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MaplePrimes Questions

How can the ODE in the second upload be fixed to e...

Asked by: Earl 1000
animation field rod
2 hours ago
0  0

The two uploads are my attempt to solve Problem 177 in the book "200 More Puzzling Physics Problems" by authors Peter Gnadig, Gyula Honyek and Mate Vigh.

The first upload of a conducting rod moving with initial velocity along two arms of a triangle in a perpendicular constant magnitic field successfully produces an animation.

The second upload of the rod moving on the arms of a parabola produces a puzzling error message when executing the ODE

What actual error in the ODE results in this error message?

What changes to the worksheet will result in successful execution of the ODE and a successful animation?

Rod_triangle.mw

Rod_parabola.mw

eBook help video?...

Asked by: Ronan 1421
ebook
4 hours ago
0  0

Are there any demonstration help videos on creating an eBook? Currently I am struggling with the pages Having a laid out example would really help.  

I would like to do an eBook version of my help pages to send to some people. Hopefully I can use the current help worksheets. The are formatted based on the Maple help structure.

My currrent structure in the help section is:

Rational Trigonometry

      (about 40 help topics)

       RTProjective

       (about 20 help topics)

       UHG

       (about 20 help topics)

     Edit:- I have made a small step of progress using the " Assistant eBook template" but I am getting this error on build. I don't know how to find the cause of the error.

How to solve the equation?...

Asked by: Alfred_F 585
solve
7 hours ago
1  3

I would like to solve an equation in the attached file as an exercise. I am looking for all solutions - including the complex ones. This is easily done using "derive". There are six solutions:

restart

solve(2^x*(2+sqrt(3))^x-2*(1+sqrt(3))^x = 2, x)

RootOf(2^_Z*(2+3^(1/2))^_Z-2*(1+3^(1/2))^_Z-2)

 (1)

NULL

edited "test":

test.mw

Five are complex, and the single real solution can be guessed simply by taking a close look. I am unable to obtain the complete solution in Maple; I cannot find my mistake and would appreciate some advice.

Formal Power Series...

Asked by: Roy Hughes 50
convert formal-series
Yesterday at 10:03 PM
2  2

I tried to evaluate the function

convert(BesselJ(nu, x), FormalPowerSeries)

only to obtain the Error message

Error, (in convert/FormalPowerSeries) input contains no or more than one variable.

Seems a rather strange error. I thought it would treat x as a single variable

Maple Support Updates...

Asked by: Roy Hughes 50
update supporttools
Yesterday at 9:51 PM
0  1

@aroche 

Is there a Maple Support Update package for Maple 2025 ? If so, how do I download it?

Thanks, Roy

How do I make a single line list?...

Asked by: Mister_Matthew_abc 30
prime
July 04 2026
1  2

Hi Maple community, and all,

Have a small ask, regarding prime numbers.

see attached

vertical_list_of_prime_numbers.mw

vertical_list_of_prime_numbers.pdf

Thanks in advance.

Regards,

Matt

Where is this form of dsolve and its constants des...

Asked by: Earl 1000
July 04 2026
1  2

I cannot find a description of the use of the form of dsolve and the following evaluation of its constants which are found in the downloaded worksheet.

Gnadig_2_problem_177_Rod_moving_on_a_wire_in_B_field.mw

Three region plots ...

Asked by: KIRAN SAJJAN 65
ode numeric differential-equations
July 04 2026
0  5

Dear sir how to plots the graphs in three region BC from -1 to 0 and 0 to 1 and 1 to 2 
3_region_work.mw

How to make ChatGPT use Maple via MCP...

Asked by: erik10 806
ai chatgpt mcp
July 03 2026
1  5

Dear Maple users

I am testing Maple 2026, which will be used at our school after the summer holiday. I see that AI have now found its way to Maple on a new level. AI can be used internally via the AI Assistant, but as I understand it will also be possible to let ChatGPT use Maple in order to provide an answer, instead of using it's own way to do math. I just cannot figure out how it is done. Having a school license for Maple means we take part in the Maplesoft Elite Maintenance Program (EMP). In Maple 2026 i have found Maple MCP on the "My Maple" båndet. When I click it I am however just referred to the main page of Maplesoft. My question: How can I make Maple MCP work for me?

