Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

How I can perform integration by parts, with respect to the x[0..1],y[0..1],t


U := (1/2)*(E*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)/(-upsilon^2+1)+E*upsilon*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)/(-upsilon^2+1))*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)+(1/2)*(E*upsilon*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)/(-upsilon^2+1)+E*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)/(-upsilon^2+1))*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)+E*(1-upsilon)*((1/2)*(diff(v(x, y), x))-z*(diff(w(x, y), x, y))+(1/2)*(diff(u(x, y), y))+(1/2)*(diff(w(x, y), x))*(diff(w(x, y), y)))^2/(-upsilon^2+1)+2*E*l^2*(diff(w(x, y), x, y))^2/(2+2*upsilon)+2*E*l^2*(-(1/2)*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), y, y)))^2/(2+2*upsilon)+2*E*l^2*((1/4)*(diff(v(x, y), x, x))-(1/4)*(diff(u(x, y), x, y)))^2/(2+2*upsilon)+2*E*l^2*((1/4)*(diff(v(x, y), x, y))-(1/4)*(diff(u(x, y), y, y)))^2/(2+2*upsilon)







 1)  Copy/paste problem .
 Looks like Maple is not able to copy/paste the output
 from a summation command . Look at my example .
 I have to use the  " lprint " command .
2)   Mysterious small box character .
 Suppose I want to edit a command . I want to replace a character with a left bracket
 (or right bracket or left accolade but strangely not the right accolade).
 I put the cursor on the character and type the left bracket (or right...) .
 The left bracket ( or right ...)  is inserted . Now when I try to delete the character,
 a small box appear . The  character I am trying to delete is shifting to the right .
  Like  I said , just a little annoying .
3)  Open file problem .
 The first file I open in Maple with the  ctrl-o command , the "open file window" appears in
  the center of the screen . All the others files I am opening , the "open file window"  show up
  in the bottom left corner , top center or top right corner ... randomly .
  Very annoying on a 27" screen . For this last one ,I am not shure  if it is a Maple 2018 problem
   or a Windows 10 64 bits problem . I have few programs in my computer .
  When I use Microsoft Paint or Wordpad ,I don't see this problem .
  I don't know if somebody else can confirm those annoying things . If I am not the only one
  then I am hoping the next updates or versions will fix that .
    Thanks !

Good morning everyone

I'm sorry if I'm asking a simple question, but I would like to create a maplet from a maple code I written.

My first problem is I would like to now how to create a table like in excel, to be fill up by the user of the maplet.

Basically, the maplet will consist of enter two parameters who define the number of colums and row needed for the table,

Then fill up this table, which gonna be plot, and then a button to fit this curve using an equation. And the starting value in order to fit the curve will also be set up by the user.

Thanks you in advance if you can help me to set up this table in the maplet.




I've just upgraded from v2017.3 to 2018. It worked OK until I installed latest service pack 2018.2.1 (server license provided by my University). Ever since I cannot use Maple. Anything I type I get Typesetting:-mparsed(...) error and the text/command I typed.


I’ve contacted our software tech support and they told me to change the typesetting level from advanced to standard and it did fix the problem.


But why does it happen in the first place? I’m running Windows 8.1 64bit. Out tech support told me to has something to do with 3D display issue on my machine and told me to bring my laptop on Monday to see if they can resolve the issue.


Anyone else have this problem? Why didn’t it happen with older Maple versions? What am I missing by using standard typesetting instead of the default advanced?








Hi everybody

I try to save an array of equations in a "mpl file", and then read file and array by command read mpl file. But system error "bad id" occurs. Previously I saved this mpl file by "save" and read array by "read" command. I ran this code several times without any problem, suddenly error "bad id" occurred. When I save mpl file by the code edit region and then read it by "read" in the same or  a new worksheet, the error doesn't happen!
 What is wrong?
"Id" refers to the array index?

