Maple 2024 Questions and Posts

How to retrieve the coefficients of a transcedenta...

Asked by: emendes 515

July 18 2024

1 5

Hello

Consider, as an example, the following (simple) transcendental equation.

alpha*((epsilon-1)*x+y-3*x*z-epsilon/3*x^3+b*sin(w)+3)

How to retrieve the coefficients and the terms considering that the unknowns are x,y,z and w? Something like [x,y,x*z,x^3,sin(w),1] and their coefficients.

many thanks

dsolve does not return solution unless given impli...

Asked by: nm 11718

July 18 2024

1 1

I have thought before that Maple's dsolve will try to return implicit solution automatically if unable to find explicit one or for some other reasons it prefers implicit.

But In this ode, we see Maple returns no solution at all for this first order quadrature ode, even though it can find solution when given implicit option.

Is this a correct behaviour? Should it not have returned this solution automatically?

>	interface(version);

>	Physics:-Version();

>

restart;

>	ode:=diff(y(x),x)=sin(y(x)); IC:=y(a)=b;

>	maple_sol:=dsolve([ode,IC]);

>	maple_sol:=dsolve([ode,IC],explicit);

>	maple_sol:=dsolve([ode,IC],implicit);

Download why_no_solution_by_dsolve_july_18_2024.mw

Update

I found another example of this problem. Maple gives no solution to this ODE unless option implicit is given. This is not right behaviour. If Maple can't give explicit solution, it should return the implicit one automatically. How is the user supposed to know there is a solution to this ode otherwise?

>

restart;

>	Physics:-Version();

>

restart;

>

libname;

$"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"$

>	ode:=(x^2+y(x)^2-2y(x))diff(y(x),x) = 2*x: IC:=y(0)=1: sol:=dsolve([ode,IC],y(x));

>	sol:=dsolve([ode,IC],y(x),'implicit');

>	sol:=dsolve([ode,IC],y(x),'useInt');

y(x) = -RootOf(exp(_Z)*x^2-(Int(_b*(_b-2)/exp(_a), _b = 0 .. -_Z))+Int(_b*(_b-2)/exp(_a), _b = 0 .. 1))

>	sol:=dsolve([ode,IC],y(x),'explicit');

>

Download why_does_not_solve_unless_implicit_august_12_2024.mw

Maple 2024.1 locks up completely when using timeli...

Asked by: nm 11718

July 17 2024

1 6

I called dsolve with timelimit on this ode. All of Maple instantly locks up.

I do not mean the worksheet, but everything. I have each worksheet using its own engine,. Not able to open new worksheet, nothing clicks. The whole front end locks up. Can't click on anything.

Killing every mserver.exe does not even resolve this. I had to terminate all of Maple from the task manager. The strange thing, is that looking at task manager I see mserver.exe doing nothing. zero CPU. Only the front end process is at high CPU (the one with the Java icon). It looks like the Java frontend is locked up for some reason.

Do others see the same thing? does this happen on the mac also? Please make sure to save all your work before trying to run this on your PC.

Maple 2024.1 on windows 10. This is first order Riccati ode.

Download maple_lock_up_july_17_2024.mw

These are GUI options on my end.

UPDATE 1

in Maple 2023.2 also on windows 10, there is no lock up at all. same code. The solution to the ode is very large. I tried using both typesetting level to EXTENDED and typesetting level MAPLE STANDARD and no hang.

I wonder if this has something to do with why Maple 2024.1 locks up? But I have not changed anything in my end. I made no change in options or anything else. same PC, same graphics card.

UPDATE 2

Found the BUG!!

In Maple 2024.1, if I change the display option typesetting level to EXTENDED, the front end do not hang.

If I change the display typesetting level MAPLE STANDARD, the ftont end hangs.

But why??

>	interface(version);

>	Physics:-Version();

>	ode:=(a2x^2+b2x+c2)diff(y(x),x)=y(x)^2+(a1x+b1)y(x)+a0x^2+b0*x+c0;

>	DEtools:-odeadvisor(ode);

>	interface(typesetting=extended):

>	timelimit(30,dsolve(ode));

>	interface(typesetting=standard):

>	#WARNING, this will hang MAPLE now. WHY?? timelimit(30,dsolve(ode));

Download maple_lock_up_july_17_2024_2.mw

ps. Reported to Maplesoft support. July 17, 2024. Hopefully this will be fixed in Maple 2024.2

Given that the solution of a PDE is known, how can...

