Hi,

Can anyone help me with the following technique?

solutions:

Are there any restrictions regarding path and filename length in Maple?

I am experiencing problems working with a file on a server, path and file length is 207 characters.

Using Maple-18 on Window 11...

I have a set of curves in a Maple 'vector.' I want to plot them all on the same figure, but if call 'display' with the vector it makes separate plots for each one. I have to all it with each plot individual to get them on the same plot:

lc is a 'vector' of curves (I use 'vector' because I want to append and that doesn't work for 'list')

display(lc) -- plots a separate plot for each element of lc

display(lc[1], lc[2], lc[3],...) puts them all on one plot as needed, but as there will be a large numbe of curvesr it's extremely tedious.

It is a Huygens principle based simulation of diffraction.

Download JFKWEdgeDifractionDirection.mwJFKWEdgeDifractionDirection.mwen.

Maple 2022.2

> restart
> expr = x^{^4}-10*x^{^2}+1
> plot(expr)

produces an error message:
com.maplesoft.maplets.ComponentAccessException: not a valid plot structure

plot(expr, x) works Ok.

Tom Dean

Hi, I'm trying to figure out, how to differentiate the following expression:

I also don't get how to properly index (indefinite) sum terms... Grateful for any advice!

How to fix the error?

How are they (tanh(a+b) , tanh(a-b)) defined in Maple?

Ger.mw

How to find the series.I'm getting this error.Please help to solve this.

AF.mw

I want to express my two variable function f using Taylor expansion. But no success yet.

Why Taylor series can not estimate my function in desired interval [-1<x,y<1]?

Download taylorProblem.mw

How I can solve a PDE on two regions with matching conditions at the common boundary?  

T1.mw

In Maple 2023 I haven't been able to sign in to the Maple Cloud.
In Maple 2022 there was no problem. In fact in my Maple 2022.2 I'm actually signed in right now.

I need this to get updates to the Physics updates. 
The toolbar in 2023.2 has a grayed out icon saying "Sign in". Nothing happens if I click on it.

PS. I'm also signed in right now to Maple 2021.2. So the problem couldn't be that I cannot be logged in to more than one Maple release.

[Moderator: long pasted output deleted - OP has provided file in reply]

For years I've been angry that Maple isn't capable of formally manipulating random vectors (aka multivariate random variables).
For the record Mathematica does.

The problem I'm concerned with is to create a vector W such that

type(W, RandomVariable)

will return true.
Of course defining W from its components w₁, .., w_N, where each w_n  is a random variable is easy, even if these components are correlated or, more generally dependent ( the two concepts being equivalent iif all the w_n  are gaussian random variables).
But one looses the property that W is no longer a (multivariate) random variable.
See a simple example here: NoRandomVectorsInMaple.mw

This is the reason why I've developped among years several pieces of code to build a few multivariate random variable (multinormal, Dirichlet, Logistic-Normal, Skew Multivariate Normal, ...).

In the framework of my activities, they are of great interest and the purpose of this post is to share what I have done on this subject by presenting the most classic example: the multivariate gaussian random variable.

My leading idea was (is) to build a package named MVStatistics on the image of the Statistics package but devoted to Multi Variate random variables.
I have already construct such a package aggregating about fifty different procedures. But this latter doesn't merit the appellation of "Maple package" because I'm not qualified to write something like this which would be at the same time perennial, robust, documented, open and conflict-free with the  Statistics package.
In case any of you are interested in pursuing this work (because I'm about to change jobs), I can provide it all the different procedures I built to construct and manipulate multivariate random variables.

To help you understand the principles I used, here is the most iconic example of a multivariate gaussian random variable.
The attached file contains the following procedures

MVNormal
  Constructs a gaussian random vector whose components can be mutually correlated
  The statistics defined in Distribution are: (this list could be extended to other
  statistics, provided they are "recognized" statitics, see at the end of this 
  post):
      PDF
      Mode
      Mean
      Variance
      StandardDeviation = add(s[k]*x[k], k=1..K)
      RandomSample

DispersionEllipse
  Builds and draws the dispersion ellipses of a bivariate gaussia, random vector

DispersionEllipsoid
  Builds and draws the dispersion ellipsoids of a trivariate gaussia, random vector

MVstat
  Computes several statistics of a random vector (Mean, Variance, ...)

Iserlis
  Computes the moments of any order of a gaussian random vector

MVCentralMoment
  Computes the central moments of a gaussian random vector

Conditional
  Builds the conditional random vector of a gaussian random vector wrt some of its components 
  the moments of any order of a gaussian random vector.
  Note: the result has type RandomVariable.

