Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

We are excited to announce that the Maple Conference will be held Novemeber 5-7, 2025!

Please join us at this free virtual event as it will be an excellent opportunity to meet other members of the Maple community, get the latest news about our products, and hear from the experts about the challenges and opportunities that our technology brings to teaching, learning, and research. More importantly, it's a chance for you to share the work you've been doing with Maple and Maple Learn. 

The Call for Participation is now open. We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. 

You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page. Applications are due July 25, 2025.

After the conference, all accepted presenters and invited speakers will be invited to submit related content to the Maple Transactions journal for consideration.

Registration for attending the conference will open in July.  Watch for further announcements in the coming weeks.

We hope all of you in the Maple Primes community will join us for this event!

Kaska Kowalska
Contributed Program Co-Chair

Regarding to this equation i want to do the same as paper did, but i am not sure how i can determine the both  point in plot and how thus point show effect of system of equation and  how find jacobian in the two different point  i think he find it in general but i think we have to find it for each one  of equalibriom point  or we just find in general .
thus plot also are emazing did he use special code in matlab or mathematica? there is some app for plot thus kind of phase portrait but they not like this this is must have a special code for plotting in matlab or mathematica

restart

with(PDEtools)

undeclare(prime, quiet)

with(LinearAlgebra)

declare(u(x, t), quiet); declare(U(xi), quiet); declare(V(xi), quiet)

NULL

DU := V

V

(1)

DV := U^2*beta/(delta*k^2)+(alpha*w/(delta*k^3)+1/(delta*k^2)-w^2/(delta*k^4))*U

U^2*beta/(delta*k^2)+(alpha*w/(delta*k^3)+1/(delta*k^2)-w^2/(delta*k^4))*U

(2)

var := U, V

U, V

(3)

J := Student:-MultivariateCalculus:-Jacobian([DU, DV], [var], 'output' = 'matrix')

Matrix(%id = 36893490902008029780)

(4)

Eigenvalues(J, implicit, output = 'list')

[RootOf(_Z^2*delta*k^4-2*U*beta*k^2-alpha*k*w-k^2+w^2, index = 1), RootOf(_Z^2*delta*k^4-2*U*beta*k^2-alpha*k*w-k^2+w^2, index = 2)]

(5)

Eigenvalues(J)

Vector[column](%id = 36893490902007993756)

(6)

NULL

NULL

DU1 := V

V

(7)

V = solve(DU1, V)

V = 0

(8)

DV1 := U^2*F[2]+U*F[1]

U^2*F[2]+U*F[1]

(9)

U = solve(DV1, U)

U = (0, -F[1]/F[2])

(10)

so*we*have*three*equalibriom*point*(0, 0)

so*we*have*three*equalibriom*point*(0, 0)

(11)

J1 := Student:-MultivariateCalculus:-Jacobian([DU1, DV1], [var], 'output' = 'matrix')

Matrix(%id = 36893490902007256836)

(12)

Eigenvalues(J1, implicit, output = 'list')

[RootOf(-2*U*F[2]+_Z^2-F[1], index = 1), RootOf(-2*U*F[2]+_Z^2-F[1], index = 2)]

(13)

Eigenvalues(J1)

Vector[column](%id = 36893490901938203092)

(14)
 

NULL

Download bi-1.mw

The attached problem is from a 1988 MO. It can be solved using complete induction, paper, and pencil, and with some effort, yields a simple answer. It's quite challenging to do by hand, but with "derive", it only takes three lines and a fraction of a second. Mow test.mw

restart

"puzzle(n):=(∑)(cos(k*Pi/(2*n+1))^())^(4);"

Download test.mw

I can't do it with Maple because I'm doing something wrong again. Therefore, I'm asking for help.

Recently, I was surprised by the fact that it is not possible to create a table, where the values of entries are tables.

Toy example:

T1:=table(["1"=table(["first"=12, "second"=15]), "2"= table(["first"=9, "second"=7])]);

The code

T1["1"];

doesn't return table(["first"=12, "second"=15])

If table has lists in right-hand side

T1:=table(["1"=[12, 15], "2"= [9, 7]]);

all works properly.

 Based on the type of coefficients in the linear equations, SolveTools[Linear] provide several method including method = Rational, Polynomial etc. 
The Polynomial method of SolveTools[Linear] however, cannot be directly called by SolveTools[Linear]. The interpreter complains that no such methd called "Polynomial".

This could only be solved if I import the SolveTools package in advance and call Linear.

I hope Maple could solve this issue. 

