Maple 2021 Questions and Posts

These are Posts and Questions associated with the product, Maple 2021

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

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.

restart

``

NULL

NULL

A := factorial(2*m2+3*m3)*c0^(1+m2+2*m3)*c2^m2*c3^m3/(factorial(1+m2+2*m3)*factorial(m2)*factorial(m3)*c1^(2*m2+3*m3+1))

factorial(2*m2+3*m3)*c0^(1+m2+2*m3)*c2^m2*c3^m3/(factorial(1+m2+2*m3)*factorial(m2)*factorial(m3)*c1^(2*m2+3*m3+1))

(1)

"P:=3, N:=4"

4

(2)

``

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

S := {seq(0 .. N)}; l := P-1; f := proc (T) options operator, arrow; [seq(seq([op(T[j]), S[i]], i = 1 .. nops(S)), j = 1 .. nops(T))] end proc; L := (f@@l)([[]])

[[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 0], [1, 1], [1, 2], [1, 3], [1, 4], [2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [4, 0], [4, 1], [4, 2], [4, 3], [4, 4]]

(3)

nops(L)

25

(4)

NULLNULL

``

nops(L)

25

(5)

Instead of using add(add(A, m2 = 0 .. 4)*m3 = 0 .. 4)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

 

add(A, `in`([m2, m3], L))

Error, illegal use of an object as a name

 

 

 

 

 

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

 

 

 

B := factorial(2*m2+3*m3+4*m4)*c0^(1+m2+2*m3+3*m4)*c2^m2*c3^m3*c4^m4/(factorial(1+m2+2*m3+3*m4)*factorial(m2)*factorial(m3)*factorial(m4)*c1^(2*m2+3*m3+4*m4+1))

factorial(2*m2+3*m3+4*m4)*c0^(1+m2+2*m3+3*m4)*c2^m2*c3^m3*c4^m4/(factorial(1+m2+2*m3+3*m4)*factorial(m2)*factorial(m3)*factorial(m4)*c1^(2*m2+3*m3+4*m4+1))

(6)

P := 4; S := {seq(0 .. N)}; l := P-1; f := proc (T) options operator, arrow; [seq(seq([op(T[j]), S[i]], i = 1 .. nops(S)), j = 1 .. nops(T))] end proc; L := (f@@l)([[]])

[[0, 0, 0], [0, 0, 1], [0, 0, 2], [0, 0, 3], [0, 0, 4], [0, 1, 0], [0, 1, 1], [0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 0], [0, 2, 1], [0, 2, 2], [0, 2, 3], [0, 2, 4], [0, 3, 0], [0, 3, 1], [0, 3, 2], [0, 3, 3], [0, 3, 4], [0, 4, 0], [0, 4, 1], [0, 4, 2], [0, 4, 3], [0, 4, 4], [1, 0, 0], [1, 0, 1], [1, 0, 2], [1, 0, 3], [1, 0, 4], [1, 1, 0], [1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 1, 4], [1, 2, 0], [1, 2, 1], [1, 2, 2], [1, 2, 3], [1, 2, 4], [1, 3, 0], [1, 3, 1], [1, 3, 2], [1, 3, 3], [1, 3, 4], [1, 4, 0], [1, 4, 1], [1, 4, 2], [1, 4, 3], [1, 4, 4], [2, 0, 0], [2, 0, 1], [2, 0, 2], [2, 0, 3], [2, 0, 4], [2, 1, 0], [2, 1, 1], [2, 1, 2], [2, 1, 3], [2, 1, 4], [2, 2, 0], [2, 2, 1], [2, 2, 2], [2, 2, 3], [2, 2, 4], [2, 3, 0], [2, 3, 1], [2, 3, 2], [2, 3, 3], [2, 3, 4], [2, 4, 0], [2, 4, 1], [2, 4, 2], [2, 4, 3], [2, 4, 4], [3, 0, 0], [3, 0, 1], [3, 0, 2], [3, 0, 3], [3, 0, 4], [3, 1, 0], [3, 1, 1], [3, 1, 2], [3, 1, 3], [3, 1, 4], [3, 2, 0], [3, 2, 1], [3, 2, 2], [3, 2, 3], [3, 2, 4], [3, 3, 0], [3, 3, 1], [3, 3, 2], [3, 3, 3], [3, 3, 4], [3, 4, 0], [3, 4, 1], [3, 4, 2], [3, 4, 3], [3, 4, 4], [4, 0, 0], [4, 0, 1], [4, 0, 2], [4, 0, 3], [4, 0, 4], [4, 1, 0], [4, 1, 1], [4, 1, 2], [4, 1, 3], [4, 1, 4], [4, 2, 0], [4, 2, 1], [4, 2, 2], [4, 2, 3], [4, 2, 4], [4, 3, 0], [4, 3, 1], [4, 3, 2], [4, 3, 3], [4, 3, 4], [4, 4, 0], [4, 4, 1], [4, 4, 2], [4, 4, 3], [4, 4, 4]]