Kind regards,

Erik V.

plotting piecewise function...

Asked by: anthonymlinar 0
plot piecewise plotting
July 03 2026
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.

Upgrading from Maple 2016.2 to Maple 2026...

Asked by: Bart_de_Jong 5
gui preferences
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
syntax 2dmath implicit-multiplication
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

a*b*c

a*b*c

 (1)

2*b*c

2*b*c

 (2)

With numbers this does not work in these cases

"a 2 c"

Error, missing operation

"a 2 c"

  

"a b 2"

Error, missing operation

"a b 2"

  

Multiplication operators are required

"2 2 c"

  

2*a*c

2*a*c

 (3)

2*a*b

2*a*b

 (4)

NULL

Download Missing_operation.mw

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

Asked by: Hullzie16 448
linearize perturbation physics
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=`-+++`):

`Systems of spacetime coordinates are:`*{X = (t, x, y, z)}

  

_______________________________________________________

 (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)

`Defined objects with tensor properties`

  

{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)))

`Defined objects with tensor properties`

  

{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]

Physics:-g_[mu, nu] = epsilon*h[mu, nu]+eta[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]

Physics:-g_[`~alpha`, `~mu`] = epsilon*h[`~mu`, `~alpha`]+eta[`~alpha`, `~mu`]

 (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)

Physics:-g_[mu, nu]*Physics:-g_[`~alpha`, `~mu`] = (epsilon*h[mu, nu]+eta[mu, nu])*(epsilon*h[`~mu`, `~alpha`]+eta[`~alpha`, `~mu`])

 (7)
> 

expand((7))

Physics:-g_[mu, nu]*Physics:-g_[`~alpha`, `~mu`] = epsilon^2*h[mu, nu]*h[`~mu`, `~alpha`]+epsilon*eta[mu, nu]*h[`~mu`, `~alpha`]+epsilon*eta[`~alpha`, `~mu`]*h[mu, nu]+eta[mu, nu]*eta[`~alpha`, `~mu`]

 (8)
> 

Substitute(eta=g_,(8))

Physics:-g_[mu, nu]*Physics:-g_[`~alpha`, `~mu`] = epsilon^2*h[mu, nu]*h[`~mu`, `~alpha`]+epsilon*Physics:-g_[mu, nu]*h[`~mu`, `~alpha`]+epsilon*Physics:-g_[`~alpha`, `~mu`]*h[mu, nu]+Physics:-g_[mu, nu]*Physics:-g_[`~alpha`, `~mu`]

 (9)
> 

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

Physics:-g_[mu, nu]*Physics:-g_[`~alpha`, `~mu`] = epsilon*Physics:-g_[mu, nu]*h[`~mu`, `~alpha`]+epsilon*Physics:-g_[`~alpha`, `~mu`]*h[mu, nu]+Physics:-g_[mu, nu]*Physics:-g_[`~alpha`, `~mu`]

 (10)
> 

Simplify(%)

Physics:-g_[nu, `~alpha`] = 2*epsilon*h[nu, `~alpha`]+Physics:-g_[nu, `~alpha`]

 (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]

Physics:-g_[`~alpha`, `~mu`] = -epsilon*h[`~mu`, `~alpha`]+eta[`~alpha`, `~mu`]

 (12)
> 

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

Physics:-g_[mu, nu]*Physics:-g_[`~alpha`, `~mu`] = -epsilon*eta[mu, nu]*h[`~mu`, `~alpha`]+epsilon*eta[`~alpha`, `~mu`]*h[mu, nu]+eta[mu, nu]*eta[`~alpha`, `~mu`]

 (13)
> 

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

Physics:-g_[nu, `~alpha`] = Physics:-g_[nu, `~alpha`]

 (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);

`Systems of spacetime coordinates are:`*{X = (x, y, z, t)}

  

_______________________________________________________

  

[coordinatesystems = {X}]

 (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 h[mu, nu], 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 delta[i, j](X) by delta[i, j])
> 