Asked by: emendes 515

July 14 2024

0 2

Hello

I am trying to understand how to use Maple to solve a PDE. Below it is a problem (Henon-Heilles system) where the answer is known.

with(PDEtools);

infolevel[pdsolve]:=3:

declare(Hamil(x,y,u,v));

PDEHamil := u*diff(Hamil(x, y, u, v), x) + v*diff(Hamil(x, y, u, v), y) + (-2*x*y - x)*diff(Hamil(x, y, u, v), u) + (-x^2 + y^2 - y)*diff(Hamil(x, y, u, v), v) = 0;

pdsolve(PDEHamil)

Maple returns no solution, but one solution is:

sH:=1/2*(u^2+v^2)+1/2*(x^2+y^2-2/3*y^3)+x^2*y;

simplify(eval(subs(Hamil(x,y,u,v)=sH,PDEHamil)));
    0=0

What am I missing?

Many thanks.

How to change datatype of multiple columns in data...

Asked by: FDS 220

July 14 2024

1 0

I was working with a Dataframe when I wanted to change the datatype of multiple columns at the same time as this is quite a large dataframe. I found in the helpfile that I can change datatype by the following command:

SubsDatatype(Data, plts, float) which then change the datatype of "plts" into float. I had hoped that using multiple columns in the command would work in this way: SubsDatatype(Data, [plts, act], float) but apparently not. Is there a way to do this or do I have to do it column by column?

Additionally I have another question about dataframes. I would like to replace "0" in the dataframe by a "blank" as you can do in excel. How do you do this in a dataframe?

Thanks in advance for any help given!

Adding H-type error bars to a plot of 2d points...

Asked by: Scot Gould 1059

July 12 2024

1 3

Using ScatterPlot (or ErrorPlot), one can add error bars to a 2d point plot of data. However, the bars are single lines. I wish to create a plot with H-type error bars in both the horizontal and vertical directions. Below is an example showing how the bars should appear. (This image is taken from a previous question about adding error bars.)

I do not need to reproduce this figure exactly. The location of the data points and the size of the error bars are irrelevant. The closest I have seen is using BoxPlot.

Has this question been asked and answered? If so, I cannot find it.

Help on how to solve (if possible) a PDE. ...

Asked by: emendes 515

July 10 2024

0 7

Hello,

I need to check if Maple can solve a specific PDE. Since I don't know much about the PDEtools package, I wonder if a user familiar with it and experienced in solving PDEs could help me.

with(PDEtools);
declare(u(x,y,z,w));
PDE1:=alpha*(y+b*(w))*diff(u(x,y,z,w),x)+(x+z-b*(w))*diff(u(x,y,z,w),y)-c*y*diff(u(x,y,z,w),z)+d*(y-x)*diff(u(x,y,z,w),w)=0;
Sol1:=pdsolve(PDE1);

Maple returns NULL as the solution. Any ideas on how to obtain a solution, if possible? In other similar PDEs, u(x,y,w,z) has a quadratic form.

Many thanks,

axis labels on the wrong side of the vertical axis...

Asked by: nmacsai 280

July 10 2024

1 4

When you look at negative horiztonal values on a basic plot, the axis labels can be obscured by gridlines or the plot itself. I have been told many times to keep axis labels and gradation labels outside of the plotting area to avoid adding more information than is neccessary in the actual plotting area. Is there a way to move the label to the other side and rotate it by 180 degree? How do people normally deal with this issue?

See my example of how the axis labels can be obscured by gridlines.

axis_label_on_wrong_side_of_axis.mw

how to improve the typesetting of the gamma's...

Asked by: Ronan 1381

July 09 2024

2 14

I am trying to improve the positioning of the gammas in the diagram (at bottom) as they are too close to the points and lines. gamma1 and gamma2 have been assigned values. This best I could come up with is shown below.

>

restart;

>	with(plots):with(plottools):

>	with(Typesetting):

>	`gamma2`:=<3\|5\|2>

(1)

>	Pgamma2:=[3/2,5/2]

(2)

>	display(point(Pbeta2,symbol=solidcircle,symbolsize=14),textplot([Pgamma2[],Typeset((`gamma2` )),align={above}]))

>

Download 2024-07-10_Typeset_gamma.mw

How to retrieve the arguments of f_1 , the solutio...

Asked by: emendes 515

July 09 2024

2 2

Hello

I am trying to solve some PDEs using Maple. In one of them, Maple returns

SolL:= HL(x, y, z) = f__1(1/2*(2*sigma*z - x^2)/sigma, rho^2 - 2*rho*z + y^2 + z^2)

How to retrieve only the arguments of f__1?

Many thanks

c__1 and _C1 do not seem to work the same way....

Asked by: nm 11718

July 09 2024

1 4

The change from _C1 to c__1 is causing me so many problems as I still do not fully understand it.

I have nothing in my Maple ini file.

I was solving from a solution to an ode for the constant of integration, which I know is c__1 inside a proc.

But this was failing to solve for it. When I copy same code to global (worksheet), it works. So it is clearly issue of name space related to c__1 vs. _C1.

So even though the solution now has the subscripted version and not the traditional one (since that is the default now), it does not solve for it when inside a proc.

