Let's say we enter an arbitrary metric with "Setup" in maple.

Also suppose the metric is a vacuum solution and therefore the Ricci tensor R[alpha,beta]=0

As soon as I enter the metric, maple will evaluate the Ricci tenso when I type R[alpha,beta] and equates it to zero.

What is the command to rather show the the equations that makes up the Ricci tensor for this metric and prevent Maple  from evaluating the equation.

This must be easy, but I just cannot find it in the manual. Must be simple to switch between displaying the constraint equation as calculated for say R[alpha,beta] from the metric and evaluating the equation.

If you are are given a contravariant metric, is there a system in maple similar to that to enter a covariant metric ?

As an example, in Maple you can enter a given arbitrary covariant metric by e.g.

ds := exp(2*psi(rho, z))*dt^2 - exp(-2*psi(rho, z))*(exp(2*sigma(rho, z))*(drho^2 + dz^2) + rho^2*dphi^2)

Coordinates(X = (rho, z, phi, t))

Then

Setup(metric = ds)

This then enters the metric into maple and from there on you can calculate all necessary tensors related the covariant metric 

My Question is;

Is there a similar structure you can enter a given CONTRAvariant metric into maple by a similar structure as above without having to resort to first manually transforming the contravariant metric to covariant in order to enter into maple ?

I cannot remember that this was an issue in Maple 6/9/11, so it must have changed later on up to 22.

The following limit fails to execute

restart;
1/(r_S^5*(_C2*r_S^4 + _C2*r_S^3 + _C2*r_S^2 + f[3](0)*r_S + f[4](0)));
limit(%, f[4](0) = infinity);

It fails to calculate the limit with result as zero.

Thanks

Is there a way to force maple not to reuse integration constant names or constant names arising from solving a differential equation.

In other words, once maple  provided e.g. an integration constant, then it may not reuse it when I solve another differential equation or integral equation in the same worksheet.

It causes problems with certain problems containing several differential equations that need to be solved sequentially.

Why can the coeff operator return the coefficient of 1/b, namely -1/x in the example below correctly,

but cannot return the coefficient of 1/x , which should be -1/b?

dummy := asympt(x*1/(1 - a*x - b*x^2), x);
coeff(dummy, 1/x);
coeff(dummy, 1/b);

What one generally wants is to be able to return the coefficients of the orders of an asymptotic expansion, but coeff seems unable to do that as soon as you want the coefficients of 1/x^n

Maple help pages is silent about this.