I'm trying to reproduce a manual asymptotic analysis (see the attached pdf file) in Maple for a two-soliton solution. Specifically, I want to evaluate the limit of a function (e.g., r[2]r[2]r[2] or ∂xq[2]\partial_x q[2]∂x​q[2]). How can I properly perform the limit a2→+−∞ as t​→+−∞ in Maple, either by substitution or by reparametrization, in order to study the asymptotic behavior of a multi-variable expression symbolically? 

restart

with(Student[Calculus1])

lambda1 := I*mu1; lambda2 := I*mu2; a1 := -2*x/mu1+mu1*t; a2 := -2*x/mu2+mu2*t

numer_r := lambda2*cosh(a1)-lambda1*cosh(a2)

denom_r := (lambda1^2+lambda2^2)*cosh(a1)*cosh(a2)-2*lambda1*lambda2*(1+sinh(a1)*sinh(a2))

r2 := I*(-lambda1^2+lambda2^2)*numer_r/denom_r

numer_dq := (sinh(a1)-sinh(a2))^2; denom_dq := ((lambda1^2+lambda2^2)*cosh(a1)*cosh(a2)-2*lambda1*lambda2*(1+sinh(a1)*sinh(a2)))^2

dq2 := 1-2*(lambda1^2-lambda2^2)^2*numer_dq/denom_dq

limit_r2 := limit(r2, a2 = -infinity); simplify(limit_r2)

Error, invalid input: limit expects its 2nd argument, p, to be of type Or(name = algebraic,set(name = algebraic),list(name = algebraic)), but received -2*x/mu2+mu2*t = -infinity

 

limit_r2

(1)

limit_r2_pos := limit(r2, a2 = infinity); simplify(limit_r2_pos)

Error, invalid input: limit expects its 2nd argument, p, to be of type Or(name = algebraic,set(name = algebraic),list(name = algebraic)), but received -2*x/mu2+mu2*t = infinity

 

limit_r2_pos

(2)

NULL

Download asymptotic.mw cooocp_(2).pdf

Any suggestions for reformulating the limit or change of variables would be appreciated. 

I have solution of this problem but how I can plot simulation on Maple?Thanks, In attach my problem

Maple 2025.1

We have just released an update to Maple. Maple 2025.1 includes several enhancements to the new interface, as well as various small corrections throughout the product. As always, we recommend that all Maple 2025 users install this update.

In particular, please note that this update includes a fix to the problem where new documents were opening in a new window instead of a new tab.  Thanks for helping us, and other users, by letting us know!

This update is available through Tools>Check for Updates in Maple, and is also available from the Maple 2025.1 download page on web site, where you can also find more details.

MapleSim 2025

We are happy to announce that we just released MapleSim 2025. This release includes a new component library to support the modeling of motor drives and updates to several in-product apps that make it even easier to perform optimization and analysis.

See What’s New in MapleSim for details.

Good day, everyone

I am trying to code HPM but it's giving me the error code "Error, invalid subscript selector
" once I increase the number of iterations above 2. 

Attached below is the code. 

HPM.mw

Thanks 

I am new to Windows 11 (edit: I was forced to migrate from 10).

I am looking for an option to resize the Window that the interupt button becomes accessible (see red box)

Also: there are no window controls (maximize minimize) visble . (edit: the title bar is clipped off).

Window key + arrow key does not work.

I have also tried the Snap Layout option to resize but cannot find Maple 2025.1 under the selectable tasks.

What else can I try?

I checked the ConsistencyTest of the system of equations but no output with 'true' or 'False'. Is it not work in 'DEtools'? Download consistency.mw

I have a piecewise density function (f).  I am trying to find the median value.

I have tried the Median function and the Percentile function, but neither work for me.  I am not sure why.

I have also tried to integrate the density function on the (0,x) interval such that the area under the curve is 1/2 and then solve for x.  This works for simple problems, but not the one attached.

There is something very simple that I'm not doing, but I am not sure what.

restart

kernelopts(version)

`Maple 2023.2, X86 64 WINDOWS, Nov 24 2023, Build ID 1762575`

(1)

with(Statistics)

 

(2)

f := 2*t*piecewise(t <= 0, 0, t <= 1, t^2+Pi-4*t, t <= sqrt(2), -(sqrt(t^2-1)*t^2+2*sqrt(t^2-1)*arcsin((t^2-2)/t^2)-4*t^2+2*sqrt(t^2-1)+4)/sqrt(t^2-1), sqrt(2) < t, 0)

2*t*piecewise(t <= 0, 0, t <= 1, t^2+Pi-4*t, t <= 2^(1/2), -((t^2-1)^(1/2)*t^2+2*(t^2-1)^(1/2)*arcsin((t^2-2)/t^2)-4*t^2+2*(t^2-1)^(1/2)+4)/(t^2-1)^(1/2), 2^(1/2) < t, 0)

(3)

plot(f, t = 0 .. sqrt(2))

 

Median(f)