If instead I solve for _C1, then it works. Even though the solution has c__1. This is bizzar to me.

I also tried adding global c__1; inside the proc, but this did not help. (did not show this version in the worksheet).

Why is solving for c__1 fail inside a proc but works outside? Clearly the c__1 in the solution of the ode is not the same c__1 I typed in to solve for, even though on the screen they look the same.

So c__1 is not really the same as _C1 in all aspects. Right?

Here is worksheet. Example 1 below shows how it fails inside proc

Maple 2024.1. Does this happen for others on Linux or the Mac?

>

restart;

>	interface(version);

>	Physics:-Version();

Example (1) solving for constant of integration fails inside proc but works outside

>

restart;

>	foo:=proc(ode::`=`) local sol,the_constant; sol:=dsolve(ode); print("sol is ",sol); the_constant:=solve(sol,c__1); print("the constant is ",the_constant); end proc;

proc (ode::`=`) local sol, the_constant; sol := dsolve(ode); print("sol is ", sol); the_constant := solve(sol, c__1); print("the constant is ", the_constant) end proc

>	#this does not work ode:=diff(y(x),x) = 3/4*y(x)/x; foo(ode)

>

restart;

>	#this works ode:=diff(y(x),x) = 3/4*y(x)/x; sol:=dsolve(ode); print("sol is ",sol); the_constant:=solve(sol,c__1);

>

Example (2). Solving for _C1 works, even though the ode has c__1 , why??

>

restart;

>	foo:=proc(ode::`=`) local sol,the_constant; sol:=dsolve(ode); print("sol is ",sol); the_constant:=solve(sol,_C1); #notice solving for _C1 now print("the constant is ",the_constant); end proc;

proc (ode::`=`) local sol, the_constant; sol := dsolve(ode); print("sol is ", sol); the_constant := solve(sol, _C1); print("the constant is ", the_constant) end proc

>	ode:=diff(y(x),x) = 3/4*y(x)/x; foo(ode)

>

restart;

>	ode:=diff(y(x),x) = 3/4*y(x)/x; sol:=dsolve(ode); print("sol is ",sol); the_constant:=solve(sol,c__1); #these both work OK in global the_constant:=solve(sol,_C1); #these both work OK in global

>

Example (3). Forcing arbitraryconstants = subscripted it still does not work inside proc. Why??

>

restart;

>	foo:=proc(ode::`=`) local sol,the_constant; sol:=dsolve(ode,arbitraryconstants = subscripted); print("sol is ",sol); the_constant:=solve(sol,c__1); print("the constant is ",the_constant); end proc;

proc (ode::`=`) local sol, the_constant; sol := dsolve(ode, arbitraryconstants = subscripted); print("sol is ", sol); the_constant := solve(sol, c__1); print("the constant is ", the_constant) end proc

>	ode:=diff(y(x),x) = 3/4*y(x)/x; foo(ode)

>

Download constant_of_integration_solving_july_9_2024_maple_2024.mw

Hyperlink Question...

Asked by: Ronan 1381

July 07 2024

1 2

I have a command called Dual in a SubPackage. RationalTrigonometry:-UHG:-Dual(..). I cannot get the hyperlink from the overview page to work.i.e RationalTrigonometry,UHG,Dual If I use Dual on its own it finds another Maple command to do with boolean logic. What syntax should I use here? I have used RationalTrigonometry,Spread without a problem to avoid another Maple command.

Error, (in RootOf) _Z occurs but is not the depend...

Asked by: nm 11718

July 07 2024

2 3

I added radnormal(sol) to my solution to workaround bug in solve hanging.

But now new problem showed up. sometimes radnormal gives internal error when there are _Z's in solution.

radnormal(sol);
Error, (in RootOf) _Z occurs but is not the dependent variable

Attached worksheet. Sorry that the solution is very large and has lots of _Zs and RootOf, but this is the first one I can see so far in the log file of my program running, so I left it as is:

Should I check in my code that solution does not contain _Z before calling radnormal on it? Is this a bug or known limitation?

>

restart;

>	interface(version);

>	Physics:-Version();

>

sol:=1/6*(-a^3 - 3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 + 6*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a + 8*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 + 3*sqrt(3)*sqrt(-RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*(RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^4 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a^3 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3*a^2 + 4*a^3 + 12*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 - 24*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a - 32*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 - 108*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))) + 54*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))^(1/3) + 1/6*(4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2 + 2*a*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2) + a^2)/(-a^3 - 3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 + 6*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a + 8*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 + 3*sqrt(3)*sqrt(-RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*(RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^4 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a^3 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3*a^2 + 4*a^3 + 12*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 - 24*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a - 32*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 - 108*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))) + 54*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))^(1/3) - 1/6*a + 1/3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2):

>	radnormal(sol);

Error, (in RootOf) _Z occurs but is not the dependent variable

>

Download bug_Z.mw

2024.1 freezing or partial lockout...