(7)

nops(L)

125

(8)

NULL


 

Download Sum_by_mapping_to_a_list_question.mw

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.
 

restart

NULL

NULL

NULL

``

``

a := -(sum(C2^(m-1)*C0^m*factorial(2*m)/(C1^(2*m-1)*factorial(m+1)*factorial(m)), m = 0 .. N))

-2*C1/(C2*(1+(-(4*C0*C2-C1^2)/C1^2)^(1/2)))+C2^N*C0^(N+1)*GAMMA(2*N+3)*(N+2)*hypergeom([1, 3/2+N], [N+3], 4*C0*C2/C1^2)/(C1^(2*N+1)*GAMMA(N+3)^2)

(1)

N := 4

4

(2)

a

-2*C1/(C2*(1+(-(4*C0*C2-C1^2)/C1^2)^(1/2)))+42*C2^4*C0^5*hypergeom([1, 11/2], [7], 4*C0*C2/C1^2)/C1^9

(3)

b := -(sum(C2^(m-1)*C0^m*factorial(2*m)/(C1^(2*m-1)*factorial(m+1)*factorial(m)), m = 0 .. N))

-C1/C2-C0/C1-2*C2*C0^2/C1^3-5*C2^2*C0^3/C1^5-14*C2^3*C0^4/C1^7

(4)

NULL

NULL``

unassign('N')

c := sum(sum((-1)^(m[3]+1)*factorial(2*m[2]+3*m[3])*C0^(1+m[2]+2*m[3])*C2^m[2]*C3^m[3]/(factorial(1+m[2]+2*m[3])*factorial(m[2])*factorial(m[3])*C1^(1+2*m[2]+3*m[3])), m[3] = 0 .. N), m[2] = 0 .. N)

sum(C2^m[2]*(-factorial(2*m[2])*C0^(1+m[2])*hypergeom([(2/3)*m[2]+1, (2/3)*m[2]+2/3, 1/3+(2/3)*m[2]], [1+(1/2)*m[2], 3/2+(1/2)*m[2]], -(27/4)*C0^2*C3/C1^3)/(factorial(1+m[2])*C1^(1+2*m[2]))-factorial(2*m[2]+3*N+3)*C0^(3+m[2]+2*N)*C3^(N+1)*hypergeom([1, (2/3)*m[2]+2+N, 5/3+(2/3)*m[2]+N, 4/3+(2/3)*m[2]+N], [N+2, 2+(1/2)*m[2]+N, 5/2+(1/2)*m[2]+N], -(27/4)*C0^2*C3/C1^3)*(-1)^N/(factorial(3+m[2]+2*N)*factorial(N+1)*C1^(4+2*m[2]+3*N)))/factorial(m[2]), m[2] = 0 .. N)

(5)

