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ecterrab

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Fixed within the Physics Updates v.1838...

ecterrab 14540
December 13 2024
2 0

As explained in a comment, this was a problem related to recent fixes in Typesetting, introduced in v.1835. This change now resolves that problem. To install the corrected version, as usual, input Physics:-Version(latest);

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Fixed - Maplesoft Physics Updates v.1837...

ecterrab 14540
December 10 2024
3 0

Thanks for the report; this one is fixed. To install the fix in Maple 2024, as usual, input Physics:-Version(latest);

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Non-commutative operators of different H...

ecterrab 14540
December 02 2024
3 0


Download Different_Hilbert_spaces.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Physics Updates v.1831...

ecterrab 14540
November 22 2024
3 1

I also don't like unnecessary brackets. I touched the Typesetting so that, at least for this example, we do not have unnecessary brackets anymore. To install, as usual, input Physics:-Version(latest). Now, the Typesetting code is tricky; could you please help posting here:

  • More cases of unnecessary brackets.
  • Any case you think the brackets are missing, so the opposite situation.

Thanks

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Fixed in the Physics Updates v.1830, and...

ecterrab 14540
November 21 2024
1 0

To have the fix installed, open Maple and input Physics:-Version(latest);

Now, clearly, "no output at all", was a bug. I don't know what you actually meant by "Did Maple always behave this way for Laplace?"

On your comparison with Maple competitors, Mathematica or any other one, I'd like to make a point clearly: neither it produces shame nor urgency. Actually, when I read these strange comparisons (like a bug with a no-bug), I personally dislike the communication style. For me, it is just not constructive or purposeless, making me automatically lower the issue's priority. Fixing issues on the fly, as is the case of the Maplesoft Physics Updates project, has the underlying idea of collaboration and excitement, say, the opposite of such adversarial comparisons of inequivalent things.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Section 7 of ?Physics,Tensors...

ecterrab 14540
November 10 2024
1 3

Section 7 of ?Physics,Tensors is called Inert Tensors. Regarding a tensor definition, e.g. for Ricci or any other one, also the ones you define using defining equations, to see the definition even when the tensor has all of its components equal to zero, use the 'definition' keyword to index the tensor, e.g. input Ricci[definition].

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

It is already like that...

ecterrab 14540
November 10 2024
1 1

With a signature where the timelike component is in position 4, e.g. (---+), both X[4] and X[0] return t, so yes you can count starting from 0. If the timelike component is in position 1, then no, you cannot start counting from 0.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

DifferentialAlgebra[Tools] SortByRank...

ecterrab 14540
October 07 2024
2 1

I understand this command does what you want to do, i.e. sort by rank. An equivalent command may be in the Grobner or RegularChains packages.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

dsolve([ode], [f, {c1, c2, c3, c4, c5}])...

ecterrab 14540
October 03 2024
3 5

This is your ODE

ODE := c1*(diff(f(x), x, x, x, x))+c2*(diff(f(x), x, x, x))/x+c3*(diff(f(x), x, x))/x^2+c4*(diff(f(x), x))/x^3+c5*f(x) = 0


Naturally, for any values of the c1, c2, c3, c4, c5 you have a different - yet perfectly valid - differential equation, so the ODE does not restrict the values of those five constants.
If I am understanding your question right, the question is which solutions can Maple find for the different cases where all these five constants are equal to 0 (then f(x) is arbitrary) or taking them different from 0, one or more at a time, such that the resulting ODE is solvable by Maple.

To answer such a question use dsolve directly, just pass the ODE enclosed within [] or {}, and note the ranking I am using [f, {c1,c2,c3,c4,c5}] (for information on that, see the help page for PDEtools:-casesplit which is used by dsolve and pdsolve on background). To avoid cluttering, close with `:`, and here I just check a few

solutions := dsolve([ODE], [f, {c1, c2, c3, c4, c5}])

 

Consider the first case:

solutions[1]

{c1 = 0, c2 = 0, c3 = 0, c4 = 0, c5 = 0, f(x) = f(x)}

 (1)

OK, that was easy. Next

solutions[2]

{c1 = 0, c2 = 0, c3 = 0, c4 = 0, c5 = c5, f(x) = 0}

 (2)

Also easy. Move forward some few

solutions[4]

{c1 = 0, c2 = 0, c3 = c3, c4 = c4, c5 = c5, f(x) = c__1*x^((1/2)*(c3-c4)/c3)*BesselJ(-(1/4)*(c3-c4)/c3, (1/2)*(c5/c3)^(1/2)*x^2)+c__2*x^((1/2)*(c3-c4)/c3)*BesselY(-(1/4)*(c3-c4)/c3, (1/2)*(c5/c3)^(1/2)*x^2)}

 (3)

Good, we are now in non-trivial territory, with three constants different from 0, J and Y are Bessel functions, and the solution depends on these three non-zero constants in a non-trivial way.

Etc.

And how many cases could Maple solve?

nops([solutions])

6``

 (4)

NULL


 

Download solve_for_f_and_c1_to_c5.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Fixed within the Maplesoft Physics Updat...

ecterrab 14540
September 18 2024
2 1

Regardless of RootOf's caching approach, this error interruption should not happen in the first place. The problem is fixed, and the fix is distributed within the Maplesoft Physics Updates v.1808 or newer. To install, open Maple and input Physics:-Version(latest)

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Unable to reproduce, this is what I get...

ecterrab 14540
September 04 2024
2 5

Using directly Maple TTY to avoid any interference: no error message.

