Questions - MaplePrimes

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

How do I prevent Maple from displaying the actual ...

Asked by: lemelinm 1535

July 09 2024

3 2

I think the question speaks for itself. I tried the search engine and he bring me one link on that subject. But when I click on it, he sent me inside many answers on everyting but that. Not even the right month. So that is why I am asking here again. Of course, I would like to keep the thickmarks and the labels on both axes. Thank you in advance for your help.

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

Asked by: nm 11353

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

What is the best way to upload several mw and m fi...

Asked by: mmcdara 7891

July 08 2024

1 2

If I'm not mistaken Mapleprimes doesn't accept m files nor folders.

TIA

get the error order of the estimated polynomial co...

Asked by: Aixleft math 120

July 07 2024

0 10

Hi all guys, when i am doing error analysis but I meet with an problem. I get the trace and determinant of one matrix which consists a lot trigonometric functions. I wanna get the approximation error order of trace and determinant (Like tr=2+O(v^6),det=1+O(v^6)). But I use Taylor expansion and series, it displays can't compute the series. How to know the other ways to get the error order of it? Thanks all !phase_error_try.mw

>

(1)

>

A := Matrix([[0, 0, 0], [-(cos((1/10)*(5+sqrt(5))*v)-1)/v^2, 0, 0], [0, -(cos((1/10)*(-5+sqrt(5))*v)-1)/(cos((1/10)*(5+sqrt(5))*v)*v^2), 0]])

>

(2)

>

(3)

>

(4)

>

G := Matrix([[0], [10*sin((1/10)*(5+sqrt(5))*v)/((5+sqrt(5))*v)], [(10*(sin((1/10)*(-5+sqrt(5))*v)*cos((1/10)*(5+sqrt(5))*v)+sin((1/10)*(5+sqrt(5))*v)*cos((1/10)*(-5+sqrt(5))*v)-sin((1/10)*(5+sqrt(5))*v)))/(v*cos((1/10)*(5+sqrt(5))*v)*(-5+sqrt(5)))]])

>

(5)

>

(6)

>

(7)

>

(8)

>

tr := N11+N44

>

det := N11*N44-N22*N33

>

Warning, computation interrupted

(9)

Download phase_error_try.mw

pansion)

Hyperlink Question...

Asked by: Ronan 1341

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.

Factor a polynomial...

Asked by: Susana30 70

July 07 2024

2 6

Good afternoon, please how to factor the following polynomial so that it gives me the following result:

x^10/36 - 4/25*y^24*z^8 = (x^5/6 - 2/5*y^12*z^4)*(x^5/6 + 2/5*y^12*z^4)

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

Asked by: nm 11353

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 1341

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?

Do I really get all values from this RootOf expres...

Asked by: C_R 3412

July 06 2024

2 5

I was about to verify two solutions of dsolve from here but could not find an agreement for negative values. This makes me wonder if all values are computed.

There is also a different behaviour that I do not understand when allvalues is given a RootOf expression or an equation containing a RootOf expression.

dsolve without method

>	ode:=diff(y(x), x) = (3x - y(x) + 1)/(3y(x) - x + 5); ic:=y(0)=0; dsolve({ode,ic}); plot(rhs(%),x=-10..10,numpoints=10); evalf(subs(x=3,%%)); evalf(subs(x=-3,%%%));

y(x) = -(-(1/36)*(x+1)^2*((-324+12*(96*x^3+288*x^2+288*x+825)^(1/2))^(2/3)-24*x-24)^2/(-324+12*(96*x^3+288*x^2+288*x+825)^(1/2))^(2/3)-x^3-x^2+x+1)/(x+1)^2

(1)

dsolve with a particular method

>	sol:=dsolve([ode,ic],[dAlembert]); odetest(sol,[ode,ic]);

y(x) = RootOf(-6*((x+_Z+3)/(5+3*_Z-x))^(2/3)*(-4*(-x+_Z+1)/(5+3*_Z-x))^(1/3)*_Z+2*((x+_Z+3)/(5+3*_Z-x))^(2/3)*(-4*(-x+_Z+1)/(5+3*_Z-x))^(1/3)*x+2*(-4)^(1/3)*3^(2/3)-10*((x+_Z+3)/(5+3*_Z-x))^(2/3)*(-4*(-x+_Z+1)/(5+3*_Z-x))^(1/3))

(2)

Since allvalues fails on this expression for real valued x, rational and integer values are tried for punctual comaprision

>	subs(x=3,sol); allvalues(%); evalf(%)

y(3) = RootOf(-6*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)*_Z-4*((6+_Z)/(2+3*_Z))^(2/3)*(-4*(-2+_Z)/(2+3*_Z))^(1/3)+2*(-4)^(1/3)*3^(2/3))

(3)

Two roots match the dsolve solution without method. However doing the same only on the right hand side produces different output. For some reason allvalues produces 3 RootOf expressions with a numerical root selector.

