Maple Questions and Posts

plotting piecewise function...

Asked by: anthonymlinar 0

5 hours ago

0 1

Why doesn't a piecewise function plot correctly?

(1) plot(sin((2*Pi)*100*t), t = 0 .. 1); Plots correctly

(2) s1 := t -> sin(200*t*Pi);
plot(s1(t), t = 0 .. 1); Plots correctly

(3) s2 := t -> piecewise(0 < t, 0, t < 10, sin(200*t*Pi), 0);
s2 := proc (t) options operator, arrow; piecewise(0 < t, 0, t < 10, sin(200*t*Pi), 0) end proc

plot(s2(t), t = 0 .. 1); Does not plot correctly. Only a blank plot is displayed.

Fermat sequence and similar sequences

by: Mister_Matthew_abc 25 Product: Maple 2026

7 hours ago

0 0

Hi Maple community and others,

I'm very proud to present my code.

Sequences are fun,
for those who know, about them

consider Fermat numbers, of the form,
F(n) = (2^(2^n)) + 1.
goes like

3, 5, 17, 257, 65537, 4294967297, 18446744073709551617,
340282366920938463463374607431768211457, ...

in oeis.org database at
https://oeis.org/A000215 .

Similarly we can have base 3,

B(a) = (3^(3^a)) + 1.
goes like, this,
4,28,19684, ...
online, in database, with Universal Resource Location (URL)
https://oeis.org/A129290

There could also be base 4, that grows even faster

double_exponential_2_and_3_and_4.mw

That is all that I have, for now.

Thank you for this free forum.
regards,
Matt

Matt's explore about Andrica's conjecture...

by: Mister_Matthew_abc 25 Product: Maple 2026

13 hours ago

0 1

Hi Maple community, and all,

Here is a little Maple worksheet, shoing an interesting property of prime numbers.

Numerical evidence supports Andreca's conjecture.

see

_Andricas_conjecture.mw

good fun

see, also
Andrica's Conjecture -- from Wolfram MathWorld
Enjoy
regards,
Matt

PS online at https://MattAnderson.fun/

PPS Have a good day, everybody.

Math Success in the Age of AI: Introducing the...

by: Karishma 965 Products: Maple , Maple Calculator , Maple Learn

Yesterday at 3:06 PM

1 3

Last week, we launched the Maplesoft Math Success Platform.

Maplesoft Math Success Platform

This launch reflects a lot of conversations I’ve had over the past year with educators and institutions about what it means to teach and learn math in the age of AI.

At first, many of those conversations were about visibility. If students were completing homework, quizzes, and other assessments with help from AI, those results became harder to interpret. Did students understand the work, or had they copied down a solution that made sense in the moment without building the understanding needed to do something similar on their own?

That visibility still matters.

Over time, though, those conversations led to a more nuanced conclusion. The question is not simply how we prevent students from taking shortcuts. It is how we help them develop the mathematical judgment, intuition, and critical thinking they will need in a world where AI is part of how they learn and work.

In some ways, that has become even more important. When answers are easy to generate, students need to be able to test ideas, recognize when something does not make sense, explain their reasoning, and trust their own thinking.

That is why I am proud to share the launch of the Maplesoft Math Success Platform.

Built on Maple, the platform brings together our math technology and extends it with analytics, AI-driven insights, targeted resources, and content expertise to help institutions support math learning in a more complete way.

It gives instructors and learning support teams better insight into where students are struggling, supports the creation of better questions and learning experiences, helps students move beyond the answer, and helps institutions respond to a world where AI is now part of how students practice, study, and get help.

You can learn more about the Maplesoft Math Success Platform on our website.

We also wrote more about the thinking behind this launch in our new whitepaper, Math Education in the Age of AI: From Grading Answers to Understanding Student Progress. It looks at why math education needs a new approach in the age of AI: one that helps instructors ask better questions, create learning experiences that build understanding, and use learning signals to see where students need support.

Math success in the age of AI requires a new approach

I’d love to hear what you think. How are you seeing AI change the way students learn, practice, and get help in math? And what kinds of tools or approaches do you think will be most important as math education continues to evolve?

Upgrading from Maple 2016.2 to Maple 2026...

Asked by: Bart_de_Jong 5

July 01 2026

1 5

A very stupid question :I want my one-dimensional output from Maple 2016 and also Maple 2026, use as one-dimensional input in my Maple 2026 , which I just bought. I'am very inpatient and think it must be very simple but too complicated for me. Before making a very extensive and timeconsuming study somebody should be able to tell me to perform this by a few clicks .
Thanking you beforehand and I'll be very gratefull for your help.

