I'm having a great time having a conversation with myself all night long.

Here is an answer to the first part of my last post:

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I'm having a great time having a conversation with myself all night long.

Here is an answer to the first part of my last post:

View 4937_Airy disc.mw on MapleNet or Download 4937_Airy disc.mw
View file details

A rose by any other name might smell the same but it wouldn't have the same connotation.  p_0 carries a lot of meaning, at least for some of us.

Again, that was a lot of key strokes but it helped me a lot.  Thank you, thank you.

Now I have something that I like better:

View 4937_Airy disc.mw on MapleNet or Download 4937_Airy disc.mw
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There is something else that I'd like to do but I can't quite make it happen.  To get the expression v := diff(p[0]*(2*BesselJ(1, k*r*sin(theta))/(k*r*sin(theta)))^2, theta) I did a cut and paste of the expression power := proc (theta) options operator, arrow; 4*p[0]*BesselJ(1, k*r*sin(theta))^2/(k^2*r^2*sin(theta)^2) end proc .  I tried to get what I needed using op(1,power) but I want only the expression to the right of theta-> and I tried rhs but nothing has worked for me yet.  Can you show me the way?

Beyond this, how would a Maple wizard calculate the same 5.2 dB that I arrived at?  What in these lines of Maple do you find ugly or less than beautiful?  At times, I am just too pleased with the stuff that comes out of the tips of my fingers.

And another thing, is dB 10 or 20 log10?  Is this "intensity" in Airy disc power or what?  Ya, it's power so 10 log10 is appropriate.

How can extrema(power, {}, theta) be put to good use?

A rose by any other name might smell the same but it wouldn't have the same connotation.  p_0 carries a lot of meaning, at least for some of us.

Again, that was a lot of key strokes but it helped me a lot.  Thank you, thank you.

Now I have something that I like better:

View 4937_Airy disc.mw on MapleNet or Download 4937_Airy disc.mw
View file details

There is something else that I'd like to do but I can't quite make it happen.  To get the expression v := diff(p[0]*(2*BesselJ(1, k*r*sin(theta))/(k*r*sin(theta)))^2, theta) I did a cut and paste of the expression power := proc (theta) options operator, arrow; 4*p[0]*BesselJ(1, k*r*sin(theta))^2/(k^2*r^2*sin(theta)^2) end proc .  I tried to get what I needed using op(1,power) but I want only the expression to the right of theta-> and I tried rhs but nothing has worked for me yet.  Can you show me the way?

Beyond this, how would a Maple wizard calculate the same 5.2 dB that I arrived at?  What in these lines of Maple do you find ugly or less than beautiful?  At times, I am just too pleased with the stuff that comes out of the tips of my fingers.

And another thing, is dB 10 or 20 log10?  Is this "intensity" in Airy disc power or what?  Ya, it's power so 10 log10 is appropriate.

How can extrema(power, {}, theta) be put to good use?

Here is some Maple that shows that with a 35% obstructed aperture the first side lobe of the airy disc is 5.2 dB higher than a clear aperture.

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Unfortunately I don't think that this is going to do anything for Dr. Dermot Hogan or any of the readers of his comparison of Mathematica and Maple.  He and they are not going to be satisfied until Maple transforms his expression into a numeric answer.

Here is some Maple that shows that with a 35% obstructed aperture the first side lobe of the airy disc is 5.2 dB higher than a clear aperture.

View 4937_Airy disc.mw on MapleNet or Download 4937_Airy disc.mw
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Unfortunately I don't think that this is going to do anything for Dr. Dermot Hogan or any of the readers of his comparison of Mathematica and Maple.  He and they are not going to be satisfied until Maple transforms his expression into a numeric answer.

Acer,

That was a lot of words and I enjoyed them all.  Thank you.

I think that the answer to Dermot Hogan's “A Real Life Test” in his review is not too many steps beyond the Maple in the following:

View 4937_Airy disc.mw on MapleNet or Download 4937_Airy disc.mw
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This Maple is based on Airy disk.  Please take a look and let me know what you think.  It's a lot simpler approach than Hogan's.  That's because I'm a lot simpler fella.