Asked by: Ronan 1381

July 06 2024

1 12

I have had this a few times this week since updating to 2024.1 on Windows 10.

I get sudden freezes in a worksheet. The !!! button greys out. The ! button is ok, so the worksheet can be run by using ctrl A and click !

Has anyone else experienced this?

two solutions, exactly the same, one hangs and the...

Asked by: nm 11718

July 06 2024

1 2

I gave up trying to figure out why Maple sometimes generates solutions from my code that look different, running the same exact code. I know Maple is not deterministic and this can happen sometimes for reasons I will never know.

The following two solutions are the same, it just sometimes Maple shuffles terms a little around. For example SQRT(6) comes out SQRT(2)*SQRT(3). I have no idea why this happens. It could be how memory inside Maple happened to be at the time and what happened before.

But my question is the following. Here is one ode, and two solutions that are exactly the same. I called one good_sol and one bad_sol.

If I do simplify(bad_sol - good_sol) I get 0 = 0 but here is the problem. When calling odetest on the good_sol, Maple returns 0 instantly, But on the bad_sol it just hangs.

Even though the two solution are exactly the same. i.e. Mathematically the same.

I'd like to know why does this happen? And if there is a permanent fix I could always use.

The following worksheet shows this problem.

After much trial and error, I found that if I do radnormal(bad_sol) then now odetest returns zero right away and the hang is gone!

I am just trying to understand why. And why odetest then itself does not use radnormal if this makes it work better?

Do I need to call randormal on every solution before calling odetest then? Will calling randormal on the final solution have any bad side effects on other computation after that? It should not I would think.

This is all done in code without looking at the screen and having to decide. So I would need a solution that will work for all cases. But for now, I will change my code and add randormal to all solutions and see what happens.

Using 2024.1 on windows. May be Maple behaves different on macOS, I do not know.

>	interface(version);

>	Physics:-Version();

>

restart;

>	ode:=4xdiff(y(x),x)^2-3y(x)diff(y(x),x)+3 = 0;

>

bad_sol:=ln(x) - c__1 - 1/2*ln((y(x)^2 - 6*x)/x) - 3*ln((sqrt(3)*y(x) + sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))/sqrt(x)) + 1/2*arctanh(1/2*(-16*sqrt(x) + 3*y(x)*sqrt(2)*sqrt(3))*sqrt(2)/(sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))) + 1/2*arctanh(1/2*(16*sqrt(x) + 3*y(x)*sqrt(2)*sqrt(3))*sqrt(2)/(sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))) = 0;

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((3^(1/2)*y(x)+((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))/x^(1/2))+(1/2)*arctanh((1/2)*(-16*x^(1/2)+3*y(x)*2^(1/2)*3^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))+(1/2)*arctanh((1/2)*(16*x^(1/2)+3*y(x)*2^(1/2)*3^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))) = 0

>

good_sol:=ln(x) - c__1 - 1/2*ln((y(x)^2 - 6*x)/x) - 3*ln((sqrt(3)*y(x) + sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x))/sqrt(x)) + 1/12*sqrt(3)*sqrt(6)*sqrt(2)*arctanh(1/2*(-16*sqrt(x) + 3*y(x)*sqrt(6))*sqrt(2)/(sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x))) + 1/12*sqrt(3)*arctanh(1/2*(16*sqrt(x) + 3*y(x)*sqrt(6))*sqrt(2)/(sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x)))*sqrt(6)*sqrt(2) = 0;

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((3^(1/2)*y(x)+((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))/x^(1/2))+(1/12)*3^(1/2)*6^(1/2)*2^(1/2)*arctanh((1/2)*(-16*x^(1/2)+3*y(x)*6^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))+(1/12)*3^(1/2)*arctanh((1/2)*(16*x^(1/2)+3*y(x)*6^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))*6^(1/2)*2^(1/2) = 0

>	simplify(bad_sol-good_sol)

>	odetest(good_sol,ode); #instant answer

>	odetest(bad_sol,ode); #hangs

Warning, computation interrupted

>

>	radnormal(bad_sol)

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((y(x)*x^(1/2)*3^(1/2)+x*(-(-3*y(x)^2+16*x)/x)^(1/2))/x)+(1/2)*arctanh((-(-3*y(x)^2+16*x)/x)^(1/2)*(3*y(x)*x^(1/2)*3^(1/2)-8*2^(1/2)*x)/(3*y(x)^2-16*x))+(1/2)*arctanh((-(-3*y(x)^2+16*x)/x)^(1/2)*(3*y(x)*x^(1/2)*3^(1/2)+8*2^(1/2)*x)/(3*y(x)^2-16*x)) = 0

>	odetest(%,ode); #instant answer

>

Download why_same_sol_hangs_july_7_2024.mw

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