Bartele de Jong The netherlands

Missing operation (multiplication) in 2D-Math...

Asked by: C_R 3862

June 27 2026

3 2

In 2-D Math input:
In a product of more than two factors space is not allways sufficient to delimite factors when one of the factors is of type numeric.

Just for my interest: Is there a reason or a rule for that?

2-D Math: space interpreted as multiplication

(1)

(2)

With numbers this does not work in these cases

Error, missing operation

Multiplication operators are required

(3)

(4)

Download Missing_operation.mw

How can I get the correct inverse metric with Phys...

Asked by: Hullzie16 448

June 23 2026

1 2

I am looking to do some gravitational perturbations around a generic background spacetime. But before doing that, I wanted to look at just linearized gravity, and make sure all the standard calculations work with Physics before throwing something a little more complicated at it. I went to ?Physics,Library and found the Linearize command, and I thought this was great! When I was reading through it however, I found that the sign infront of the perturbation h in the inverse metric is incorrect. Now, this does not give any invalid results for the Ricci tensor as displayed in the worksheet, since we are only going to linear order, but if we want to go beyond linear order, this will start to cause issues.

Is there a way that Maple can handle this? Or do I have to do some sort of double Define for the metric: one with all downstairs indices, and one with all upstairs indices? If so, how do I do that?

Any help would be greatly appreciated!

>	restart: with(Physics): with(Library):

>	Setup(coordinates = cartesian,signature=`-+++`):

(1)

>

g_[];

$g_[mu, nu] = (Matrix(4, 4, {(1, 1) = -1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1}))$

(2)

>	Define(h[mu, nu],symmetric)

${Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], h[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}$

(3)

>	Define(eta[mu,nu]=rhs((2)))

${Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], eta[mu, nu], Physics:-g_[mu, nu], h[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}$

(4)

>	g_[mu,nu]=eta[mu,nu]+epsilon*h[mu,nu]

(5)

Lets "define" the inverse metric as it appears from the Library:-Linearize worksheet.

>	g_[~mu,~alpha]=eta[~mu,~alpha]+epsilon*h[~mu,~alpha]

(6)

If we multiply the metric and its inverse together, we should expact that we return the KroneckerDelta by definition -- if we consider only to linear order.

>

(5)*(6)

(7)

>	expand((7))

(8)

>	Substitute(eta=g_,(8))

(9)

>	subs(epsilon^2=0,(9))

(10)

>	Simplify(%)

(11)

>

As we can see, we do not get delta alone on the right-hand-side, but instead we still have the perturbation still.

If we instead, use the proper way the inverse should look, which of course comes from the definition of the inverse, it should have minus sign.

>	g_[~mu,~alpha]=eta[~mu,~alpha]-epsilon*h[~mu,~alpha]

(12)

>	subs(epsilon^2=0,expand((5)*(12)))

(13)

>	Simplify(Substitute(eta=g_,(13)))

(14)

Which is the desired result we want. So, my question: is there a way that Maple can produce the correct inverse metric not only to linear order, but to say quadratic, without explicitly deriving it ourselves?

Here is the Physics:-Library(Linearize) Worksheet/Example with some comments

>	restart: with(Physics): with(Library):

>	Setup(coordinates = cartesian);

(1)

The default metric when Physics is loaded is the Minkowski metric, representing a flat (no curvature) spacetime

>

g_[];

$g_[mu, nu] = (Matrix(4, 4, {(1, 1) = -1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = -1, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1}))$

(2)

Suppose you want to define a small perturbation around this metric. For that purpose, define a perturbation tensor , that in the general case depends on the coordinates and is not diagonal, the only requirement is that it is symmetric (to have it diagonal, change symmetric by diagonal; to have it constant, change by )

>	h[mu, nu] = Matrix(4, (i, j) -> delta[i, j](X), shape = symmetric);

(3)

In the above it is understood that are small quantities, so that quadratic or higher powers of it can be approximated to 0 (i.e., discarded). Define the components of accordingly

>	Define((3));

${Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], h[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}$

(4)

Define also a tensor representing the unperturbed Minkowski metric

>	eta[mu, nu] = rhs((2));

eta[mu, nu] = (Matrix(4, 4, {(1, 1) = -1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = -1, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1}))

(5)

>	Define((5));

${Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], eta[mu, nu], Physics:-g_[mu, nu], h[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}$

(6)

