MaplePrimes Questions

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

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)

Hi all guys, I don't know how to simplify this easy expression? I have tried simplify command, and expand command, no use. Welcome to answer and thank you!

 

y1(x) = 2*sin(x)-sin(2*x)+cos(2*x); y2(x) = 4*sin(x)+sin(2*x)-cos(2*x); diff(y1(x), x); diff(y1(x), x); simplify*(1/2*((diff(y1(x), x))^2+(diff(y2(x), x))^2)+1/2*(3*y1(x)^2-y1(x)*y2(x)+y2(x)^2))

simplify*((1/2)*(diff(y1(x), x))^2+(1/2)*(diff(y2(x), x))^2+(3/2)*y1(x)^2-(1/2)*y1(x)*y2(x)+(1/2)*y2(x)^2)

(1)

 

Download simplify_expression.mw

I have four symmetries as

1] \frac{\partial}{\partial t)

2] \frac{\partial}{\partial x)

3] \frac{\partial}{\partial y)

4] 2t \frac{\partial}{\partial t)+x\frac{\partial}{\partial x)+y\frac{\partial}{\partial y)-2u\frac{\partial}{\partial u)

Kindly help me out to find 1D optimal system with structural constants.

I will be greatful.

There exists a new (?) checkbox  in the Interface tab of the Options dialog: 

But I cannot find any find any explanation about it in the corresponding help page. What is the purpose of this feature? 

I have a Dataframe of data, although I assume this question applies to any type of rTable-like structure.

What is a simple/elegant way to export the image of the data to a JPG file?  I would be happy to see it in the format when I ask it to print the Dataframe, or when I use DocumentTools:-Tabulate.

I have created two graphs*, each is a combination of multiple plots. From this, I use "plots:-display" to create an array of the two graphs.  I wish to export this array of graphs to a jpg file. Is this possible?  (Yes, I can export each graph, but I would like it combined in the array image that Maple displays.)

* Why the asterisk: I make two plots. When I combine them through the plots:-display procedure, what type of output is produced? I've called it a graph. The help implies the output is a plot array. However, that is different from displaying an array of graphs through plots: display (Array([plot1, plot2])). Correct?

i have made a full working code for differential quadrature method now i am  changing examples and it is not working although i have properly defined new parameters i am attaching my code kindly help me out
one more thing one example include summation n=0..ininity it is not even evaluating taking alot of time i am attaching both codes kindly help me out
A+B_example.mw
chelishkov_comparison.mw

Is there a way to install 2024.1 and keep 2024 there also? i.e. install 2024.1 along side 2024? This way if I find a problem and want to check 2024 I still have it? 

i.e. install Maple 2024.1 in its own folder, separate from Maple 2024, and have its own icon on desktop. 

If I install 2024.1 using Tools->Check for update,  it will overwrite 2024 and not ask me if I want to keep it. At least this is what happened in Maple 2023 and earlier versions. So wanted to ask before I try to do this again, else it will be too late.

If I do not use Tools->Check for updates, and instead download 2024.1 manually from the product web page, will one then be able to install 2024.1 and keep 2024? Or will it also overwrite 2024? I have not tried because I do not know if it will ask me or not.

Maple 2024.

Dear all, in Maple Help exists the documentation of how to use the OpenMaple API Library. But I didn't found a link where to download the necessary libraries. I found e.g. the library maple-0.17.4.jar but it doesn't contain com.maplesoft.openmaple.*

http://www.java2s.com/example/jar/m/maple-index.html

Tahnks for help

Circular_gears_meshing_blunt_teeth_shape_from_involute_of_circle.mw

My worksheet has suddenly begun producing the following error message when executing legitimate commands:

Error, (in cos) type `SymbolicInfinity` does not exist

Why has this worksheet suddenly begun issuing these mysterious error messages and how can it be restored to working order?

What is the command to stopat and showstat the proc  DEtools:-odeadvisor ?

I tried

ode:=y(x)*(2*x^2*y(x)^3+3)+x*(x^2*y(x)^3-1)*diff(y(x),x)=0;
DEtools:-odeadvisor(ode);

showstat(`DEtools/odeadvisor`);

showstat(`ODEtools/odeadvisor`);

And few other variations. It works on other proc's  such as

stopat(`ODEtools/symtest`); 
stopat(`ODEtools/test`); 
stopat(`ODEtools/normal/expanded`); 
stopat(`ODEtools/odepde`); 

But I was never able to figure the name for `DEtools:-odeadvisor`

Is there a general method to determine the correct name to use for printing or stopping at Maple command code to see it?