I suggest you to revise you don't have anything interfering, and if you still see this error message you posted, then input 'tracelast;' and post its output here so that I could see how this message you get is produced. If entering tracelast results in nothing, executing the odetest line again, reproducing the error, then tracelast again.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Fixed within the Maplesoft Physics Updat...

ecterrab 14540
August 28 2024
2 1

To install the fix (works only for Maple 2024), as usual, open Maple and input Physics:-Version(latest)

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Adjusted in the Maplesoft Physics Update...

ecterrab 14540
August 22 2024
3 0

Hi @nm
Note first that you show how to compute an implicit solution, for which dsolve([ode, IC], implicit) works fine and returns, exactly, the solution you show as my_new_sol.

The problem was related to computing an explicit solution, a process involving computing a series that happened to interrupt with that error you saw. That problem is solved and the adjustment is distributed within the latest Maplesoft Physics Updates for Maple 2024. (install via Physics:-version(latest))

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Issue in solve (not dsolve)...

ecterrab 14540
August 19 2024
2 0

While solving the ode + IC, the following call to solve is what hangs

> 

ee := ((y(x)-1)*(y(x)+1))^(1/2)/(y(x)-1)^(1/2)/(y(x)+1)^(1/2)*ln(y(x)+(y(x)^2-1)^(1/2))-1/2*(y(x)^2-1)^(1/2)*(-ln(-y(x)^2+1)+2*ln((y(x)^2*x+((x^2-1)*(y(x)^2-1))^(1/2)*(y(x)^2-1)^(1/2)-x)/(y(x)^2-1)^(1/2)))/(y(x)-1)^(1/2)/(y(x)+1)^(1/2)-1/2*(y0^2-1)^(1/2)*(2*ln(y0+(y0^2-1)^(1/2))+ln(-y0^2+1)-2*ln((y0^2*x0+((x0^2-1)*(y0^2-1))^(1/2)*(y0^2-1)^(1/2)-x0)/(y0^2-1)^(1/2)))/(y0-1)^(1/2)/(y0+1)^(1/2)

((y(x)-1)*(y(x)+1))^(1/2)*ln(y(x)+(y(x)^2-1)^(1/2))/((y(x)-1)^(1/2)*(y(x)+1)^(1/2))-(1/2)*(y(x)^2-1)^(1/2)*(-ln(-y(x)^2+1)+2*ln((y(x)^2*x+((x^2-1)*(y(x)^2-1))^(1/2)*(y(x)^2-1)^(1/2)-x)/(y(x)^2-1)^(1/2)))/((y(x)-1)^(1/2)*(y(x)+1)^(1/2))-(1/2)*(y0^2-1)^(1/2)*(2*ln(y0+(y0^2-1)^(1/2))+ln(-y0^2+1)-2*ln((y0^2*x0+((x0^2-1)*(y0^2-1))^(1/2)*(y0^2-1)^(1/2)-x0)/(y0^2-1)^(1/2)))/((y0-1)^(1/2)*(y0+1)^(1/2))

 (1)
> 

solve(ee, y(x));  # hangs
> 

NULL


 

Download issue_in_solve.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

This is a problem in solve, not PDEtools...

ecterrab 14540
August 15 2024
3 0

This is a problem in solve.

> 

restart;
> 

eqs := [-2*arctanh((_C1-1)^(1/2)/_C1^(1/2)) = _C2, 0 = _C1^(3/2)*tanh(1/2*_C2)*sech(1/2*_C2)^2];
unknowns := {_C1,_C2};

[-2*arctanh((_C1-1)^(1/2)/_C1^(1/2)) = _C2, 0 = _C1^(3/2)*tanh((1/2)*_C2)*sech((1/2)*_C2)^2]

  

{_C1, _C2}

 (1)

Good:

> 

solve(eqs, unknowns)

{_C1 = 1, _C2 = 0}

 (2)

Simpler:

> 

tanh(_C2/2):
% = expand(%)

tanh((1/2)*_C2) = (cosh(_C2)-1)/sinh(_C2)

 (3)
> 

simplify((lhs-rhs)(%))

0

 (4)
> 

EQS := subs(%%, eqs)

[-2*arctanh((_C1-1)^(1/2)/_C1^(1/2)) = _C2, 0 = _C1^(3/2)*(cosh(_C2)/sinh(_C2)-1/sinh(_C2))*sech((1/2)*_C2)^2]

 (5)

Not good:

> 

solve(EQS, unknowns)

Warning, solutions may have been lost

  

The step that seems to be failing within solve: normalize functions in terms of independent exponentials

> 

convert(EQS, exp)

[-2*arctanh((_C1-1)^(1/2)/_C1^(1/2)) = _C2, 0 = 4*_C1^(3/2)*(exp(_C2)-1)/((exp(_C2)+1)*(exp((1/2)*_C2)+exp(-(1/2)*_C2))^2)]

 (6)
> 

solve(%, unknowns)

{_C1 = 1, _C2 = 0}

 (7)

NULL
Note as well that PDEtools:-Solve is not a solver 'itself' but a wrapper around the many Maple solvers (as explained in its help page), that returns results with a unified syntax and in addition performs an elimination step before forwarding to the corresponding solver. Expanding tanh(a/b) should not make solve fail - it seems a normalization of the expression in terms of independent exponentials, in solve, before proceeding, is failing. I will track this. Independent of that, the expansion is useful in several contexts but for tanh in particular it may be simpler to first do tanh -> sinh/cosh before expanding; that will probably workaround this issue in solve, but the problem itself, in solve, needs to be fixed.


PS: I added the workaround to solve's limitation mentioned, so that now PDEtools:-Solve returns a result. The adjustment is present in the latest Maplesoft Physics Updates for Maple 2024; as usual to install input Physics:-Version(latest).

Download why_PDEtools_Solve_fail_august_14_2024_(reviewed).mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

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