The weakly perturbed metric is given by

>	g_[mu, nu] = eta[mu, nu] + h[mu, nu];

(7)

Make this be the definition of the metric

>	Define((7));

Physics:-g_[mu, nu] = Matrix(%id = 36893488152142178892)

${Physics:-D_[mu], Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-Ricci[mu, nu], Physics:-Riemann[mu, nu, alpha, beta], Physics:-Weyl[mu, nu, alpha, beta], Physics:-d_[mu], eta[mu, nu], Physics:-g_[mu, nu], Physics:-gamma_[i, j], h[mu, nu], Physics:-Christoffel[mu, nu, alpha], Physics:-Einstein[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}$

(8)

The linearized form of the Ricci tensor is computed by introducing this weakly perturbed metric in the expression of the Ricci tensor as a function of the metric. This can be accomplished in different ways, the simpler being to use the conversion network between tensors, but for illustration purposes, showing steps one at time, a substitution of definitions one into the other one is used

>	Ricci[definition];

(9)

>	Christoffel[~alpha, mu, nu, definition];

Physics:-Christoffel[`~alpha`, mu, nu] = (1/2)*Physics:-g_[`~alpha`, `~beta`]*(Physics:-d_[nu](Physics:-g_[beta, mu], [X])+Physics:-d_[mu](Physics:-g_[beta, nu], [X])-Physics:-d_[beta](Physics:-g_[mu, nu], [X]))

(10)

>	Substitute((10), (9));

(11)

Introducing the perturbed metric, and the inert form of Ricci for simplification purposes

>	Substitute((7), Ricci = %Ricci, (11));

(12)

The sign infront of the perturbation in the inverse metric is wrong, it should be minus.

This expression contains several terms quadratic in the small perturbation . The routine to filter out those terms is Linearize, that takes as second argument the symbol representing the small quantities (perturbation)

Lets look at the metric times inverse in this setup

>	g_[mu,nu,definition]*g_[~mu,~alpha,definition]

(13)

>	Linearize((13),h)

(14)

>	Simplify(subs(eta=g_,(14)))

(15)

The result is not correct, left-hand-side does not match right-hand-side, this is because the inverse metric has the wrong. If it were a minus, we would get:

>	g_[mu, nu]g_[~alpha, ~mu] = eta[mu, nu]eta[~alpha, ~mu] - eta[mu, nu]h[~alpha, ~mu] + eta[~alpha, ~mu]h[mu, nu]

(16)

>	Simplify(subs(eta=g_,(16)))

(17)

Which is correct. The continued calculation from the Help page is below.

>	Linearize((12), h);

(18)

In this result, is the flat Minkowski metric. To further simplify this expression using the internal algorithms for a flat metric it is practical to reintroduce representing that Minkowski metric

>

g_[min];

Physics:-g_[mu, nu] = Matrix(%id = 36893488152069364060)

(19)

Replace in the expression for the Ricci tensor the intermediate Minkowski by

>	subs(eta = g_, (18));

(20)

Simplifying, results in the linearized form of the Ricci tensor

>	Simplify((20));

%Ricci[mu, nu] = -(1/2)*Physics:-d_[mu](Physics:-d_[nu](h[tau, `~tau`], [X]), [X])-(1/2)*Physics:-dAlembertian(h[mu, nu], [X])+(1/2)*Physics:-d_[nu](Physics:-d_[tau](h[mu, `~tau`], [X]), [X])+(1/2)*Physics:-d_[mu](Physics:-d_[tau](h[nu, `~tau`], [X]), [X])

(21)

This is correct result, because we are going to linear order only the +/- does not have an effect on the end result.

Download LinearizedWorksheet-Comments.mw

Download LinearQuestion.mw

What if my permutation has a fixed point?...

Asked by: wkehowski 30

June 23 2026

1 2

I am trying to use the Perm command in the GroupTheory package to create permutations. The problem is when the permutation has fixed points. For example, neither of the forms

[[1,4,7],[2,8,5],[3],[6]]

[[1,4,7],[2,8,5],[3,3],[6,6]]

will work. Any suggestions?

repeated equation labels...

Asked by: C_R 3862

June 22 2026

1 7

Has anybody seen something like that? I do not use Maple 2026 very often.

Does this vanish when the document is executed on another machine?

repeated_equation_labels.mw

Update:

expanding the document block by "show command" makes the equation labels disappear.
copying the input to another document block seems to fix the problem

How to get consistent output from dsolve for syste...

Asked by: nm 12308

June 22 2026

2 3

Consider these two output, both for solving system of 2 first order different equations.

