Carl Love

Carl Love

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12 years, 132 days
Himself
Wayland, Massachusetts, United States
My name was formerly Carl Devore.

MaplePrimes Activity


These are replies submitted by Carl Love

Your values for n = 8, 9, and 23 are obviousy wrong. And why do some have only 9 digits?

Considering how difficult this is to compute, I think that you should post your Mathematica code so that it can be verified.

Recursively, we have a(n) = n^a(n-1), a(1)=1. And we're displaying a(n) mod 10^10.

I don't know how to use Maple to compute this for n > 6. Anyone have an idea? How does Mathematica do it? How do you reduce the exponent to a computable value in modular arithmetic? In other words, we want to compute

(A &^ B) mod 10^10

where B itself is too large to compute. Is there some way to reduce B using the modulus? Surely Mathematica cannot compute a(49) directly. Surely that number has more bits in its representation than there are electrons in the Universe.

But there is a pattern to the moduli of a(n) based on the last digit of n.

Marvin Ray Burns wrote:

I've been playing around with power towers and thought my latest might be interesting enough to post.

It's only interesting to me if we discuss algorithms for computing such things.

Do you see that as being substantially different from having a single worksheet with all the code in one execution group?

@tuGUTS Yes, you can add initial and boundary conditions. These will, if they work at all, remove some or all of the arbitrary functions and constants from the solution. I also don't know what would be appropriate initial and boundary conditions for this PDE. But see ?pdsolve for numerous examples.

@tuGUTS Yes, you can add initial and boundary conditions. These will, if they work at all, remove some or all of the arbitrary functions and constants from the solution. I also don't know what would be appropriate initial and boundary conditions for this PDE. But see ?pdsolve for numerous examples.

You equations are effectively a system of ordinary differential equation. Try changing alpha(r,t) to alpha(r) and then using dsolve. (Although I wouldn't be surprised if pdsolve had already tried that.) It might help to make assumptions on c and kappa such as assume(c>0, kappa>0).

I would try these things myself, but I don't feel like typing in your equations. Please post them in plaintext or upload a worksheet.

Are you saying that you want to extract the point data from the plot?

What is Veq?

Can you post the equations?

Are you getting an error message from pdsolve, or no result at all?

A simplified version of your plotting command:

plot(
     [zip(`[]`,X1, Y1), zip(`[]`, X2, Y2)],
     color= [blue, red],
     style= point, symbol= solidcircle, symbolsize= 8,
     view= [0 .. 2, 0 .. 1], scaling= constrained
);

A simplified version of your plotting command:

plot(
     [zip(`[]`,X1, Y1), zip(`[]`, X2, Y2)],
     color= [blue, red],
     style= point, symbol= solidcircle, symbolsize= 8,
     view= [0 .. 2, 0 .. 1], scaling= constrained
);

It is not clear what you mean by "solve", "solving for", "equation", and "plotting". Do you mean

to solve the equations x/(x+1) = .5, x/(x+1) = .9, etc., for x?

Or do you mean

to evaluate the expression x/(x+1) at x = .5, .9, etc.?

And, in either of the above situations, it is not clear what "plotting" means. We can plot expressions (but not equations) with one variable. We can plot equations with two variables. We can plot a sequence (not a series) by using the index number into the sequence as one of the coordinates.

@andy.zhou.nuaa I recommend you download the free DirectSearch package from the Maple Applications Center. It contains a solver similar to fsolve, but with more flexibility in the precision.

@Markiyan Hirnyk He means the Answer by Alec Milhailovs to which you referred.

@Markiyan Hirnyk He means the Answer by Alec Milhailovs to which you referred.

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