Correct, I had to use some human ingenuity there. That type of ``reasoning'' is not (currently?) in Maple, as far as I know. Maple knows a lot of math, some simple, some extremely advanced. However, there is still a lot more math out there; and some of that math which Maple does not know is covered in first and second year courses at university.

Correct, I had to use some human ingenuity there. That type of ``reasoning'' is not (currently?) in Maple, as far as I know. Maple knows a lot of math, some simple, some extremely advanced. However, there is still a lot more math out there; and some of that math which Maple does not know is covered in first and second year courses at university.

Without more details, I don't think anyone will really be able to help you. I definitely suggest that you pack up your worksheet and send it off to support@maplesoft.com, to ensure that the developers have a record of this bug so that they can fix it. If you post your worksheet here, people on primes might be able to find a workaround for you.

As I said before, with is of no use in this context. march returns a list (of lists) with names, timestamp, start and length information. You only really need the name. libname := "C:\\MyDocs\\MyMaple\\Mylib" , libname; interface(verboseproc=3); lst := map[2](op, 1, "MyLib"); loaded := map(proc(x) local y; y := convert(x[1..-3],'name'); eval(y,2) end, lst); and then you can print any of the results in 'loaded'.

As I said before, with is of no use in this context. march returns a list (of lists) with names, timestamp, start and length information. You only really need the name. libname := "C:\\MyDocs\\MyMaple\\Mylib" , libname; interface(verboseproc=3); lst := map[2](op, 1, "MyLib"); loaded := map(proc(x) local y; y := convert(x[1..-3],'name'); eval(y,2) end, lst); and then you can print any of the results in 'loaded'.

Only has 2 lines, 2 numerical evaluations (at least, that is what I see). Did you mean to post something longer? Also, notice how `Bessel/realJI` is invoked inside an evalf call? That means that the code is actually in `evalf/Bessel/realJI`, which does 'print'.

Only has 2 lines, 2 numerical evaluations (at least, that is what I see). Did you mean to post something longer? Also, notice how `Bessel/realJI` is invoked inside an evalf call? That means that the code is actually in `evalf/Bessel/realJI`, which does 'print'.

Is this herd available somewhere? If I have some time one day, I'll try to derive where that matrix recursion comes from. Yes, it indeed has to come from the quadratic transformation of the hypergeometric, but that's still pretty vague!

This is the kind of stuff where Maple is a real life-saver. Most mortals cannot manipulate that many symbols (correctly) in finite time! Question: do you have any intuition at all for where that 3-variable recurrence comes from? [I did not look at Forrey's article]. The inner 2-variable coupled recurrence is rather intriguing.

Give us an example! The answer is completely different depending on the details.

Maple is very well equipped with lots of functions to deal with polynomials over finite fields. See ?modp as one entry point.

Maple is very well equipped with lots of functions to deal with polynomials over finite fields. See ?modp as one entry point.

In any case, the book's derivation of the solution is rather sloppy, since you don't quite have 2 arbitrary functions -- Maple's solution takes all 3 equations into consideration properly. You are correct that the integral does represent a function of x and y. In your worksheet, here are two ways to get different solutions: 1) simplest -- make all arbitrary functions 0

> value(eval(opl, {_F1=0, _F2=0}));
            {Ay(x, y, z) = -a z, Ax(x, y, z) = b z - c y}

2) get the book solution:

> value(eval(subs({_F1=((x,y)->:-`*`(c,x)), _F2=0},opl)));

            {Ay(x, y, z) = -a z + c x, Ax(x, y, z) = b z}

Interestingly, the 'right' way to do 2 above brings out a bug in Maple:

> value(eval(opl, {_F1=((x,y)->c*x), _F2=0}));
Error, (in depends/internal) improper op or subscript selector

And it also brings out the issue that using with(VectorCalculus) is a mixed blessing, since that shadows the normal *, so that the ugly :-`*` must be used instead!

In any case, the book's derivation of the solution is rather sloppy, since you don't quite have 2 arbitrary functions -- Maple's solution takes all 3 equations into consideration properly. You are correct that the integral does represent a function of x and y. In your worksheet, here are two ways to get different solutions: 1) simplest -- make all arbitrary functions 0

> value(eval(opl, {_F1=0, _F2=0}));
            {Ay(x, y, z) = -a z, Ax(x, y, z) = b z - c y}

2) get the book solution:

> value(eval(subs({_F1=((x,y)->:-`*`(c,x)), _F2=0},opl)));

            {Ay(x, y, z) = -a z + c x, Ax(x, y, z) = b z}

Interestingly, the 'right' way to do 2 above brings out a bug in Maple:

> value(eval(opl, {_F1=((x,y)->c*x), _F2=0}));
Error, (in depends/internal) improper op or subscript selector

And it also brings out the issue that using with(VectorCalculus) is a mixed blessing, since that shadows the normal *, so that the ugly :-`*` must be used instead!

Thanks. And that probably means I am spending too much time on here instead of doing something else (like writing more computer algebra papers!).