Why is the first result is put in a list, then each solution is in a set inside the list, while the second one is just a set of the two solutions?

My guess is that because the first system is non-linear. Is this why?

This makes it little harder to parse the result later on, as it can change each time.

Is there a way to get same output for the first example as in the second example?

Mapkle 2026.1

ode:=diff(x(t),t) = x(t)^2, diff(y(t),t) = exp(t);
sol:=dsolve([ode],[x(t),y(t)])

ode:=diff(x(t),t) = x(t), diff(y(t),t) = t;
sol:=dsolve([ode],[x(t),y(t)])

ps. the ode's are not even coupled in these example. So each can be solved on its own if needed.

And if there is one ode with multiple solutions, now dsolve returns expression sequence. No set, no list.

ode:=2*x*diff(y(x),x)*diff(diff(y(x),x),x) = -1+diff(y(x),x)^2; 
dsolve(ode,y(x));

This whole thing is a mess.

There should be one consistent way to return solutions for all cases.

Regadless if it is one ode with one solution, or one ode with mutliple solutions, or coupled systems of odes, linear or not and so on.

The output should be the same form in all cases. A list of lists or list of sets or whatever it is decided on.

But it should not change.

what is mistake in this transformation ?...

Asked by: salim-barzani 1775

June 21 2026

1 14

i do same trasnformation but i don't know what is issue the result is near to same but parameter (t) appear in my which that make my ode not be correct so i can't see the problem in here and i am intrested in finding this, regarding to this i will put here my result and the papers result rregarding to resolve the issue

pde1

pde2

T1.mw

Series Solutions of ODEs in Maple Followup

by: senthooran 0 Product: Maple

June 21 2026

0 1

Little bit of a followup on the "Series Solutions of ODEs in Maple" online seminar.

According to Mathematical Methods for Physicists, 7th Edition by Arfken, Weber and Harris,

Pages 343-345,

Singular points are classified as regular or irregular

Irregular points are called essential singularies.

They show how to apply these to famous differential equations in Quantum Mechanics and other physical applications (examples given in Farlow's Partial Differential Equations for Scientists and Engineers).

In Section 12.1 of Mathematical Methods for Physicists, the complex series Laurent expansion (chapter 11 of the book) is applied to generalized to the complex plane (see Saff and Snider Fundamentals of Complex Analysis for Mathematics, Science and Engineering, 2nd Edition). Not too sure how Maple handles contour integrals though.

It seems that a regular point is the same as a ordinary point, as per Elementary Differential Equations and Boundary Value Problems, 8th Edition by Boyce and DiPrima, Chapter 5.

How to make debugger not show intermediate results...

Asked by: nm 12308

June 21 2026

0 0

I was trying to use the debugger into a proc that has this call

P:=plots:-contourplot(RHS,':-colorbar' = false,':-contours' = L):

Even though the proc has : at its end, and the above call to plots also ends with :, the debugger insists in printing to the debugger window the contour cuves lines. i.e the value of P

Is there a way to tell the debugger not to do this? i.e. not show the value of P. It seems it does that automatically.

Here is the worksheet. Simply evaluate the call foo(); this will open a debugger windows. Then click on next button and now debugger will print the output of plots:-contourplot(RHS,':-colorbar' = false,':-contours' = L):

Download hang_maple_2026_1_on_timelimit.mw

Here is screen shot

In my main actual code, the output was so large that it hanged Maple UI when stepping into the debugger and hitting that line. I had to kill Maple from task manager as Java UI got stuck due to large output.

Why is it showing value of P when I have : at the end? Is there an option to turn automatic display of variables in debugger as one steps in?

Double infinite summations in Maple...

Asked by: Roy Hughes 40

June 20 2026

0 3

I have a rather involved double summation which I am trying to evaluate for various values of the four parameters. Is there a straightforward way that Maple can evaluate this summation?

For example, lambda=nu= +1/2 and/or -1/2 and kappa=mu=1/2 for a start. I would like an expression as a .mw file into which I could put various values and get varying degrees of simplification, rather than trying to do "handraulic" evaluations.

regarsd, RJH

Calculation of the integral and Green's integr...

Asked by: Alfred_F 580

June 20 2026

2 11

The integral shown in the attached file "test" was posted on another forum for calculation. I unsuccessfully attempted to apply Green's theorem in Maple and—as befits a Maple beginner—failed. Does Maple offer a sequence of commands to carry this out? I would appreciate some advice. If this is possible, I would then tackle the line integral using the residue theorem.