For me, it seems like trial and error process. For example DEtools:-command   becmes ODEtools:-command to stop at. Notice the extra O needed for tracing or printing. Do not know why extra O is needed. But showstat(`DEtools/symtest`); gives error, and showstat(`ODEtools/symtest`); works even though the command itself has no O.

So my question is, what would be the command to stop at DEtools:-odeadvisor? Is there a place to read more about how to find the correct path to give so do not have to guess?

Maple 2024

Context of My Code:

I want to determine the SU(2) field strength tensor for a specific field configuration(later the equations of motion). I have managed to implement the covariant derivative and the gauge field, but now I am encountering problems with the field strength tensor. When substituting the definitions of my gauge field (7) and my covariant derivative (13) into my field strength tensor (14), the following problems occur:

  1. The derivatives do not act on f(r) or r (r should be the radial component of my coordinate system).
  2. The unit vectors are not explicitly multiplied together. Mixed terms should vanish and quadratic terms should result in one.

I am not even sure if I can properly form F[]^2 due to my definition in (4). I have seen in the setup that there are SU(2) indices, but I couldn't find anything helpful on how to handle this. Is it better to use SU(2) indexing?

It would be nice if someone could tell me why my terms are not simplifying or direct me to where I need to look to understand it.

Here is my code: 

SU(2)_Field_Strength.mw

Maple gives type of this first order ode as _homogeneous, `class C`, but it is also dAlembert ode.

When asking it to solve as  dAlembert using the method option, it solves it.

But it returns singular solution which is wrong as it does not satisfy the IC. Singular solution should also satisfy IC like particular solutions do.

Is this a bug or Am I overlooking something?

Should not the solution returned satisfy the IC even though method used is not listed from odeadvisor?
 

29028

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1764 and is the same as the version installed in this computer, created 2024, June 28, 12:19 hours Pacific Time.`

restart;

29028

ode:=diff(y(x), x) = (3*x - y(x) + 1)/(3*y(x) - x + 5);
ic:=y(0)=0;

diff(y(x), x) = (3*x-y(x)+1)/(3*y(x)-x+5)

y(0) = 0

sol:=dsolve([ode,ic],[dAlembert]); #this solution is singular solution.

y(x) = x-1

odetest(sol,[ode,ic]); #notice, solution do not satisfy IC

[0, 1]

sol2:=dsolve([ode,ic]):
odetest(sol2,[ode,ic]); #this is OK since used default method, not dAlembert

[0, 0]

DEtools:-odeadvisor(ode)

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

 


 

Download dsolve_dalembert_july_2_2024.mw

 

Dear All,

I have a polynomial in terms of time. I know that based on the nature of the problem, the real function that governs this problem is the sum of exponential functions with a negative power, for example, in the form of alpha[0]+add(alpha[i]*exp(-beta[i]*t), i=1.. 5).

Can you help me if there is a method that can be used to obtain these exponential functions using following polynomial?

The polynomial function is as follow:

f:=0.020399949322360296902872908942 + 0.0261353198432118595103693714851*t^3 + 0.0240968505875842806805439681431*t^4 + 0.0148456155621193706595799212802*t^5 + 0.0239969764160351203722354728376*t^2 + 0.0204278458408370651586217048716*t - 0.00450853634927256388740864146173*t^6 - 0.0355389767483113696513996149731*t^7 - 0.0766669789661906882315038416910*t^8 - 0.120843030849135239578151569663*t^9 - 0.153280689906711146639066606024*t^10 - 0.150288711858517536713273977277*t^11 - 0.0808171080937786380164380347445*t^12 + 0.0872390654213369913348407061899*t^13 + 0.373992140377042586618283139889*t^14 + 0.766807288928470485618700282187*t^15 + 1.19339994493571167326973251788*t^16 + 1.49476369302534328383069681700*t^17 + 1.41015598591182237492637420929*t^18 + 0.593451797299651247527539427688*t^19 - 1.31434443870999971750661332301*t^20;

Best wishes

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