MaplePrimes - Maple 2025 Posts and Questions

Maple Support Updates

Roy Hughes — Mon, 06 Jul 2026 01:51:17 Z

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

Thanks, Roy

Missing operation (multiplication) in 2D-Math

C_R — Sat, 27 Jun 2026 11:34:01 Z

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?

Download Missing_operation.mw

How can I get the correct inverse metric with Physics?

Hullzie16 — Tue, 23 Jun 2026 21:44:57 Z

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_[];

(2)

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

(3)

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

(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_[];

(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));

(4)

Define also a tensor representing the unperturbed Minkowski metric

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

(5)

>	Define((5));

(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));

(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];

(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];

(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));

(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

Why do the indices on tensor expressions move to different locations?

Hullzie16 — Sat, 20 Jun 2026 00:47:56 Z

The title says it all. Nevertheless, I am doing some symbolic computation/manipulations with tensors in the Physics pacakge. When I type out my expressions and execute it changes some positions of the indices -- example below. Why?
**Sorry, contents will not post.

Download IndexQuestion.mw

How to simplify this radical expression

C_R — Sat, 13 Jun 2026 07:40:12 Z

The below problem has already occured several times to me. In all such instances Maple did not realise that extracting a factor from a square root is the key for further simplification. Doing this by hand is obvious and often easy when extracted factors are positive.

Did I overlook something? Are there other ways avoid disassembling an expression with the op command?
Should simplify or other commands be improved to adress such problems?

How to transform the left-hand side by commands that it matches the right-hand side

(1)

(2)

(3)

I have tried the usual simplify and combine commands to remove the square root from the numerator.
Extracting a factor for -2 from the square root would probably make further simplification possible but there is no simple command to do so.

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Second approach after "discovering" that content works also on square roots

(11)

(12)

(13)

(14)

Context: The left-hand side in an integrand which was produced by a change of variables in a elliptic integral. Maple simplifies only halfway which makes validation of the result of the variable change difficult.

Related functional programming question: Is a onliner from the above content-primpart construct possible?

Download Simplify_radical_02.mw

Creating a Bar Chart

Elisha — Fri, 12 Jun 2026 12:14:21 Z

Help me rewrite the code to create visible Bar chart of different colors. I can't figure out why this code is not giving me a visible bar graph

Download Bargraph.mw