@icegood you should do step by step.

Already myint does not compile: if you would test all what you process
later, then you would get the message.

And the reason is: myint(a) just returns the symbol int(...), which of
course is not known in the language C.

And that's what the error message says.

For the last question (what can be compiled or not?) you just have to
find it out by yourself, the help pages tells you about it (roughly all
what is known in C and some small numerical extensions): it is really
much better to do it by hand looking at the expressions. If you are
very much used to Maple I doubt you can set up a routine doing that
for you (besides the question, why one should do it for one special
case).

Otherwise said: it is better to adopt your style of working with Maple,
not the other way round (adopt Maple to your C coding style)

At least one reduce the problem to a similar type of the other task you posted today,
http://www.mapleprimes.com/questions/127918-How-To-Count-Grains-Of-Sand-In-A-Heap-With-Maple
since obviously y+z = 0 modulo 2 (hence both are either even or odd) and solving
for x is by deviding by 2 (and possible: if both are odd, than 3*y+5*z is even).

The remaining condition is

3*n+5*m+4*t <= C where C = 10^r/2 or C= 10^r/2 - 4, r = 2012

Edited: no, it is only the boundary ... so it still is 'equal', not 'less or equal',
time to look up linaer diophantic equations

Edited^2: I am really stupid - that's the value for x, which is demanded to be
positive, thus the in-equation ... should stop for today :-(

neat trick, indeed

neat trick, indeed

Having solved a task is always a pleasure :-)

However I still ask myself, why Maple can not find it directly
(not so surprising after all this pondering), but can 'confirm'
that Sum(...) = 45 as you showed in #comment127440 (which
I like, but did not vote up, since I refuse to vote at www boards).

Having solved a task is always a pleasure :-)

However I still ask myself, why Maple can not find it directly
(not so surprising after all this pondering), but can 'confirm'
that Sum(...) = 45 as you showed in #comment127440 (which
I like, but did not vote up, since I refuse to vote at www boards).

Hm ... 

the 'only' complicated thing in the sheet is, that explicit (minimal) polynomials
are used (=theory+Maple) and are symbolically evaluated for the summands (=Maple).

For the rest:

- We have 6 polynomials and all their roots are different (minimal polynomials
  are unique), and there are 45 roots.

- We do have 45 values = tan(...) and each is a root of some of those polynomials
  Thus the set of tan(...) equals the set of all roots.

Decompose the set of tan(..) into the 6 subsets of the roots of each polyomial,
i.e. Sum(tan(...)) = Sum( Sum(RootsPolynom[k]), k=1 ..6). 

Now apply the following:

- For a polynomial with leading coefficient = 1 the next coefficient is the Sum
  of its roots (but with negative sign)

Then - Sum(RootsPolynom[k]) = coefficient in topdegree-1). Having them at hand
explicitly we get - Sum(tan(...)) = Sum( -1, 4, -4, -12, 16, -48 ) = - 45.


Edited: however I unfortunately have no idea how to group the summands in an
elementary way, such that the result comes out.

Hm ... 

the 'only' complicated thing in the sheet is, that explicit (minimal) polynomials
are used (=theory+Maple) and are symbolically evaluated for the summands (=Maple).

For the rest:

- We have 6 polynomials and all their roots are different (minimal polynomials
  are unique), and there are 45 roots.

- We do have 45 values = tan(...) and each is a root of some of those polynomials
  Thus the set of tan(...) equals the set of all roots.

Decompose the set of tan(..) into the 6 subsets of the roots of each polyomial,
i.e. Sum(tan(...)) = Sum( Sum(RootsPolynom[k]), k=1 ..6). 

Now apply the following:

- For a polynomial with leading coefficient = 1 the next coefficient is the Sum
  of its roots (but with negative sign)

Then - Sum(RootsPolynom[k]) = coefficient in topdegree-1). Having them at hand
explicitly we get - Sum(tan(...)) = Sum( -1, 4, -4, -12, 16, -48 ) = - 45.


Edited: however I unfortunately have no idea how to group the summands in an
elementary way, such that the result comes out.

Of course it would be interesting to see an elementary solution (I do not have one).

The thing is that I would not expect there is one under the given subject title
and thus would not search for it. That's the nature of tasks.

For the suggested way: not sure how to explain, since I do not know what you miss.

More or less: the sheet says, that each of those tan(...) is a root of those
given polynomials and the roots are all different. By degrees we know there are
45 roots (possibly multiple). Thus we have all of them.

Collect the Sum according to degrees. In each part we have: Sum = coefficient
in topdegree - 1, thus overAllSum = Sum over all parts of such.

Of course it would be interesting to see an elementary solution (I do not have one).

The thing is that I would not expect there is one under the given subject title
and thus would not search for it. That's the nature of tasks.

For the suggested way: not sure how to explain, since I do not know what you miss.

More or less: the sheet says, that each of those tan(...) is a root of those
given polynomials and the roots are all different. By degrees we know there are
45 roots (possibly multiple). Thus we have all of them.

Collect the Sum according to degrees. In each part we have: Sum = coefficient
in topdegree - 1, thus overAllSum = Sum over all parts of such.

I do not know (and have not use that command before).

But as errors are quite large you may need quite high precision,
that's why pagan asked (I guess). But simply using Maple as a
brute weapon seems not to work here.

That's all I can say.

I do not know (and have not use that command before).

But as errors are quite large you may need quite high precision,
that's why pagan asked (I guess). But simply using Maple as a
brute weapon seems not to work here.

That's all I can say.

Wiki is your friend: http://en.wikipedia.org/wiki/Condition_number

Roughly; how many Digits you need to expect certain accuracy.

I would expect, that you have 16 points (with multiplicity), since
it is roughly asking for intersecting surfaces of (mixed) degree=4

Wiki is your friend: http://en.wikipedia.org/wiki/Condition_number

Roughly; how many Digits you need to expect certain accuracy.

I would expect, that you have 16 points (with multiplicity), since
it is roughly asking for intersecting surfaces of (mixed) degree=4

Yes, but I thought you posted a 'false' question, which is not the case.

One can (more or less) reduce to the following problem

given X^2+Y^2 = exp(arctan(Y/X)*A) over the Reals - solve for Y.

Or shorter: X^2+Y^2 = (alpha)^(arctan(Y/X)), 0 < alpha.