Hi,

is there any package out there to calculate Wigner J symbols and Clebsch-Gordon coefficients in Maple

Good day to all of you nice people.
I'm currently attempting to plot a vector field where each component of the vector is defined by the equations S_x, S_y, and S_z, which are functions of the radial coordinate. Here is a depiction of how the vectors change with respect to r:

The next step, which I'm unsure how to do, is to plot the vectors around the z-direction, or I should say, in phi direction, to achieve something similar to this example:

Thank you a lot for your kind help. 

Here is my code:
Maple_Question.mw

I am running Maple 2023 - yes I should update - and I found a weird "bug" if you could call it that. For different versions of the Physics package I am getting different answers on the same problem. 
 

This is what I was getting when I run Version 1410:

And this is what I get if I used the latet update for 2023, Version 1683:

Strange right? I bring this up because it makes me wonder about potential errors in other computations...

The answer - equation 6 - in 1410 is the correct answer. This is simply a derivation of the Einstein Tensor. 

Or some other type of calculation in indexed set. I tried the maple android app with no luck. How is done in maple?

Hey there guys, was wondering if I could get some help with this - I'm pretty new to maple. 

I'm trying to take a collection of coupled ODEs I have and get maple put them in state-space form for me. I've tried a few different approaches and messed around with a few different commands but havent managed to quite make it work. At the moment I'm trying to make a DiffEquation object and then use StateSpace to get the state space representation, but I keep getting this "diff-eq is not a polynomial" line as a warning when I run the DiffEquation command and as an error when I try to conver to state space.

Could anyone tell me why I'm getting this and what the best/correct way to go about this is?

Cheers

Download 403TripleCart.mw

I`m trying execute the example of Deeplearnig:

with(DeepLearning);
v1 := Vector(8, i -> i, datatype = float[8]);
v2 := Vector(8, [-1.0, 1.0, 5.0, 11.0, 19.0, 29.0, 41.0, 55.0], datatype = float[8]);
model := Sequential([DenseLayer(1, inputshape = [1])]);
model := Vector(2, {(1) = Typesetting:-mi("`DeepLearning 

   Model`"), (2) = Typesetting:-mi("`<keras.engine.sequential.Se\

  quential object at 0x000001C5B6520700>`")})

model:-Compile(optimizer = "sgd", loss = "mean_squared_error");
model:-Fit(v1, v2, epochs = 500);
"<Python object: <keras.callbacks.History object at 0x000001C5CC\

  EE9DE0>>"

convert("<Python object: <keras.callbacks.History object at 0x000001C5CCEE9DE0>>", 'symbol');
<Python object: <keras.callbacks.History object at 0x000001C5CCE\

  E9DE0>>

model:-Predict([10]);

But, finally, there is this error:

Error, (in Predict) AttributeError: 'CatchOutErr' object has no attribute 'flush'

['Traceback (most recent call last):\n', '  File "C:\\Program Files\\Maple 2023\\Python.X86_64_WINDOWS\\lib\\site-packages\\keras\\utils\\traceback_utils.py", line 70, in error_handler\n    raise e.with_traceback(filtered_tb) from None\n', '  File "C:\\Program Files\\Maple 2023\\Python.X86_64_WINDOWS\\lib\\site-packages\\keras\\utils\\io_utils.py", line 80, in print_msg\n    sys.stdout.flush()\n', "AttributeError: 'CatchOutErr' object has no attribute 'flush'\n"]

What`s is happening?

Thanks!

I have a complicated bivariate function f(Gamma,rho) that is a RootOf of a quartic. I know that it is strictly positive (one of the four roots at least) for Gamma=0..10 and rho in (-1,+1), with bounds excluded.

I need to find the signs of its first and second derivatives (wrt to Gamma and wrt to rho: 4 derivatives in total).

I encounter numerical issues when I plot3d the derivatives using D[]() vs. fdiff() (numerical function evaluations of the RootOf). I was hoping for the two commands to produce the same output, but they don't it seems. What's going on?

Script:

Download signs_derivatves_bivariate.mw

Why does no substitution work on functions with s(n+1,t) (see eqns (2-8))? Also (&PartialD;)/(&PartialD; (sigma2*t))=1/(sigma2)(&PartialD;)/(&PartialD; t), how can I do it on Maple?shift.mw

I am trying to load the third-party package 'CPC Program Library (qub.ac.uk)' by following the instructions as in 'how to install wkptest? - MaplePrimes'. But encounter with Errors: '

Error, `:` unexpected
with(wkptest);
Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received wkptest

Download exam_wkptest1.mws

When I calculate the difference between two dates with the same day using the DateDifference Calendar function, I don't get an integer number of months, but results with extra days, hours, minutes, seconds and milliseconds. How can I calulate the actual number of months?

I appreciate any help.

Download DateDifference.mw

How can I calculate the integral of Legendre function P(n,theta) ?

int(cos(theta)*P(n,theta),theta=0..pi) ;

I never used Maple's StringTools:-RegSubs before.

I have a Latex string generated by Maple that has this form

"......    \\textrm{ ......   }  .... "

Where the dots mean anything, including space characters.  I need to change the part of the string  "\\textrm{ ...... }" to this

"......  \\begin{minipage}{\\linewidth}\\textrm{  ......   }\\end{minipage}  .... "

It is easy to change the opening part. Here is an example

s:="A& B& \\textrm{The fundamental matrix has } &C ";
s:=StringTools:-SubstituteAll(s,"\\textrm{","\\begin{minipage}{\\linewidth}\\textrm{");

Gives

The problem is how to replace the closing "}"  with "}\\end{minipage}".   I can't just replace "}" with "}\\end{minipage}" using SubstituteAll because I need to only change the "}" that closes the corresponding "\\textrm{" and not any other "}" that could be in the string.

So I need to use pattern matching or regular expression substitutions. The examples in help are not easy to understand.

Basically I need regular expression that matches 

                        "\\textrm{ WILDCARD * }" 

and change it to 

                        "\\begin{minipage}{\\linewidth}\\textrm{ WILDCARD * }\\end{minipage}" 

Any one know how to use Maple's egular expression to do this substitution using the above example?

Maple 2024 on windows 10.

Update

Thanks for the replies. I ended up writing small function that simply scan the string and do the replacement. 

Hi,

I want to analyze a quartic equation: rho-analysis.mw. I am interested in positive roots, which I need expressed in explicit/closed form.

I include four questions in the script.

Thanks!

EDIT (since my question was originally tagged as incomplete and even duplicate):
Above all I am trying to understand:

1. Why implicitplot3d returns a unique strictly positive root for all rho and Gamma but plot() of the quartic evaluated for a specific pair of value returns three positive roots?
2. rho is a correlation coefficient, thus bounded in (-1,+1): how to adjust the precision of the slider in Explore() so that I can play around with multiple rho values within said range?

Can this be better done in Maple ? , see worksheet.