>	subs(x=3,rhs(sol)); allvalues(%); evalf(%)

(4)

Why this change?
Now the same with a negative value. Now the root does not match the solution of the dsolve call without method.

>	subs(x=-3,sol); allvalues(%); evalf(%)

y(-3) = RootOf(-6*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3)*_Z-16*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3)+2*(-4)^(1/3)*3^(2/3))

(5)

>	subs(x = -3, rhs(sol)); allvalues(%); evalf(%);

RootOf((3*I)*3^(1/6)*2^(2/3)-6*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3)*_Z+2^(2/3)*3^(2/3)-16*(_Z/(8+3*_Z))^(2/3)*(-4*(4+_Z)/(8+3*_Z))^(1/3), 1.302775638+0.*I)

(6)

>

Download allvalues.mw

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

Asked by: nm 11353

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

Floating-point values...

Asked by: felixiao 15

July 06 2024

0 4

Why does it appear floating-point values?

How a figure evolves when a point moves...

Asked by: JAMET 425

July 06 2024

1 2

restart;
with(plots);
with(geometry);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
xA := 5;
yA := 0;
point(A, xA, yA);
xB := 5;
yB := -7;
point(B, xB, yB);
midpoint(C, A, B);
segment(sg1, A, B);
xP := -12;
yP := 0;
point(P, xP, yP);
PerpenBisector(L, C, P);
line(YYp, y = yB);
line(XXp, y = 0);
intersection(M, L, YYp);
line(PM, [P, M]);
projection(H, C, PM);
triangle(CMP, [C, M, P]);
triangle(ABH, [A, B, H]);
distance(B, H);
circle(cir, [B, 7]);
display(textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B "], [coordinates(C)[], "C"], [coordinates(M)[], "M"], [coordinates(H)[], "H"], [coordinates(P)[], "P"]], align = {"above", 'right'}),
draw([YYp(color = red), XXp(color = black), PM(color = green), L(color = green), sg1(color = black), cir(color = magenta), P(color = black, symbol = solidcircle, symbolsize = 10), M(color = black, symbol = solidcircle, symbolsize = 10), H(color = black, symbol = solidcircle, symbolsize = 10), A(color = blue, symbol = solidcircle, symbolsize = 10), B(color = blue, symbol = solidcircle, symbolsize = 10), CMP(color = blue, filled = true, transparency = 0.8), ABH(color = red, filled = true, transparency = 0.8), C(color = blue, symbol = solidcircle, symbolsize = 10)]),
axes = none, view = [-15 .. 14, -15 .. 3]);
I want to change this figure when xP varies from -12 to 12; Is it possible to use Explore or animate ? Thank you.

How to use Intc() and Fundiff() in spherical coord...

Asked by: hendriksdf5 65

July 05 2024

1 2

Is there a way to apply Intc() and Fundiff() in spherical coordinates? If I initialize a spherical coordinate system X and then want to calculate the effect with Intc(), r, theta phi and t are integrated from -inf to inf but thtea:(0, pi) phi:(0, 2Pi). I would also need a second spherical coordinate system Y, if I have understood Fundiff() correctly, but how can I define this Coordinates(X = spherical, Y = spherical) does not work.

I would like to vary my Lagrange density (16) with respect to f_A(r). Where r is the radial coordinate of the spherical coordinate system.

YANG-MILLS-Theorie.mw

Piecewise function defining...

Asked by: imparter 175

July 05 2024

0 3

Dear maple user,for defining the piecewise function please rectify this

h:z-> piecewise(do+Lo<z<do+4*Lo+0.3, 1-cos(2*pi*(z-L), other wise 1)

E-Mail Address:
Password:
Remember Me:	Automatically sign in on future visits

E-Mail Address:
Password:
Remember Me:	Automatically sign in on future visits

Ask a Question

Create a Post

MaplePrimes Questions

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

How do I prevent Maple from displaying the actual ...

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

What is the best way to upload several mw and m fi...

get the error order of the estimated polynomial co...

Hyperlink Question...

Factor a polynomial...

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

2024.1 freezing or partial lockout...

Do I really get all values from this RootOf expres...

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

Floating-point values...

How a figure evolves when a point moves...

How to use Intc() and Fundiff() in spherical coord...

Piecewise function defining...

Save this setting as your default sorting preference?

Ask a Question

Create a Post

Generating PDF…

Save this setting as your default sorting preference?
Note: You can change your preference any time in your account settings
Don't show this again