlinear equations symbolically and display the steps in the solution?

Here are two systems over the reals:

The following results indicate that both and are satisfiable 

QuantifierElimination:-QuantifierEliminate(exists([s,q,r],sys__1));
                              true

QuantifierElimination:-QuantifierEliminate(exists([s,q,r],sys__1));
                              true

but RealDomain:-solve simply returns an empty list (that is, no solution exists) in both cases

RealDomain:-solve(sys__1,[q,s,r]); # ⟹ sys1 cannot be satisfied
                               []

RealDomain:-solve(sys__2,[q,s,r]); # ⟹ sys2 cannot be satisfied
                               []

As discussed in the previous problem, in contrast to using QuantifierElimination:-QuantifierEliminate, the use of RealDomain:-solve is unsafe. Nevertheless, the above output suggests that even the much-more-sophisticated QuantifierElimination:-QuantifierEliminate is still not always reliable (since the correct returnedvalue appears to be in lieu of ). So, what is the right command to handle polynomial systems over real domains in Maple? 

Can i get this ode in a "standardform"  ?

verg:= (-delta*eta^2 + alpha*eta)*diff(diff(U(xi), xi), xi) - U(xi)*(2*eta*gamma*theta*(delta*eta - alpha)*U(xi)^2 + eta^2*delta*k^2 + (-alpha*k^2 - 2*delta*k)*eta + 2*k*alpha + delta) = 0;

Since the puzzle task "A circle is to be disturbed ..." makes no fun, here is a Maple task:
The term to be simplified step by step:
(2+10/(3*sqrt(3)))^(1/3)+(2-10/(3*sqrt(3)))^(1/3)

A circle with radius r is given. The circle should be divided into three
parts of equal area such that the circumference of each part is equal to the circumference of the circle.
(Note: There are several solutions.)

I have learned that the SPECTRA.mla library can solve SDP problems. I have tried to download and use it, but I am still missing the FGb module

How can I resolve this issue on a Windows environment, beause I don't see install file for Windows, only MacOS and Linux:

• FGb page: https://www-polsys.lip6.fr/~jcf/FGb/FGb/index.html
• Spectra page: https://homepages.laas.fr/henrion/software/spectra/