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

h[mu, nu] = (Matrix(4, 4, {(1, 1) = delta[1, 1](x, y, z, t), (1, 2) = delta[1, 2](x, y, z, t), (1, 3) = delta[1, 3](x, y, z, t), (1, 4) = delta[1, 4](x, y, z, t), (2, 1) = delta[1, 2](x, y, z, t), (2, 2) = delta[2, 2](x, y, z, t), (2, 3) = delta[2, 3](x, y, z, t), (2, 4) = delta[2, 4](x, y, z, t), (3, 1) = delta[1, 3](x, y, z, t), (3, 2) = delta[2, 3](x, y, z, t), (3, 3) = delta[3, 3](x, y, z, t), (3, 4) = delta[3, 4](x, y, z, t), (4, 1) = delta[1, 4](x, y, z, t), (4, 2) = delta[2, 4](x, y, z, t), (4, 3) = delta[3, 4](x, y, z, t), (4, 4) = delta[4, 4](x, y, z, t)}))

 (3)
  

In the above it is understood that delta[i, j] are small quantities, so that quadratic or higher powers of it can be approximated to 0 (i.e., discarded). Define the components of h[mu, nu] accordingly
> 

Define((3));

`Defined objects with tensor properties`

  

{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 eta[mu, nu] 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));

`Defined objects with tensor properties`

  

{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];

Physics:-g_[mu, nu] = eta[mu, nu]+h[mu, nu]

 (7)
  

Make this be the definition of the metric
> 

Define((7));

_______________________________________________________

  

`Coordinates: `[x, y, z, t]*`. Signature: `(`- - - +`)

  

_______________________________________________________

  

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

  

_______________________________________________________

  

`Setting `*lowercaselatin_is*` letters to represent `*space*` indices`

  

`Defined objects with tensor properties`

  

{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];

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

 (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));

Physics:-Ricci[mu, nu] = Physics:-d_[alpha]((1/2)*Physics:-g_[`~alpha`, `~kappa`]*(Physics:-d_[nu](Physics:-g_[kappa, mu], [X])+Physics:-d_[mu](Physics:-g_[kappa, nu], [X])-Physics:-d_[kappa](Physics:-g_[mu, nu], [X])), [X])-Physics:-d_[nu]((1/2)*Physics:-g_[`~alpha`, `~tau`]*(Physics:-d_[mu](Physics:-g_[tau, alpha], [X])+Physics:-d_[alpha](Physics:-g_[tau, mu], [X])-Physics:-d_[tau](Physics:-g_[alpha, mu], [X])), [X])+(1/4)*Physics:-g_[`~beta`, `~iota`]*(Physics:-d_[nu](Physics:-g_[iota, mu], [X])+Physics:-d_[mu](Physics:-g_[iota, nu], [X])-Physics:-d_[iota](Physics:-g_[mu, nu], [X]))*Physics:-g_[`~alpha`, `~lambda`]*(Physics:-d_[beta](Physics:-g_[lambda, alpha], [X])+Physics:-d_[alpha](Physics:-g_[lambda, beta], [X])-Physics:-d_[lambda](Physics:-g_[alpha, beta], [X]))-(1/4)*Physics:-g_[`~beta`, `~omega`]*(Physics:-d_[mu](Physics:-g_[omega, alpha], [X])+Physics:-d_[alpha](Physics:-g_[omega, mu], [X])-Physics:-d_[omega](Physics:-g_[alpha, mu], [X]))*Physics:-g_[`~alpha`, `~chi`]*(Physics:-d_[nu](Physics:-g_[chi, beta], [X])+Physics:-d_[beta](Physics:-g_[chi, nu], [X])-Physics:-d_[chi](Physics:-g_[beta, nu], [X]))

 (11)
  

