Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

_z i believe is the placeholder when Solve is intending to indicate a restriction to any integer value  only, for one of my recent projects im getting the placholder "_L" in my solutions, and would like to know where the reference table is for the full list of these global in built variable types if possible, have not been able to find it in the help interface and did sincerely look

Hi all!

I am using the solve command for solving 200 equations (linear in 200 unknowns) symbolically. The solve command computes efficiently for 50 equations, after which the efficiency decreases (RAM memory and computation issues).

Is there some other better way available to solve a system of algebraic equations symbolically?


With the launch of Maple 2017, we really wanted to showcase some of the amazing people that work so hard to make Maple. We wanted to introduce our developers to our awesome user community, put names to faces, and have some fun in the process.

We’ll be doing this Q&A session from time to time with team members from the Maple, MapleSim, Maple T.A. and Möbius development groups.

My first Q&A is with Math Architect, Paulina Chin. If you’re a regular MaplePrimes user, you’ll know her as @pchin. Let’s get right into the questions.

  1. What do you do at Maplesoft?

I’m a member of the Math Software group. Much of my time goes toward developing and maintaining parts of the Maple library, but I occasionally develop Maple content related to math education as well.

  1. What did you study in school?

I started in Applied Mathematics and then continued with graduate work in Computer Science and Electrical Engineering. My graduate and post-doc research  were in the area of numeric computation.

  1. What area(s) of Maple are you currently focusing on in your development?

For many years, I’ve been working on the plotting and typesetting features in Maple. I also work on the Grading package and related applications.

  1. What’s the coolest feature of Maple that you’ve had a hand in developing?

The Typesetting (2-D math) system in Maple is undoubtedly the most challenging and complex project I’ve worked on, and it involves careful coordination among a team of developers. I’m not sure others would see it as cool, because the features are not flashy like some of the visualization features I’ve worked on. However, whenever we implement a new feature and it works well, it’s really satisfying because it makes mathematics that much more accessible to users.

  1. What do you like most about working at Maplesoft? How long have you worked here?

I’ve been at Maplesoft 17 years and my work has never been boring. I especially enjoy being surrounded by a very diverse and dedicated group of co-workers, and it’s terrific when we get new students, interns and visitors who come from all parts of the world. All of these people contribute to the great atmosphere here.

  1. Favorite hobby?

I like discussing books as much as reading them. I run several book clubs, including the one here at Maplesoft. I also enjoy working with young people and volunteer at my daughter’s high school, helping students train for programming contests.

  1. What do you like on your pizza?

Pineapple and hot peppers.

  1. What’s your favourite movie?

I have so many favourites that it’s hard to answer this question. At the moment, I might say Notorious, The Empire Strikes Back, and Annie Hall, but ask me again next week and I’ll probably give you a different list.

  1. What skill would you love to learn? (That you haven’t already) Why?

I wish I could play a musical instrument. I know a number of highly skilled amateur and professional musicians, and I’ve always admired their abilities.

  1. Who’s your favourite mathematician?

I’d have to say it’s Euclid. When I was in Grade 6, my teacher saw I was bored with the math exercises we were doing and gave me a book on geometric constructions. That was the start of a life-long fascination with math. I even named my cat Euclid but she didn’t live up to the name, as she turned out to be lovable but not very smart.

Dear all,


I've just discover something quite surprising for me... It turns out like if Maple didn't take in account the linearity of the integral.


In the middle of a calculation, I need to compute the following integral

int(3628800 / (y * (1 / 2 + y)^11) - 3628800 / (y * (39 / 2 + y)^11), y = 39 / 2..infinity);

Maple 17 is not able to instantly answer me, and I'm not so patient... (I've waited more than 30s)

Nevertheless, if I ask Maple 17 to compute

3628800 * int(1 / (y * (1 / 2 + y)^11) - 1 / (y * (39 / 2 + y)^11), y = 39 / 2..infinity);

as well as

int(3628800/(y*(1/2+y)^11), y = 39/2..infinity)-int(3628800/(y*(39/2+y)^11), y = 39/2..infinity);

Maple 17 answer me instantly... which turn out to be quite surprising!

Is there someone, here, who has some ideas of what is happening in this calculation? Why Maple17 has this strange behaviour?

Many thanks for all your answers,


Dear friends!

Hope you would be fine. I want to solve the following system of ODEs

restart; L := 1; with(plots); Digits := 30;

a[1] := 0; a[2] := 1; a[3] := 2; a[4] := .2; a[5] := 4; a[6] := 6;

S := 1; Pr := 6.2; a := 1; a1 := 1; a2 := 1; lambda := 1; delta := 1; Bi := 1; A := 1; B := 1;

HA := [a[1], a[2], a[3]];

Eq1 := diff(F(eta), eta, eta, eta)+a*(a1*((F(eta)+G(eta))*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2)-M1*(diff(F(eta), eta))) = 0;

Eq2 := diff(G(eta), eta, eta, eta)+a*(a1*((F(eta)+G(eta))*(diff(G(eta), eta, eta))-(diff(G(eta), eta))^2)-M1*(diff(G(eta), eta))) = 0;

Eq3 := (A+B)*(diff(H(eta), eta, eta))+a2*Pr*(F(eta)+G(eta))*(diff(H(eta), eta)) = 0;

IC1 := F(0)+G(0)=0, (D(F))(0) = 1+delta*((D@@2)(F))(0), (D(G))(0) = lambda+delta*((D@@2)(G))(0), (D(H))(0) = -Bi*(1-H(0)), (D(F))(L) = 0, (D(G))(L) = 0, H(L) = 0;

params := {B111 = .2};
associated with the above (mentioned as red) boundary conditions. The problem which I faced in first condition i.e., F(0)+G(0)=0 because its combine condition for F(eta) and G(eta) which should be use for both function. The rest part of my program is below:

for k to nops(HA) do;

P || k := plots:-odeplot(dsolve(eval({Eq1, Eq2, Eq3, IC1}, `union`(params, {M1 = .5, phi = HA[k]})), numeric), [[eta, diff(F(eta), eta)]], linestyle = [solid, solid, solid, solid][k], color = [red, green, blue, red][k], labels = [eta, f], thickness = 3) end do;

f1 := plots:-display(P || (1 .. nops(HA)));

display(f1, axes = boxed, size = [380, 310], title = "Ethylene glycol/Cu: M = 2, S = -5", titlefont = ["Arial", 12, bold]);

Please fix my problem ASAP. I also attach the maple file. Thanks in advance.