2*t*piecewise(t <= 0, 0, t <= 1, t^2+Pi-4*t, t <= 2^(1/2), -((t^2-1)^(1/2)*t^2+2*(t^2-1)^(1/2)*arcsin((t^2-2)/t^2)-4*t^2+2*(t^2-1)^(1/2)+4)/(t^2-1)^(1/2), 2^(1/2) < t, 0)

(4)

Percentile(f, 50)

2*t*piecewise(t <= 0, 0, t <= 1, t^2+Pi-4*t, t <= 2^(1/2), -((t^2-1)^(1/2)*t^2+2*(t^2-1)^(1/2)*arcsin((t^2-2)/t^2)-4*t^2+2*(t^2-1)^(1/2)+4)/(t^2-1)^(1/2), 2^(1/2) < t, 0)

(5)

myMedian := solve(int(f, t = 0 .. x) = 1/2, x)

Warning, solutions may have been lost

 

(6)

NULL

Download Median.mw

When calculating limits of real-valued functions, sometimes (especially in competitions) tricky approaches are taken using pen and paper. I repeatedly encountered the simple conclusion that, for example, for natural k, the value sin(k*pi) = 0. Thus, the function value is determined logically without specifying a specific number. There are numerous other examples of this that can easily be constructed.
My question after unsuccessful attempts using "assume" is:
How, for example, does Maple determine the value of sin(k*pi) from the assumption "k is natural" alone? Are such prominent values ​​implemented in tables?

 

As I was comparing visually the first terms of a priori identical sums produced by add , I was surprised to find them different.
So I suspected some error in what I have done, until I realized that add randomly permuted the terms.
Each term is of the form (R + P)2 where R is a random number and P a polynomial.

This behaviour is illustrated in worksheet add_changes_ranks.mw and appears only when random numbers are used (provided the seed is not forced to some constant value)

Does someone ever onserved that or have any idea of what happens here (maybe this behaviour no longer happens in recent versions?) ?

Thanks in advance

I am trying to find the standard deviation for a piecewise density function (f).  The interval is (0, sqrt(3))  I am convinced the density function is what I want.  I calculate the expected value of the density function (evE) and the answer is correct -- about 0.66145

When I try to calculate the standard deviation (stdE), I get an answer that is "off" by a large degree.  Via simulating values, I should get a value of about 0.24936.  Each time I "re-run" the calculation, I get varying results, all of which are "off" by a large degree.

I am only guessing, but my integration function might be missing some sort of assumption and/or option.

My work is attached.  Does anyone know what I am doing wrong?

restart

with(Statistics)

f := -t*piecewise(t <= 0, 0, t <= 1, t*(t^3+6*Pi*t-8*t^2-4*Pi), t <= sqrt(2), -(2*(4*t^2*sqrt(t^2-1)*arcsin((t^2-2)/t^2)+4*t^2*arctan(sqrt(t^2-1))*sqrt(t^2-1)+(t^4+(2*Pi+3)*t^2-4*t*Pi+3*Pi-1/2)*sqrt(t^2-1)-8*t^4+4*t^2+4))/sqrt(t^2-1), t <= sqrt(3), (8*arctan((t^3+t^2-3*t-1)/(sqrt(t^2-2)*(t^3-t^2-t-1)))*t*sqrt(t^2-2)-4*arccot((t^2-t-1)/sqrt(t^2-2))*t^2*sqrt(t^2-2)+4*t*sqrt(t^2-2)*(t+2)*arctan((t^2+t-1)/sqrt(t^2-2))+(8*t^2-4)*sqrt(t^2-2)*arcsin((t^2-3)/(t^2-1))+16*arcsin(sqrt(t^2-2)/sqrt(t^2-1))*sqrt(t^2-2)-16*arcsin(1/sqrt(t^2-1))*sqrt(t^2-2)+((t^2+5)*sqrt(t^2-2)-8*t^2+16)*(t^2+1))/sqrt(t^2-2), sqrt(3) < t, 0)

-t*piecewise(t <= 0, 0, t <= 1, t*(t^3+6*Pi*t-8*t^2-4*Pi), t <= 2^(1/2), -2*(4*t^2*(t^2-1)^(1/2)*arcsin((t^2-2)/t^2)+4*t^2*arctan((t^2-1)^(1/2))*(t^2-1)^(1/2)+(t^4+(2*Pi+3)*t^2-4*t*Pi+3*Pi-1/2)*(t^2-1)^(1/2)-8*t^4+4*t^2+4)/(t^2-1)^(1/2), t <= 3^(1/2), (8*arctan((t^3+t^2-3*t-1)/((t^2-2)^(1/2)*(t^3-t^2-t-1)))*t*(t^2-2)^(1/2)-4*arccot((t^2-t-1)/(t^2-2)^(1/2))*t^2*(t^2-2)^(1/2)+4*t*(t^2-2)^(1/2)*(t+2)*arctan((t^2+t-1)/(t^2-2)^(1/2))+(8*t^2-4)*(t^2-2)^(1/2)*arcsin((t^2-3)/(t^2-1))+16*arcsin((t^2-2)^(1/2)/(t^2-1)^(1/2))*(t^2-2)^(1/2)-16*arcsin(1/(t^2-1)^(1/2))*(t^2-2)^(1/2)+((t^2+5)*(t^2-2)^(1/2)-8*t^2+16)*(t^2+1))/(t^2-2)^(1/2), 3^(1/2) < t, 0)