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

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

%Ricci[mu, nu] = (1/2)*Physics:-d_[alpha](eta[`~alpha`, `~kappa`]+h[`~alpha`, `~kappa`], [X])*(Physics:-d_[nu](eta[kappa, mu]+h[kappa, mu], [X])+Physics:-d_[mu](eta[kappa, nu]+h[kappa, nu], [X])-Physics:-d_[kappa](eta[mu, nu]+h[mu, nu], [X]))+(1/2)*(eta[`~alpha`, `~kappa`]+h[`~alpha`, `~kappa`])*(Physics:-d_[alpha](Physics:-d_[nu](eta[kappa, mu]+h[kappa, mu], [X]), [X])+Physics:-d_[alpha](Physics:-d_[mu](eta[kappa, nu]+h[kappa, nu], [X]), [X])-Physics:-d_[alpha](Physics:-d_[kappa](eta[mu, nu]+h[mu, nu], [X]), [X]))-(1/2)*Physics:-d_[nu](eta[`~alpha`, `~tau`]+h[`~alpha`, `~tau`], [X])*(Physics:-d_[mu](eta[alpha, tau]+h[alpha, tau], [X])+Physics:-d_[alpha](eta[mu, tau]+h[mu, tau], [X])-Physics:-d_[tau](eta[alpha, mu]+h[alpha, mu], [X]))-(1/2)*(eta[`~alpha`, `~tau`]+h[`~alpha`, `~tau`])*(Physics:-d_[mu](Physics:-d_[nu](eta[alpha, tau]+h[alpha, tau], [X]), [X])+Physics:-d_[alpha](Physics:-d_[nu](eta[mu, tau]+h[mu, tau], [X]), [X])-Physics:-d_[nu](Physics:-d_[tau](eta[alpha, mu]+h[alpha, mu], [X]), [X]))+(1/4)*(eta[`~beta`, `~iota`]+h[`~beta`, `~iota`])*(Physics:-d_[nu](eta[iota, mu]+h[iota, mu], [X])+Physics:-d_[mu](eta[iota, nu]+h[iota, nu], [X])-Physics:-d_[iota](eta[mu, nu]+h[mu, nu], [X]))*(eta[`~alpha`, `~lambda`]+h[`~alpha`, `~lambda`])*(Physics:-d_[beta](eta[alpha, lambda]+h[alpha, lambda], [X])+Physics:-d_[alpha](eta[beta, lambda]+h[beta, lambda], [X])-Physics:-d_[lambda](eta[alpha, beta]+h[alpha, beta], [X]))-(1/4)*(eta[`~beta`, `~omega`]+h[`~beta`, `~omega`])*(Physics:-d_[mu](eta[alpha, omega]+h[alpha, omega], [X])+Physics:-d_[alpha](eta[mu, omega]+h[mu, omega], [X])-Physics:-d_[omega](eta[alpha, mu]+h[alpha, mu], [X]))*(eta[`~alpha`, `~chi`]+h[`~alpha`, `~chi`])*(Physics:-d_[nu](eta[beta, chi]+h[beta, chi], [X])+Physics:-d_[beta](eta[chi, nu]+h[chi, nu], [X])-Physics:-d_[chi](eta[beta, nu]+h[beta, nu], [X]))

 (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 h[mu, nu]. 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]

Physics:-g_[mu, nu]*Physics:-g_[`~mu`, `~alpha`] = (eta[mu, nu]+h[mu, nu])*(eta[`~mu`, `~alpha`]+h[`~mu`, `~alpha`])

 (13)
> 

Linearize((13),h)

Physics:-g_[mu, nu]*Physics:-g_[`~alpha`, `~mu`] = eta[mu, nu]*eta[`~alpha`, `~mu`]+eta[mu, nu]*h[`~alpha`, `~mu`]+eta[`~alpha`, `~mu`]*h[mu, nu]

 (14)
> 

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

Physics:-g_[nu, `~alpha`] = Physics:-g_[nu, `~alpha`]+2*h[nu, `~alpha`]

 (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]

Physics:-g_[mu, nu]*Physics:-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)))

Physics:-g_[nu, `~alpha`] = Physics:-g_[nu, `~alpha`]

 (17)

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

 
> 

Linearize((12), h);

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

 (18)
 
  

In this result, eta[mu, nu] is the flat Minkowski metric. To further simplify this expression using the internal algorithms for a flat metric it is practical to reintroduce g[mu, nu] representing that Minkowski metric
> 

g_[min];

_______________________________________________________

  

`The Minkowski metric in coordinates `*[x, y, z, t]

  

`Signature: `(`- - - +`)

  

_______________________________________________________

  

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

 (19)
  

Replace in the expression for the Ricci tensor the intermediate Minkowski eta[mu, nu]by g[mu, nu]
> 

subs(eta = g_, (18));

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

 (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
permutation group-theory
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
document-block userinfo infolevel
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
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