Maple 18 and Windows 10

is possible to solvethis equation via maple?

hank you


alpha := 1.2*10^(-4); Betaa := 4.0*log(2); J := 13.4; delta := 15.3*10^(-9); tp := 10^(-13); tq := 8.5*10^(-12); tu := 90.0*10^(-12); kapa := 315; r0 := 2.0*10^(-7); Lx := 5.0*10^(-7); Ly := 5.0*10^(-7); Lz := 1.0*10^(-7); a := 0.7e-1*(Betaa/Pi)^.5*J/(15.3*10^(-22)); bb := exp(-((10^(-7)*x-(1/2)*Lx)^2+(10^(-7)*y-(1/2)*Ly)^2)/(2*r0^2)); print(aa = a); Q := a*exp(-z*10^(-7)/delta)*exp(-1.88*abs(t-2*tp)/tp)*bb





























aa = 0.6917775548e21*ln(2)^.5




(diff(U(x, y, z, t), t)+tq*(diff(U(x, y, z, t), t, t)))/alpha = diff(U(x, y, z, t), x, x)+diff(U(x, y, z, t), y, y)+tu*(diff(U(x, y, z, t), x, x, t)+diff(U(x, y, z, t), y, y, t))+tu*(diff(U(x, y, z, t), z, z, t))+(Q+tq*(diff(Q, t)))/kapa

8333.333333*(diff(U(x, y, z, t), t))+0.7083333333e-7*(diff(diff(U(x, y, z, t), t), t)) = diff(diff(U(x, y, z, t), x), x)+diff(diff(U(x, y, z, t), y), y)+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), x), x))+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), y), y))+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), z), z))+0.2196119222e19*ln(2)^.5*exp(-6.535947712*z)*exp(-0.1880000000e14*abs(t-1/5000000000000))*exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)-0.3509398517e21*ln(2)^.5*exp(-6.535947712*z)*abs(1, t-1/5000000000000)*exp(-0.1880000000e14*abs(t-1/5000000000000))*exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)




Boundary condition:

U(0, y, z, t) = 300; U(Lx, y, z, t) = 300; U(x, 0, z, t) = 300; U(x, Ly, z, t) = 300; U(x, y, 0, t) = 300; U(x, y, Lz, t) = 300




U(x, y, z, 0) = 300; (D[1](U))(x, y, z, 0) = 0

(D[1](U))(x, y, z, 0) = 0









help pls how to convert a data surface into a region:

surfdata([[1, 1, .69], [1, 2, .48], [2, 1, .37], [2, 2, .44]], axes = frame, labels = [x, y, z], filled = true)

I've tried to fill the volume below using the option "filled " without any results. I will appreciate any suggestion

how to find back the system which solution is maxwell equations?

as maxwell equations is an invariant, 

if solution is maxwell which is invariant, how to find back the system which solve it, the solution is maxwell?

will there a multiple systems which solution is maxwell equations?

if can not find, how to enumerate all combinations of systems to search maxwell equations?


Recently a few questions concerning the sampling of the Cauchy distribution and the sampling of a truncated Normal distribution have been posted (mainly by  @jalale).
This post is concerned by the sampling of a truncated (standard) Cauchy distribution.

In a first part the efficiency fo two methods is adressed in the case of a non-truncated Cauchy distribution:

  • The "standard" Maple's command Statistics:-Sample(Cauchy(0, 1), N)
  • And a general method a priori very efficient if one knows the ICDF (Inverse Cumulative Function Distribution). It happens that this ICDF is just cot(U*Pi)  where U is a Uniform RV over [0, 1].

