@Carl Love I think that your supposition about the principal cause of failure is not correct for this particular example.

What's happening for this example (in Maple 2016.2 at least) is that the iterative approach is not converging (even close to any root) for the very first chosen initial point. And then (strangely, and as the principal problem here) it is returning as failed and trying no additional initial points.

It ought to be trying additional initial points. That's what it does when I simply switch the variable names (ie. a->C and c->A) with the new names being in the opposite alphabetical order.

I have yet not pinpointed the problem in the code and a good (reliable) fix. But I will definitely be submitting this as a bug report.

@Rouben Rostamian  

1) The visible edges of the rendered 3d surface are not anti-aliased. That is clearly visible for a variety of simple 3D plots. I have previously inquired about this, and was recently told that enabling some related options in the graphics renderer (JOGL?) might produce some undesirable effects alongside anti-aliasing.

2) The OP already noted that he'd experimented with the projection option, and found it wanting (esp, wrt lighting drop-off as a function of projection effect).

3) A custom light source is already possible, using options.

4) Multiple light sources are not currently possible, that's true. I have previously submitted requests about this (SCR=Software Change Request), as have certain other people.

@emendes Try using,

  IntegrationTools:-Parts

It's pretty straightforward, here.

Is your objection a solution (depending on the particular example) for which some of the individual log calls evaluate to a nonreal value?

You have not explained your issue clearly.

Someone defaced this page and its title.

Originally is was titled,

"Modular Square Root of a number (mod n), knowing factorization of n"

And its contents were,

"ModularSquareRoot can't handle a really big n because of the factorization problem. But I would like to know if there is any other function than can use as parameters the factorization of n.

I already have an algorithm that does that for n=pq with p, q primers, and could generalize it, but I was wondering whether there was a built-in function that does that."

@Teep I would agree with Tom that it's more straightforward to specify the grid size in terms of the number of blocks horizontally and vertically (rather than as a refinement ratio).

Here is a more general example (uglier end-points, without just an integer range).

It uses seq in a similar manner than I had above, but adjusted for this way of specifying the numbers of blocks.

The procedure C can compute the position of an inner block.
 

Download Grid_Example_ac2.mw

@MapleUser2017 The name of the module is MyMat.

So you'd load it using the  with(MyMat)  call.

You keep trying to utilize the name MyLib to refer to the module which you had assigned to MyMat, but that's wrong. The name MyLib is just a name that you introduced for referring to the .mla filename or its location.

This has been mentioned about 4 or 5 times now. It seems that the problem lies not in your Maple installation.

Upload an attachment that contain a definition for f(x,y).

It need not recreate f by previous computations (integrations or what have you). You may be able to lprint the call f(x,y).

But being able to reproduce the issue is important.

Long explanations alone are less useful, for a performance issue.

Could you upload an attachment which can be used to recreate the precise issue?

It only need contain the definition of f(x,y), not all the lead-up computations (integrations, say) to it.

You might be able to just lprint the result of the call f(x,y).

@Adam Ledger My point was not about the fact that `^` is a kernel builtin. My point was that there's no reason to think that the implementation would be the most naive full iterated multiplication.

For big integers it might call a GMP function, so perhaps see here. But why wouldn't all integers be handled as well as that.

I don't understand what you mean by "which factorization". The exponent is stored in binary.

@ThU The OP asked how to combine all the exp terms. But your collect suggestion does not combine all the products of exp terms. I feel that I may be missing your point, sorry. Could you please clarify?

@Adam Ledger You are equating the Maple call x^n with "multiplying x n times".

And that's what I was trying to clarify -- the nature of that belief by you.

I wrote nothing about your code's quality. I am wondering why you think that the Maple kernel implements (large) integer powering with full iterated multiplication. Why do you not imagine that it too might be doing something better?

What is your justification for your expectation that you would be able to write Library-level code that implements binary powering that is faster than the Maple kernel?

You write, "...exponentiation by squares should be faster." Well, to what precisely do you think you are comparing that?

@lima_daniel The line which initially assigns to x has strange output in your original attachment. Does the call to sqrt in that line really produce just a float? Is Asch unassigned? Do you have any initialization file?

Is you Maple otherwise behaving normally? (If you had issues similar to this I'd have expected it to be noticed by you before now...)

@Kitonum  I forgot about this issue (with the NAG LP function in hardware floats). I know it happened for some (but definitely not all!) people's machines, and seems relevant to Windows 64bit rather than Linux.