MaplePrimes - Unanswered Questions

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

How to get consistent output from dsolve for system of ode's?

nm — Mon, 22 Jun 2026 06:41:21 Z

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.

How to make debugger not show intermediate results?

nm — Sun, 21 Jun 2026 05:08:54 Z

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?

Should dsolve return this?

nm — Wed, 17 Jun 2026 04:31:03 Z

given

ode:=2*x^(1/2)*diff(y(x),x)-y(x) = -sin(x^(1/2))-cos(x^(1/2)); 
ic:=y(infinity) = y__0; 
sol:=dsolve([ode,ic]);

It gives

This solution satisfies the ode itself. Now cos(sqrt(x)) when x=infinity is -1..+1

But IC says y(infinity)=y0 so odetest do not verify the IC and gives this

odetest(sol,[ode,ic]);

I think dsolve should not have returned a solution at all.

What do the experts here think of this result?

Maple 2026.1 on windows 10

evala,Sqrfree output

C_R — Tue, 16 Jun 2026 16:10:35 Z

I am new to evala (and the math behind).

On ?evala,Sqrfree at the first bullet point I was wondering if there isn't a "u" missing here

Can someone confirm?

Stacked tabs for open worksheets

nm — Sun, 14 Jun 2026 13:01:03 Z

WHen I open many worksheets at same time, say 10. The new UI do not stack them all (i.e. the tab at the top), forcing one to use the small arrow to navigate to each worksheet.

Is there a way to tell the UI to show all tabs (may be double rows and 3 rows as needed) to make it easier to jump from one worksheet to the other?

I do not know if this is new feature in the new ribbon UI or not.

Here is screen show where I have 10 worksheets open

There is also a pull down menu, but it only shows 8 worksheets and one can have more open but they do not show. So have to scroll down looking for the rest. Even that does not work well. many times when I try to scroll down, the window closes. It will not give me time to move the mouse to the scroll bar to move it before it closes.

Both of these solutions are not good. Having to use the arrow key to look and navigate for a different worksheet is bad UI design.

How to see all tabs for all open worksheet in same UI? If the tabs do not fit on one row, why not make second row? If two rows do not fit, make 3rd row. This should be an option for the user. But I did not see one so far. But will keep looking.

I find tabs where all worksheet show much better design that this UI design.

I only use worksheet and not document mode. Windows 10.

To give you idea what I mean, These are examples found on the net of stacked tabs

Where in Maple, each tab above will have the name of the worksheet open. Font can be small, is OK.

Is it possible to have this in the new UI for open worksheets?

One option I might try to make my worksheets names much shorter. May be then they will fit all in same window.