## How do I solve the heat equation in spherical coor...

I'm trying to understand what I need to do to get Maple to solve the heat equation in spherical coordinates. I'm considering a test problem: a spherical shell with inner radius 1 and outer radius 2. Boundary conditions require the temperature of the inner and outer surfaces are to always equal zero. The initial condition requires the temperature inside the shell to be -sin(pi*r).

The attached worksheet provides my attempt to solve this problem. Executing this worksheet will quickly give a general solution but this does not include the initial condition. If this is included then Maple fails to give a solution even after a 20 min wait.

Could someone offer me guidance on how to proceed?

shell.mw

## Is it possible to Add/sum by mapping multiple valu...

I want to sum a series by getting multiple values from a list.  Based on the list L I was trying

add(A, [m2, m3] in L)   This seem to have dissapeared from the document but the error message remains.

 (1)

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I found this code by Kitonum 16740  https://www.mapleprimes.com/questions/138955-How-Do-I-Create-A-Variable-Number-Of-Nested-Loops-

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Instead of using I would like to map m2 and m3 to the values in list L and sum them. This should give a method for having a variable number of loops

I tried variants off without success

for the next higher order would need to map m2,m3, m4 to the generated list.

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## Sums as hypergeometric. Why?...

I have two summations that Maple converts to hypergeometric outputs. Is there a way to stop that?

I dont know how to get Maple to expand the Hyper geometric output for a given walue of N

if the value of N is defined first the output is as I would expect.

The real problem, the sumations are nested and when I get to four nested sums Maple sits there for hours trying to evaluate the general case.

I have only included the first 2 summations.

Any insights on this would be appreciated.

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## Warning, no iterations performed as initial point ...

What is the reason for the warning?

restart;
f := (x, y, z) -> 1 - x^4 + ln(x^4) + z^4 - y^4 - y^4*(ln(z^4) - ln(y^4));

with(Optimization);
Minimize(f(x, y, z), {x^2 + y^2 - z^2 - 1 = 0, 0 <= x - 1, 0 <= y - x, 0 <= z - y});
Warning, no iterations performed as initial point satisfies first-order conditions
[0., [x = 1., y = 1., z = 1.]]

## Invalid Minus Error...

I'm trying to lad a comma separated data set and I get an "Invalid minus error".  Neither the filename nor the data set has a minus anywhere in them.  See attached file:  SST Gm Stats.mw

Since I can't upload a .csv file here are its contents:

5248.65,5178.95,5231.01,5161.78,5329.23,5258.52,5311.33,5241.1,5268.2,5198.26,5250.5,5181.03,5348.75,5277.8,5330.79,5260.32,5248.91,5179.21,5231.27,5162.03,5329.49,5258.77,5311.59,5241.35,5268.47,5198.53,5250.77,5181.29,5349.02,5278.06,5331.06,5260.58,5238.16,5168.61,5220.56,5151.47,5318.58,5248.01,5300.72,5230.63,5257.68,5187.88,5240.02,5170.68,5338.06,5267.25,5320.15,5249.81,5238.42,5168.86,5220.82,5151.72,5318.84,5248.27,5300.98,5230.88,5257.95,5188.14,5240.28,5170.94,5338.33,5267.52,5320.41,5250.07,5249.41

Where's the "minus" let alone an invalid one?

John

## how to modify includepath in a worksheet and an mp...

Let's say I have an mpl file and in this file there are several lines `\$include<~/~/~.mpl>` and in some of those called mpl files, there are also some more include lines. And assume the paths of these files are given relative to a specific folder. Now I guess this specific folder has to be mentioned by modifying `includepath`. But looking at the help pages related to includepath (here and here) I get this sentence "it can be modified by calling kernelopts(includepath)", but I tired typing things like `kernelopts(includepath):="C:\\Homes\\testFolder";` and still I see `""` for `kernelopts(includepath);`. How can I tell Maple to look for the files relative to this location either by typing something at the Maple worksheet before typing `read("C:\\Home\\testFolder\\main.mpl);` or by adding a line at my main mpl file?

## Why is it converted to a latex file and then run ...

It is said that the LaTeX export of maple2021 has been improved , but unfortunately I still encounter the following problems.