I am tasked with making a table in Maple that gives the Taylor approximation of sin(x) from 0 degrees to 45 degrees accurate to four digits. The order selected is supposed to give an error from 0 to pi/4 less than 0.00005. I can't seem to create a table with a recurring task. Is there anyone that knows how to do this? Thank you!





There are 13214 days between these two dates.

with(Finance): DayCount("Jan-01-1981", "MAR-7-2017");

But how can I find the end date, given the beginning date and the days between?

This doesn't work (of course, because the date is not a number):

fsolve(DayCount("Jan-01-1981", x)=13214)

is there a direct way? in excel i would do it indirectly using Goal Seek

Maple has had object-oriented features since about version 15, implemented with modules and records and the ability to define exports of these. Methods can be defined and called using module:-Method() and properties in a similar way including hierarchical constructs. Overloading of functions is possible, although I have run into trouble trying to overload build-in function. While this mechanism is not fully oo, I have found it enormously helpful for larger projects and a distinguishing feature of Maple.

More recently, the option object was added to modules. What are the true new functionalities? I see that the syntax for methods has changed (Method(object,arguments) rather than module:-method(arguments)) but I do not see how that is an improvement. I guess there are also now bona-fide constructors, doing what used to be done with a module factory (a proc that returns an instance of a module). And Object(object) seems to do what copy(module) does.

I am conceptualizing a larger package that will make use of the oo features of modules. I know I can write this using the established :- syntax using modules. Are there any benefits to using the newer objects rather than modules and records (& I know that all these are essentially modules)?



Why does



not simplify to




Is any package or algorithm which enable me to compute constraint structure of a singular Lagrangian in physical phenomena?

i would be very thankfull if someone help me in thisway please :)

g3 := tanh(x+1);
a:=eval(diff(g3,x$n)/n!, x=0) assuming n>=0:
tanhx := sum(a*x^n, n=0..infinity):
tanhx2 := subs(x^n=subs(_C1=0, subs(t=n!, g2))*x^n, tanhx):
diff(tanhx2, x) - tanhx2;

would like to find a operator to make it equalt to itself , a new differential operator for new transcendental function tanhx2

in reference to the definition prescribed in the maple help interface and the attached worksheet, i cant understand how hypergeom(n,d,z) handles empty values of the lists n,d eg hypergeom([],[],pi)  

hypergeom([n[1], n[2], n[3], () .. (), n[p]], [d[1], d[2], d[3], () .. (), d[q]], z) = sum(z^k*(product(GAMMA(k+n[i])/GAMMA(n[i]), i = 1 .. p))/(factorial(k)*(product(GAMMA(k+d[j])/GAMMA(d[j]), j = 1 .. q))), k = 0 .. infinity)





I am struggling to obtain solutions for two bi-variate euqations numerically. A command line that I am currently using (for a dummy problem) is as follows: 

soln := {solve({f(x,y)=0, g(x,y)=0}, {x,y})}; 

There are mainly two issues:

1. For some reasons, Maple 2017 takes ages to obtain solutions for certain parameter values. At times, it does not provide any solution which should not happen. I am assuming that this is to do with the "solve" command.

2. Also, I am not sure how to limit search procedure within feasible ranges for variables. In this case, how do I incorporate conditions 0 <= x, y <=1? If I can incorporate these constraints in the "solve" (or any better) command, then I can automatically get rid of complex solutions as they are not relevant for me. 

I would appreciate inputs in this regard. Thank you,




Is there a simple way to reverse the handedness of the axes? I have the following figure:

shadebetween(0, 2-x-y, x = 0 .. 1, y = x^2 .. sqrt(x), scaling = unconstrained, color = yellow, axes = normal, labels = [Z, Y, X], transparency = .9)

and I want the X and Y-axes reversed from a left-handed orientation to a right-handed orientation.

I recently changed to a very high resolution monitor. The worksheet material is fine, since I can control the  zoom level, but the material at the top panel, the menus and information in the help page panels is much too small,  How can it be controlled?


Thank you,                        --Micha Hofri

Comment:   The responder tomleslie indeed identified the problem --- fixed pixel-count programming  Some software products, such as the FireFox browser provide access to hundreds of configuration parameters.  Surely the Maple tools have such a file, but I have seen no access.

The monitor I use is indeed of high resolution, the manufacturer says it is 3840x2160, (24'' -- I use 2 of them in a T configuration).  It is a delight, except when trying to read minute characters.

I suppose I need a pointer from the people in the know........Micha Hofri


Responding to a comment by Mac Dude that the issue may have to do with Windows.  I assume he refers to the MIcroSoft OS.

My computers run the Mint distribution of linux (window manager is Mate).  These matters are important, yet my needs would likely be addressed by the Maple user interface mechanisms.

My difficulty is finding a way to interact with these mechanisms, I suppose.   --Micha Hofri



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