(1)

plot(f, t = 0 .. sqrt(3))

 

evE := simplify(int(t*f, t = 0 .. sqrt(3)))

(1/105)*(294*(2^(1/2)-3/2)*(-2+3^(1/2))*ln(1+2^(1/2))+168*(2^(1/2)-3/2)*(-2+3^(1/2))*ln(1+3^(1/2))-252*(2^(1/2)-3/2)*(-2+3^(1/2))*arccoth(2^(1/2))+((-14*Pi-84*ln(2)-19)*3^(1/2)+28*Pi+168*ln(2)+50)*2^(1/2)+(21*Pi+126*ln(2)+20)*3^(1/2)-42*Pi-252*ln(2)-58)/((2*2^(1/2)-3)*(-2+3^(1/2)))

(2)

evalf(evE)

.6617071838

(3)

stdE := simplify(sqrt(int(f*(t-evE)^2, t = 0 .. sqrt(3))))

(1/210)*(-4808607312140100*(2^(1/2)-3880899/2744210)*(3^(1/2)-70226/40545)*ln(1+2^(1/2))^2+(-5495551213874400*(2^(1/2)-3880899/2744210)*(3^(1/2)-70226/40545)*ln(1+3^(1/2))+8243326820811600*(2^(1/2)-3880899/2744210)*(3^(1/2)-70226/40545)*arccoth(2^(1/2))+((457962601156200*Pi+2747775606937200*ln(2)+631290043332900)*3^(1/2)-793214493249360*Pi-4759286959496160*ln(2)-1093426429714584)*2^(1/2)+(-647656921614780*Pi-3885941529688680*ln(2)-892778941072368)*3^(1/2)+1121774694224184*Pi+6730648165345104*ln(2)+1546338486359352)*ln(1+2^(1/2))-1570157489678400*(2^(1/2)-3880899/2744210)*(3^(1/2)-70226/40545)*ln(1+3^(1/2))^2+(4710472469035200*(2^(1/2)-3880899/2744210)*(3^(1/2)-70226/40545)*arccoth(2^(1/2))+((261692914946400*Pi+1570157489678400*ln(2)+360737167618800)*3^(1/2)-453265424713920*Pi-2719592548283520*ln(2)-624815102694048)*2^(1/2)+(-370089669494160*Pi-2220538016964960*ln(2)-510159394898496)*3^(1/2)+641014110985248*Pi+3846084665911488*ln(2)+883621992205344)*ln(1+3^(1/2))-3532854351776400*(2^(1/2)-3880899/2744210)*(3^(1/2)-70226/40545)*arccoth(2^(1/2))^2+(((-392539372419600*Pi-2355236234517600*ln(2)-541105751428200)*3^(1/2)+679898137070880*Pi+4079388822425280*ln(2)+937222654041072)*2^(1/2)+(555134504241240*Pi+3330807025447440*ln(2)+765239092347744)*3^(1/2)-961521166477872*Pi-5769126998867232*ln(2)-1325432988308016)*arccoth(2^(1/2))+((-392539372419600*ln(2)^2+(-130846457473200*Pi-180368583809400)*ln(2)-10903871456100*Pi^2-30061430634900*Pi+1205966071986042)*3^(1/2)+679898137070880*ln(2)^2+(226632712356960*Pi+312407551347024)*ln(2)+18886059363080*Pi^2+52067925224504*Pi-2088794509063308)*2^(1/2)+(555134504241240*ln(2)^2+(185044834747080*Pi+255079697449248)*ln(2)+15420402895590*Pi^2+42513282908208*Pi-1705493574764511)*3^(1/2)-961521166477872*ln(2)^2+(-320507055492624*Pi-441810996102672)*ln(2)-26708921291052*Pi^2-73635166017112*Pi+2954001523727854)^(1/2)*(5*2^(1/2)-7)*(-5+3*3^(1/2))/((70*2^(1/2)-99)*(15*3^(1/2)-26)*(-2+3^(1/2))*(4*3^(1/2)-7)*(12*2^(1/2)-17)*(2*2^(1/2)-3))

(4)

evalf(stdE)

7031348.295

(5)
 

NULL

Download StdE.mw

3 4 5 6 7 8 9 Last Page 5 of 2216