My Maple 17 does not have the command dividend.

But along the same lines there is

evalindets(y=a*(b-c), `+`, x-> b*expand(x/b));
                                /    c\
                        y = a b |1 - -|
                                \    b/

Why do you ask? Is it because you have an system of ODEs that you think would be best solved by one of those methods? Is it because you want to study the method? Or is it some other reason?

@Markiyan Hirnyk Markiyan, do you have a specific question about my code? Perhaps it would help to say that my V is not a Vector; rather, it is a procedure which returns a Vector. In particular, it returns a numeric Vector when passed a numeric argument.

The code

V||(1..4):= 'V(k)' $ 'k'= 1..4;

does exactly the same thing as

(V1, V2, V3, V4):= seq(V(k), k= 1..4);

@Markiyan Hirnyk Markiyan, do you have a specific question about my code? Perhaps it would help to say that my V is not a Vector; rather, it is a procedure which returns a Vector. In particular, it returns a numeric Vector when passed a numeric argument.

The code

V||(1..4):= 'V(k)' $ 'k'= 1..4;

does exactly the same thing as

(V1, V2, V3, V4):= seq(V(k), k= 1..4);

@Markiyan Hirnyk Did you have in mind a 3D plot in cylindrical coordinates?

I tell calculus III students that to plot a surface over a region in the xy-plane, use plot limits that are the same as the limits of integration that you would use for double integral over that region.

I tell calculus III students that to plot a surface over a region in the xy-plane, use plot limits that are the same as the limits of integration that you would use for double integral over that region.

You said that Eigenvalues(M) returns 17 eigenvalues. Are any of those 17 expressed in terms of the parameter x?

@vshyam But I am still curious to know: Do you have an integral for which Maple's default quadrature routines failed? Perhaps some tweaking of the optional parameters to Int is all that is needed. See ?int,numeric.

@vshyam But I am still curious to know: Do you have an integral for which Maple's default quadrature routines failed? Perhaps some tweaking of the optional parameters to Int is all that is needed. See ?int,numeric.

Could you show me an example of using the command Inverse? What packages do you have loaded? Show me an example that indicates to you that it is some sort of approximation to MatrixInverse.

MatrixInverse on a 4x4 totally symbolic matrix takes 125 milliseconds on my computer.

To avoid confusion for other readers, you should say if you have the Physics package loaded, or perhaps some other package that changes the behaviour of diff. Your subs command would certainly not work with the ordinary diff.

@vshyam Did Maple's default quadratures not work on your problem? Is this the same integral as we discussed in your "Fsolve in an integral" Question from last week?

Let me know if you need higher precision and/or higher speed. I could make some small adjustments for both.

@vshyam Did Maple's default quadratures not work on your problem? Is this the same integral as we discussed in your "Fsolve in an integral" Question from last week?

Let me know if you need higher precision and/or higher speed. I could make some small adjustments for both.

@Paul 4.33 seems close to 4.49. How close is it when measured in standard deviations?

I would guess that they have not used the same batting order in every game.

It would be interesting to run the model for all the teams---just for their current lineups, not all permuations---and compare with actual performance. That would give some credence to the validity of the Markov model. I'd make a rough guesstimate that if a majority of teams come within 1/2 a standard deviation of actual performance, then the model is good.

The baseball data is probably available for free download online. Access to that could be built right into the worksheet.