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Equation of motion of a vibrational elastic plate...

Asked by: alamir 10
differential-equations incomplete-question
November 01 2024
1  10

Hi, I am trying to build a code to get the equation of motion of a vibrational elastic plate in Maple 18. Could anybody help me?

why order of odetest makes difference in how it wo...

Asked by: nm 11398
ode remember differential-equations
October 31 2024
3  8

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.

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1824 and is the same as the version installed in this computer, created 2024, October 31, 14:22 hours Pacific Time.`

> 

kernelopts('assertlevel'=2):

CASE 1. Calling odetest on explicit first with assumptions, make odetest hang when calling on implicit after

 
> 

restart;

> 

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

> 

#find explicit solution first
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):

> 

#NOw check the explicit solution. Using assumptions to see the problem
timelimit(30,  ( odetest(y(x)=EXPLICIT_SOL,[ode,IC]) assuming positive, y(x)::positive) );

Error, (in evalr) time expired

> 

#Now odetest hangs on the implicit solution

> 

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

Error, (in is/internal/rename) time expired

> 

 

> 

 

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

y(x)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

CASE 2. Calling odetest on implicit solution first, then it DOES NOT hang !!

 
> 

restart;

> 

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

> 

#notice, no hang now, since called before
timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

[0, 0]

> 

#NOw check the explicit solution. This will timeout which is OK
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):
timelimit(30,  ( odetest(y(x)=EXPLICIT_SOL,[ode,IC]) assuming positive, y(x)::positive) );

Error, (in type/complex) time expired

> 

#check again that odetest still verifies the implicit solution OK

> 

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

[0, 0]

> 

 

CASE 3. Calling odetest with no assumptions on explicit solution, then it also does not hang

 
> 

restart;

> 

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

> 

#Now check the explicit solution. but DO NOT use assumptions
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):
timelimit(30, odetest(y(x)=EXPLICIT_SOL,[ode,IC]));

Error, (in factor/remember) time expired

> 

#check again that odetest still verifies the implicit solution OK

> 

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

[0, 0]

> 

 


 

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.

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1824 and is the same as the version installed in this computer, created 2024, October 31, 14:22 hours Pacific Time.`

> 

libname;

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

CASE 1. without PHYSICS on libname, it works !!

 
> 

restart;

> 

kernelopts('assertlevel'=2):

> 

libname;

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

> 

libname:=libname[2]; #remove PHYSICS

"C:\Program Files\Maple 2024\lib"

> 

libname;

"C:\Program Files\Maple 2024\lib"

> 

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

> 

#find explicit solution first
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):

> 

#NOw check the explicit solution. Using assumptions to see the problem
timelimit(30,  ( odetest(y(x)=EXPLICIT_SOL,[ode,IC]) assuming positive, y(x)::positive) );

Error, (in evalr/ln) time expired

> 

#Now try odetest  on the implicit solution

> 

infolevel[odetest]:=5;

5

> 

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

odetest: Performing an implicit solution test

odetest: Performing an explicit (try soft) solution test

odetest: Performing an implicit solution (II) test

[0, 0]

> 

 

> 

 

CASE 2. With Physics on libname, it fails !

 
> 

restart;

> 

kernelopts('assertlevel'=2):

> 

libname;

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

> 

IMPLICIT_SOL:=ln(10*x^2 + (10*y(x) + 12)*x + 5*y(x)^2 + 8*y(x) + 4)/5 - (4*arctan((5*y(x) + 5*x + 4)/(5*x + 2)))/5 = (3*ln(2))/5 + (4*arctan(3))/5;
ode:=2*x+3*y(x)+2+(y(x)-x)*diff(y(x),x) = 0;
IC:=y(0) = -2;

(1/5)*ln(10*x^2+(10*y(x)+12)*x+5*y(x)^2+8*y(x)+4)-(4/5)*arctan((5*y(x)+5*x+4)/(5*x+2)) = (3/5)*ln(2)+(4/5)*arctan(3)

2*x+3*y(x)+2+(y(x)-x)*(diff(y(x), x)) = 0

y(0) = -2

> 

#find explicit solution first
EXPLICIT_SOL:=solve(IMPLICIT_SOL,y(x)):

> 

timelimit(30,  ( odetest(y(x)=EXPLICIT_SOL,[ode,IC]) assuming positive, y(x)::positive) );

Error, (in evalr/shake) time expired

> 

#Now try odetest  on the implicit solution

> 

infolevel[odetest]:=5;

5

> 

timelimit(30,  odetest(IMPLICIT_SOL,[ode,IC]) );

odetest: Performing an implicit solution test

odetest: Performing an explicit (try soft) solution test

odetest: Performing an implicit solution (II) test

Error, (in is/internal/rename) time expired

 

 

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?

