Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

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

Hello,

I’m currently a student working with vectors as part of my electrical AC calculations. Up until now, I’ve been using GeoGebra to add and plot vectors, but I’m trying to transition fully to Maple, since I already use it for everything else in my studies.

All of my assignments are either given in — or require answers in — polar form (magnitude and angle), so I would really like to work directly in polar coordinates without converting everything to Cartesian and back.

I’ve already tried to figure this out on my own, but so far, I’ve only been able to make it work using Cartesian notation. I’ve attached a PDF with a typical example of the kind of tasks I work on, in case that helps clarify my needs.

Could you guide me on how to best set up and work with polar vectors in Maple — including how to define, add, and plot them directly in polar notation?

Vector_Help.pdf

Thanks in advance for your help!

Best regards,
Mads Bach Nielsen

- Yes this was written with the help of Chat GPT

why this error is getting. but in the published paper for the same parameter it is converging. what is the mistake in this worksheet please rectify it in sachin_base_paper.mw

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