NULL

NULLN := 4

4

(6)

c

-C0*hypergeom([1/3, 2/3], [3/2], -(27/4)*C0^2*C3/C1^3)/C1-273*C0^11*C3^5*hypergeom([1, 16/3, 17/3], [6, 13/2], -(27/4)*C0^2*C3/C1^3)/C1^16+C2*(-C0^2*hypergeom([1, 4/3, 5/3], [3/2, 2], -(27/4)*C0^2*C3/C1^3)/C1^3-6188*C0^12*C3^5*hypergeom([1, 19/3, 20/3], [13/2, 7], -(27/4)*C0^2*C3/C1^3)/C1^18)+(1/2)*C2^2*(-4*C0^3*hypergeom([5/3, 7/3], [5/2], -(27/4)*C0^2*C3/C1^3)/C1^5-162792*C0^13*C3^5*hypergeom([1, 20/3, 22/3], [6, 15/2], -(27/4)*C0^2*C3/C1^3)/C1^20)+(1/6)*C2^3*(-30*C0^4*hypergeom([7/3, 8/3], [5/2], -(27/4)*C0^2*C3/C1^3)/C1^7-4883760*C0^14*C3^5*hypergeom([1, 22/3, 23/3], [6, 15/2], -(27/4)*C0^2*C3/C1^3)/C1^22)+(1/24)*C2^4*(-336*C0^5*hypergeom([10/3, 11/3], [7/2], -(27/4)*C0^2*C3/C1^3)/C1^9-164745504*C0^15*C3^5*hypergeom([1, 25/3, 26/3], [6, 17/2], -(27/4)*C0^2*C3/C1^3)/C1^24)

(7)

NULL

e := sum(sum((-1)^(m[3]+1)*factorial(2*m[2]+3*m[3])*C0^(1+m[2]+2*m[3])*C2^m[2]*C3^m[3]/(factorial(1+m[2]+2*m[3])*factorial(m[2])*factorial(m[3])*C1^(1+2*m[2]+3*m[3])), m[3] = 0 .. N), m[2] = 0 .. N)

-C0/C1-5*C2^3*C0^4/C1^7-C2*C0^2/C1^3-2*C2^2*C0^3/C1^5-3*C0^5*C3^2/C1^7+12*C0^7*C3^3/C1^10-55*C0^9*C3^4/C1^13-14*C0^5*C2^4/C1^9+C0^3*C3/C1^4+330*C0^7*C2^4*C3/C1^12-5005*C0^9*C2^4*C3^2/C1^15+61880*C0^11*C2^4*C3^3/C1^18-678300*C0^13*C2^4*C3^4/C1^21+5*C0^4*C2*C3/C1^6-28*C0^6*C2*C3^2/C1^9+165*C0^8*C2*C3^3/C1^12-1001*C0^10*C2*C3^4/C1^15+21*C0^5*C2^2*C3/C1^8-180*C0^7*C2^2*C3^2/C1^11+1430*C0^9*C2^2*C3^3/C1^14-10920*C0^11*C2^2*C3^4/C1^17+84*C0^6*C2^3*C3/C1^10-990*C0^8*C2^3*C3^2/C1^13+10010*C0^10*C2^3*C3^3/C1^16-92820*C0^12*C2^3*C3^4/C1^19

(8)

NULL


 

Download why_hypergeom.mw

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.]]

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  

Download SST_Gm_Stats.mwDownload 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

 

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?

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)]:
DrawGraph(s1,width=4,stylesheet = [vertexcolor = "Blue",vertexpadding=20])

 

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(
s1[1],width=4,stylesheet = [vertexcolor = "Blue",vertexpadding=20])

 

 

 

 

 

graph1.mw

 

 

 

 

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? 

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.

 

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

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?

Thanks in advance for your guidance.

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.

 

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.

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).

Hi there.

It looks strange but simplify/symbolic cannot handle expression in file:

example.mw

Only after expanding numerator and denominator by hand.

I think simplify/symbolic should be smarter.

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