MarginalizeAgainst
  Builds the marginal random vector of a gaussian random vector wrt some of its components 
  the moments of any order of a gaussian random vector.
  Note: the result has type RandomVariable.

MardiaNormalityTest
  The multi-dimensional analogue of the Shapiro-Wilks normality test

HZNormalityTest
  Henze-Zirkler test for Multivariate Normality

MVWaldWolfowitzTest
  A multivariate version of the non-parametrix Wald-Folfowitz test

Do not hesitate to ask me any questions that might come to mind.
In particular, as Maple introduces limitations on the type of some attributes (for instance Mean  must be of algebraic type), I've been forced to lure it by transforming vector or matrix quantities into algebraic ones.
An example is

Mean = add(m[k]*x[k], k=1..K)

where m[k] is the expectation of the kth component of this random vector.
This implies using the procedure MVstat to "decode", for instance, what Mean returns and write it as a vector.

MultivariateNormal.mw

About the  statistics ths Statistics:-Distribution constructor recognizes:
To get them one can do this (the Normal distribution seems to be the continuous one with the most exhaustive list os statistics):

restart
with(Statistics):
X := RandomVariable(Normal(a, b)):
attributes(X);
      protected, RandomVariable, _ProbabilityDistribution

map(e -> printf("%a\n", e), [exports(attributes(X)[3])]):
Conditions
ParentName
Parameters
CharacteristicFunction
CDF
CGF
HodgesLehmann
Mean
Median
MGF
Mode
PDF
RousseeuwCrouxSn
StandardDeviation
Support
Variance
CDFNumeric
QuantileNumeric
RandomSample
RandomSampleSetup
RandomVariate
MaximumLikelihoodEstimate

Unfortunately it happens that for some unknown reason a few statistics cannot be set by the user.
This is for instance the case of Parameters serious consequences in certain situations.
Among the other statistics that cannot be set by the user one finds:

• ParentName,
• QuantileNumeric  whose role is not very clear, at least for me, but which I suspect is a procedure which "inverts" the CDF to give a numerical estimation of a quantile given its probability.
  If it is so accessing  QuantileNumeric would be of great interest for distributions whose the quantiles have no closed form expressions.
• CDFNumeric  (same remark as above)

Finally, the statistics Conditions, which enables defining the conditions the elements of Parameters must verify are not at all suited for multivariate random variables.
It is for instance impossible to declare that the variance matrix (or the correlation matrix) is a square symmetric positive definite matrix).

According to the documentation of MmaTranslator:-Mma:-PolynomialReduce, this command yields . However, 

restart;
MmaTranslator:-Mma:-PolynomialReduce(x**2+y**2,{x-y,y+a});
 = 
                       [         2    2]
                       [[0, 0], x  + y ]

In[1]:= PolynomialReduce[x^2+y^2,{x-y,y+a}](*Mathematica*)

Out[1]= {{x + y, -2 a + 2 y}, 2 a^2}

In SymPy and in MuPAD: 

The output of both is the same as that of Mma; only the result given by Maple is inconsistent with Mathematica's. 

The example above is so simple that the desired result can be found simply by hand. Here is a larger example: 
Given two polynomials .txt and .txt, as well as a list of polynomials .txt, I would like to evaluate 

# Suppose that one has downloaded these three files. 
poly1, poly2 := fscanf("poly1.txt", "%a")[], fscanf("poly2.txt", "%a")[]:
pList := MmaTranslator:-Mma:-ReadList("pList.txt"):
MmaTranslator:-Mma:-PolynomialReduce((a - poly1)*(a - poly2), pList);

 But its result is just “[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], …]”, while when a＝0 it should be “[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 1, 0, 2, 2, 3, 1, 1, 1, 2, 1, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0], 0]”.
So why does  return a distinct value?

How would I solve for the product of two terms ( s*V or s^2*V). This is a simple example but I would be applying this on much higher order equations.

     V = Vx/(a*s^2 + b*s + c)

How do i retrieve the expression fra a "Fit" command so that i can use the expression for later calculations.

As you can see from the picture below, i use the "Fit" command to find an expression based on the values specified in X and Y. From there i would like to use the expression to find points on the line and to automate the proces. I can succesfully retrieve the expression by using the reference label, but is there another way to retrieve the expression so that i can avoid having to display the expression after evaluating?

I guess the question can be rephrased to: How do i retrieve the same information as the label reference does, but with a command and without using a label reference?