Maple Transactions Autumn Issue 2024 is now up

by: rcorless 740 Maple
October 31 2024
8  0

Maple Transactions has just published the Autumn 2024 issue at mapletransactions.org

From the header:

This Autumn Issue contains a "Puzzles" section, with some recherché questions, which we hope you will find to be fun to think about.  The Borwein integral (not the Borwein integral of XKCD fame, another one) set out in that section is, so far as we know, open: we "know" the value of the integral because how could the identity be true for thousands of digits but yet not be really true? Even if there is no proof.  But, Jon and Peter Borwein had this wonderful paper on Strange Series and High Precision Fraud showing examples of just that kind of trickery.  So, we don't know.  Maybe you will be the one to prove it! (Or prove it false.)

We also have some historical papers (one by a student, discussing the work of his great grandfather), and another paper describing what I think is a fun use of Maple not only to compute integrals (and to compute them very rapidly) but which actually required us to make an improvement to a well-known tool in asymptotic evaluation of integrals, namely Watson's Lemma, just to explain why Maple is so successful here.

Finally, we have an important paper on rational interpolation, which tells you how to deal well with interpolation points that are not so well distributed.

Enjoy the issue, and keep your contributions coming.

Maple and MapleSim 2024.2 updates

by: TechnicalSupport 790 Maple 2024 , MapleSim 2024
October 31 2024
3  0

We have just released updates to Maple and MapleSim.

Maple 2024.2 includes ability to tear away tabs into new windows, improvements to scrollable matrices, corrections to PDF export, small improvements throughout the math engine, and more.  We recommend that all Maple 2024 users install this update.

This update also include a fix to the problem with the simplify extension mechanism, as first reported on MaplePrimes. Thanks, as always, for helping us make Maple better.

This update is available through Tools>Check for Updates in Maple, and is also available from the Maple 2024.2 download page, where you can find more details.

At the same time, we have also released an update to MapleSim, which contains a variety of improvements to MapleSim and its add-ons. You can find more information on the MapleSim 2024.2 download page.

Content of exported SVG files is always outside th...

Asked by: mafitch 10
export svg
October 31 2024
2  0

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 m...

Asked by: GFY 65
matrix ode differential-equations
October 31 2024
0  3

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

Change of coordinates: Are there other ways to loo...

Asked by: C_R 3442
coords
October 31 2024
1  2

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

How do i define a tensor with an equation of three...

Asked by: Steve255 15
tensor differentialgeometry physics
October 30 2024
3  4

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

Solving Nonlinear Systems Symbolically in Maple...

Asked by: repromag 15
solve step-by-step
October 30 2024
0  0

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

Standard form ode ...

Asked by: janhardo 700
ode differential-equations duplicate-question
October 30 2024
0  8

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;

How to simplify the following term?...

Asked by: Alfred_F 345
step-by-step radical simplification
October 30 2024
1  3

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)

How can I use SPECTRA.mla in Maple on Windows?...

Asked by: bathudaide 25
package fgb spectra
October 29 2024
0  12

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

> with(SPECTRA);
> M := Matrix(6, 6, [[10, 1, 0, m[1], -m[3], m[2]], [1, -2*m[1]+27, m[3], -27/2, -m[4], -m[5]], [0, m[3], -2*m[2], m[4], m[5], 0], [m[1], -27/2, m[4], 10, 0, m[6]], [-m[3], -m[4], m[5], 0, -2*m[6], 0], [m[2], -m[5], 0, m[6], 0, 1]]);
> SolveLMI(M);
=> Error, (in SPECTRA:-SolveLMI) `FGb` does not evaluate to a module

 

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

Which of the following is a possible value of 𝑥?...

Asked by: yangtheary 290
gcd recreational-mathematics
October 29 2024
0  4

CUDA - Can I use it to speed up symbolic computati...

Asked by: Calin 10
performance linearalgebra cuda
October 28 2024
2  1

We are working to obtain a fully symbolic dynamic model for a robot. 

Using the CPU (I9-12900K) and 128 GB of DDR5 RAM (5600 MHZ) did not compute a 7x7 Inverse of a symbolic matrix

Is is possible to exploit the CUDA functions to compute it on the GPU? I have a NVidia RTX A6000 (48 GB of DDR6 GPU memory)

I tried this: 

CUDA:-Enable(true)

CUDA: -MatrixInverse(D_Q):

But it does not use the GPU to compute this. 

Maybe I'm doing smth wrong. 

Thank you, 

Calin

2F1 hypergeometric...

Asked by: masa13 15
mathematica import hypergeom
October 28 2024
3  8

Hi

Dear friends, I am a relatively new user and I have a problem in entering and calculating the 2F1 hypergeometric function. My question is how to enter this function in Maple in equations so that Maple recognizes it? Because hypergeom ([1], [2], [3]) Maple itself is a 3-element function, while 2F1 hypergeometric ([1], [2], [3], [4]) is a four-element!

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