The second part adresses the sampling of a truncatedCauchy distribution with two methods:

  • The "standard" Maple's command Statistics:-Sample(Cauchy(0, 1), N, method=[envelope, range=...])
  • The method based on the use of the ICDF



Test1 (non-truncated Cauchy distribution) 

  • "Standard" Maples sampling outperforms the ICDF based method in terms of :
    • memory occupation: ICDF is twice more demanding
    • cpu time: ICDF is ten times slower

Test2 (truncated Cauchy distribution) 

  • ICDF based method i outperforms "Standard" Maples sampling oin terms of :
    • memory occupation: Maples "envelope sampling" method is twice more demanding
    • cpu time: Maples "envelope sampling" method is two times slower

But, beyond these simple observations, a disturbing problem is: the "envelope sampling" method seems to not return the correct distribution (at least when used this waymethod=[envelope, range=a..b]  with a < b)
This is confirmed by the two last plot where histogram and PDF are uperimposed.

Do you think this problem can be avoided by another parameterization of the "envelope sampling" method or that it reveals some underlying problem with it?

PS: I did not investigate further for other distributions .




Sampling the Cauchy distribution

Maple's default sampling method outperformes the adhoc method



C := RandomVariable(Cauchy(0, 1))



f := unapply(CDF(C, t), t);

proc (t) options operator, arrow; 1/2+arctan(t)/Pi end proc


finv := unapply(-solve(f(t)=u, t), u)

proc (u) options operator, arrow; cot(u*Pi) end proc


# "natural" way to proceed

N  := 10^6:

S1 := CodeTools:-Usage(Sample(C, N)):

memory used=7.71MiB, alloc change=39.63MiB, cpu time=69.00ms, real time=69.00ms, gc time=8.72ms


# Let's try the sampling strategy based on the inverse of the CDF
# Usually it starts from sampling a Uniform RV on [0, 1] and
# next applies finv to the result.
# Smart but inefficient

U  := RandomVariable(Uniform(0., 1)):
S2 := CodeTools:-Usage(finv~(Sample(U, N))):

memory used=145.02MiB, alloc change=7.63MiB, cpu time=4.94s, real time=3.04s, gc time=2.61s


# Much more efficient
# Given the special form of finv it's simpler to sample a Unirorm RV
# on [0, Pi] and apply "cot" to the result

pi := evalf(Pi):
U  := RandomVariable(Uniform(0., pi)):
S2 := CodeTools:-Usage(cot~(Sample(U, N))):

memory used=15.28MiB, alloc change=0 bytes, cpu time=652.00ms, real time=237.00ms, gc time=577.78ms


Sampling a truncated Cauchy distribution

Example 1:
with(Statistics) + method=[envelope, range=-10..10]

The adhoc method outperforms Maple's default sampling method

S1 := CodeTools:-Usage(Sample(C, N, method=[envelope, range=-10..10])):


memory used=8.88MiB, alloc change=-7.63MiB, cpu time=322.00ms, real time=260.00ms, gc time=93.77ms



p  := Probability(C < -10, numeric);
q  := 1-Probability(C > +10, numeric);
U  := RandomVariable(Uniform(p*pi, q*pi)):
S2 := CodeTools:-Usage(cot~(Sample(U, N))):






memory used=15.28MiB, alloc change=7.63MiB, cpu time=170.00ms, real time=113.00ms, gc time=92.11ms



Sampling a truncated Cauchy distribution

Example 2:
with(Statistics) + method=[envelope, range=-1..1]

The adhoc method outperformes Maple's default sampling method

S1 := CodeTools:-Usage(Sample(C, N, method=[envelope, range=-1..1])):

scaling := Probability(C < +1, numeric) - Probability(C < -1, numeric);
plots:-display( Histogram(S1), plot(PDF(C, t)/scaling, t=-1..1, thickness=3, color=red) );

memory used=8.08MiB, alloc change=0 bytes, cpu time=246.00ms, real time=215.00ms, gc time=46.62ms





p  := Probability(C < -1, numeric);
q  := 1-Probability(C > +1, numeric);
U  := RandomVariable(Uniform(p*pi, q*pi)):
S2 := CodeTools:-Usage(cot~(Sample(U, N))):

plots:-display( Histogram(S2), plot(PDF(C, t)/scaling, t=-1..1, thickness=3, color=red) );





memory used=15.28MiB, alloc change=7.63MiB, cpu time=163.00ms, real time=106.00ms, gc time=85.93ms







Please download the attachment.


