Nice. So your degree 9 polynomial is of the form f(x^3) where f is degree 3, hence it is solvable.

@User7843 Markiyan's answer shows that it is not pixelation. And, yes, I noticed the absence of any improvemnet with varying the thickness. I wonder what is going on that causes this. Markiyan, you probably have an idea.

Whoever gave me a vote up for this answer should take it away.

@User7843 Markiyan's answer shows that it is not pixelation. And, yes, I noticed the absence of any improvemnet with varying the thickness. I wonder what is going on that causes this. Markiyan, you probably have an idea.

Whoever gave me a vote up for this answer should take it away.

@sakhan

You wrote:

I may be wrong but I think getting all the integrals is easy, we just need to do
seq( op(i, lhs(eq10_1), i=1..nops(lhs(eq10_1));

You're missing a right parenthesis after the first 10_1. But, putting that in, that command will only give you the terms, not the integrals within the terms. Indeed that command is equivalent to simply op(lhs(eq10_1));

If you want the terms that have a[j] to the 1st power, and do not have a[j+1] or a[j+1/2], then do

coeff(coeff(coeff(lhs(eq10_1), a[j], 1), a[j+1], 0), a[j+1/2], 0);

Likewise, for any exponents m, n, k, the terms for a[j]^m*a[j+1]^n*a[j+1/2]^k can be extracted by

coeff(coeff(coeff(lhs(eq10_1), a[j], m), a[j+1], n), a[j+1/2], k);

Does that do what you want?

@sakhan

You wrote:

I may be wrong but I think getting all the integrals is easy, we just need to do
seq( op(i, lhs(eq10_1), i=1..nops(lhs(eq10_1));

You're missing a right parenthesis after the first 10_1. But, putting that in, that command will only give you the terms, not the integrals within the terms. Indeed that command is equivalent to simply op(lhs(eq10_1));

If you want the terms that have a[j] to the 1st power, and do not have a[j+1] or a[j+1/2], then do

coeff(coeff(coeff(lhs(eq10_1), a[j], 1), a[j+1], 0), a[j+1/2], 0);

Likewise, for any exponents m, n, k, the terms for a[j]^m*a[j+1]^n*a[j+1/2]^k can be extracted by

coeff(coeff(coeff(lhs(eq10_1), a[j], m), a[j+1], n), a[j+1/2], k);

Does that do what you want?

@sakhan Yes, the indices do change on different runs. That's one reason that I suggest using indets.

@sakhan Yes, the indices do change on different runs. That's one reason that I suggest using indets.

To proceed, we need numeric values for a, b, and c.

Do you mean a situation like this?

for x in L do
   if cond(x) then break end if;
   ...
end do;

Or like this?

for k to nops(L) while not cond(L[k]) do
   ...
end do;

Or somethings else, perhaps with seq? And, do you want to make sure that cond is applied to every element of the list, perhaps because cond has a side effect?

You'll need to show the rest of the code, especially the point at which you get the error message.  Also, I don't see any derivatives, so how are they ODEs?

This might be a change in newer versions of Maple, but currently a with command performed inside a procedure has no effect on other commands in the procedure. But the execution of such a procedure causes the with to be performed globally. The procedures that are called within a procedure depend on what name-bindings are in effect at the time the procedure was defined, not the time that it is executed.

This might be a change in newer versions of Maple, but currently a with command performed inside a procedure has no effect on other commands in the procedure. But the execution of such a procedure causes the with to be performed globally. The procedures that are called within a procedure depend on what name-bindings are in effect at the time the procedure was defined, not the time that it is executed.

@Markiyan Hirnyk At the bottom of Markelov's LiveJournal post to which you gave a link there a link to a 1988 article in Russian: http://kvant.mccme.ru/1988/06/tri_formuly_ramanudzhana.htm. I don't read Russian, but it looks like this article attributes the formula to a Ramanujan. I am not sure. Could you check that please?

@Markiyan Hirnyk Thank you Markiyan for that stunningly beautiful identity. Where did you get that? It is reminiscent of Ramanujan.

The identity can indeed be proved in Maple. I feel that the proof warrants a separate post, so I am branching off. Put any replies there.

Actually, the theorem is more general than that: n can be a product of a power of 2 and any number of distinct Fermat primes.

But a proof of "A and B" is also a proof of "A" alone, so I don't think that it is fair to nitpick when someone cites a specific case of a more-general theorem. I was just using the case that I needed to make my point.