When I execute the following related graph theory code,

restart;
with(GraphTheory):
s1:=[NonIsomorphicGraphs(4,restrictto = connected,output=graphs,outputform=graph)]:

It is strange that all graphs(.eps) are not produced in  corresponding folder  when I exported it as latex file . So it leads to the lack of graphs in the running results of latex.

If it is a single graph, there seems to be no problem.

restart;
with(GraphTheory):
s1:=[NonIsomorphicGraphs(4,restrictto = connected,output=graphs,outputform=graph)]:
DrawGraph(

graph1.mw

## Maple toolbar keeps disappearing, how do I make it...

Hi all,

When I open up Maple the toolbar which says insert: 'Math, Text etc' has disappeared. However sometimes when I restart the program the tool bar re-appears again. I have attached a screenshot have a look. I want to know is anyone else experiencing this in Maple 2021?

## How do I check the equality of two equations?...

I have two equations (assignments, to be accurate) from which I know they are equal:

f__1 := sqrt(4*a^2 + lambda__g^2)*c/(2*lambda__g*a)

f__2 := c*sqrt(1/lambda__g^2 + 1/(4*a^2))

However:

testeq(f__1 = f__2) returns FAIL

verify(f__1, f__2, equal) returns  FAIL

and

simplify(f__1 - f__2, sqrt)

does not return 0 but

-c*(sqrt((4*a^2 + lambda__g^2)/(lambda__g^2*a^2))*lambda__g*a - sqrt(4*a^2 + lambda__g^2))/(2*lambda__g*a)

What is the best method for checking such equalities?

I am sorry for not using the Maple Math input option but fpr such reason it did not accept the expressions in this question. I am sure I made a mistake but I do not know what mistake.

I tested all methods mentioned above with the 1. Binominal equation sucessfully.

## Not giving the correct output...

I was trying to get an aproximation of an expression, but it doesnt seem to provide the correct answer. for the following

((12*sqrt(13))/13 - 3/4)/(1 + ((12*sqrt(13))/13)(3/4))

maple provides 0.59568 and the actual answer is 0.73744

I dont know what I am doing wrong

## find a weak form to Navier equations...

I want to find a weak form to Navier equations and obtain a solution formulation . I am interested in solving this problem using a finite element solver for which we need to introduce these equations in weak form. Can anyone help me in this regard? What is a higher-order continuity in the FEM approximation. This is challenge with the FEM which is based the Lagrange basis functions. To overcome the shortcomings, should we use the isogemetric analysis being based on the NURBS basis functions? How FEM cover this shortage for solving this type of equations?

## Is it possible to write a table type together with...

We can write a list, set, MutableSet and array type together with their entries types. For example `list(polynom)` or `array(array(integer))`. But what about a table? For example how can I emphasize a type table with indices of the type integer and entries a list of integers? I was guessing `table(integer,list(integer))` which is not working, so my guess is not correct. I tried some other combinations which they didn't work too. I can't see anything in the programming guide and the help of Maple or a post here that is addressing this question.

Example:

```test:=table([1=[1,2,3],2=[6,5,4]]):
type(test,table(integer,list(integer))): # which of course is not working.```

## How to remove several entries from an array effici...

Consider 1-dimensional arrays in Maple. To add one element at the end of an array, there is a pre-defined command `ArrayTools:-Append` (or using `ArrayTools:-Insert` if one wants to add an element at another location of the array) and to remove one entry from an array there is another pre-defined command `ArrayTools:-Remove`. Now let's say I want to add several elements and remove several elements. If I want to add all of the new elements at the end of the array, there is a predefined command `ArrayTools:-Extend`. If I want to remove several entries that are sequal, then I can give the second argument of `ArrayTools:-Remove` as a range `n1..n2`. But now let's say I want to remove several entries that are not sequal, for examples entries with indices in `[5,8,14]`. Is there any special efficient way to do it or just defining a loop to do the removals one by one? Removing by a loop is not very nice since the number of indices will change after each removal. Then another idea is to redefine the whole array using a `select` or a `seq`. But I'm guessing that none of these are the best way to do so. If I was dealing with `MutableSet`, I would use `&minus`, but I can't use MutableSets in every situation, because MutableSets change the order of elements and have more special properties like no repeated elements etc.

## Lack of parentheses in displaying substitution in ...

Hi there.

I noticed some little bug:

example.mw

As you can see the second term in serie C looks like -M/sqrt(-M^2 + E) - k, but not like M*k/sqrt(-M^2 + E).