I try to find a relation between EL and Lap(EL) in polar coordinate for one variable function w(r), where Lap is laplacian and EL is Euler Lagrange equation. Please check the Maple code and help me to do some manipulations to find a general relation (if any relation exists!).

In fact I need the inverse of Euler Lagrange equation to obtain f(r) for an arbitrary function g(r) in equation below

EL(f) = Lap(EL(g))

Or f=inverseEL(Lap(EL(g)))

Thank you for taking your time




restart; s := proc (f) subs(d[0] = w(r), seq(d[n] = diff(w(r), `$`(r, n)), n = 1 .. 10), f) end proc; ss := proc (f) subs(seq(diff(w(r), `$`(r, 11-n)) = d[11-n], n = 1 .. 10), w(r) = d[0], f) end proc; EL := proc (eq) s(diff(ss(eq), d[0]))+add((diff(s(diff(ss(eq), d[n])), `$`(r, n)))*(-1)^n, n = 1 .. 10) end proc

f := (diff(w(r), r, r))^2*r^4+4*r^6*(diff(w(r), r, r, r))^2:

a1 := EL(F):

a2 := VectorCalculus:-Laplacian(EL(f), 'polar[r, t]'):


8*r^6*(diff(diff(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r), r), r))+248*r^5*(diff(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r), r))+2582*r^4*(diff(diff(diff(diff(diff(diff(w(r), r), r), r), r), r), r))+10910*r^3*(diff(diff(diff(diff(diff(w(r), r), r), r), r), r))+17786*r^2*(diff(diff(diff(diff(w(r), r), r), r), r))+8192*r*(diff(diff(diff(w(r), r), r), r))-92*(diff(diff(w(r), r), r))





Is possible to solve this differential equation by maple?



I'm using the eBookTools package to convert a .mw file as a chapter into a PDF file. However, a problem arises when I convert a document with a few repeated plotting commands (such as plot(x^2)). The issue is that in the final PDF the images of the various plots overlap, and that the individual plots can't be clearly seen. Is there a resolution to this?


Is package SumTools supposed to be a superset of the sum command in Maple? Or is it supposed to be a complementary to it? When should one use SumTools vs. sum?

The help on SumTools says

The SumTools package contains commands that help find closed forms of definite and indefinite sums. The package consists of three commands and three subpackages.

But does not make it clear when to use it vs. sum or what is its relation to sum command.

I am asking because on one example, sum is able to give an answer, while SumTools can't. I have expected the other way, where if sum failed, then one will try SumTools.

sum(1/n*sin(n*x),n=1..infinity) assuming 0<x,x<Pi

SumTools:-IndefiniteSummation(1/n*sin(n*x),n=1..infinity) assuming 0<x, x<Pi




I am trying to solve CVRPSD by integer L shape method. I have some problems.

d=(0, 20,20,25,15,10): Demand
p=(1,1,1/3,1/2,1/4): the probability demand

1) How to write properly Recourse Policy (Q) in maple (I attached my problem) ? Recourse (Penalty cost) is applied when the demand exceed the vehicle capacity. We know that in CVRPSD, we don't know the demand until vehicle arrive at the node(customer).
(Look at my program)

Hopefully anybody could help me to solve this.

Thank you any way.

for example, there is an expression exp1=(a+b)*(a+c),  I want to find all the position in DAG of a specific operand, such as 'a' ; also I want to find the position in the DAG of  sub-expression which type is '+' .
 is there any function in maple which can return the  integers indicating position of an operand or type in an expression? i.e. with this function, assume its name is 'find',then
find(exp1, a) will return  [1,1],[2,1];
find(exp1,'+') will return  [1,0],[2,0];

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