Acer,

That was a lot of words and I enjoyed them all.  Thank you.

I think that the answer to Dermot Hogan's “A Real Life Test” in his review is not too many steps beyond the Maple in the following:

View 4937_Airy disc.mw on MapleNet or Download 4937_Airy disc.mw
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This Maple is based on Airy disk.  Please take a look and let me know what you think.  It's a lot simpler approach than Hogan's.  That's because I'm a lot simpler fella.

Acer,

I think that you misunderstood me when I said:

“I would think that someone would have taken notice of this review and by this time figured out how to get Maple to produce the correct answer.”

I didn’t think that Maple 13 was necessary.

I was thinking that you, Doug Meade, Robert Israel, Jacques Carette or another Maple expert would have, by now, magically wiggled your nose or your digits and fix the problem, just like you fix my problems.  I assumed that there must be something wrong with the way that Dermot Hogan used Maple to try to solve his particular obstructed circular optical aperture diffraction problem.

en.wikipedia.org/wiki/Diffraction

en.wikipedia.org/wiki/Airy_disc

www.bitwisemag.com/copy/reviews/software/maths/maple10_mathematica52.html

nvl.nist.gov/pub/nistpubs/jres/103/5/j35mie.pdf

By the way, how do you get nice little discriptive names to appear rather than big ugly URLs?

Acer,

I think that you misunderstood me when I said:

“I would think that someone would have taken notice of this review and by this time figured out how to get Maple to produce the correct answer.”

I didn’t think that Maple 13 was necessary.

I was thinking that you, Doug Meade, Robert Israel, Jacques Carette or another Maple expert would have, by now, magically wiggled your nose or your digits and fix the problem, just like you fix my problems.  I assumed that there must be something wrong with the way that Dermot Hogan used Maple to try to solve his particular obstructed circular optical aperture diffraction problem.

en.wikipedia.org/wiki/Diffraction

en.wikipedia.org/wiki/Airy_disc

www.bitwisemag.com/copy/reviews/software/maths/maple10_mathematica52.html

nvl.nist.gov/pub/nistpubs/jres/103/5/j35mie.pdf

By the way, how do you get nice little discriptive names to appear rather than big ugly URLs?

Is there anything that a novice like me might do to make this happen.

I would think that someone would have taken notice of this review and by this time figured out how to get Maple to produce the correct answer.

Is there anything that a novice like me might do to make this happen.

I would think that someone would have taken notice of this review and by this time figured out how to get Maple to produce the correct answer.

Doug,

Thank you.

Think first.  I've heard that before.  Unfortunately, I also too often hear myself saying, self: why didn't you, think of that.  But I know why I didn’t think of that.  It’s simple.  You're way smarter than I am.

I was trying to plot because this problem came from this review:

www.bitwisemag.com/copy/reviews/software/maths/maple10_mathematica52.html

and the ultimate answer is a plot (kind of looks like a pulse) in the review.

Please look at this Maple:

View 4937_More Maple vs Mathematica.mw on MapleNet or Download 4937_More Maple vs Mathematica.mw
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I've only been able to get this to run with 5001.  Can you make it run with 50001?

Doug,

Thank you.

Think first.  I've heard that before.  Unfortunately, I also too often hear myself saying, self: why didn't you, think of that.  But I know why I didn’t think of that.  It’s simple.  You're way smarter than I am.

I was trying to plot because this problem came from this review:

www.bitwisemag.com/copy/reviews/software/maths/maple10_mathematica52.html

and the ultimate answer is a plot (kind of looks like a pulse) in the review.

Please look at this Maple:

View 4937_More Maple vs Mathematica.mw on MapleNet or Download 4937_More Maple vs Mathematica.mw
View file details

I've only been able to get this to run with 5001.  Can you make it run with 50001?

Robert,

You should be a teacher.  [I know that you are, at least now and then to a few lucky younglings.]

If it weren't you I would almost be certain that that stuff (Of course ... exp(-1/e).) had to be crap but since it is you, I'll be spending the best part of a day or two trying to figure out what it means and perhaps where it comes from.  The fact that you begin "Of course..."  kills me.  You draw from a very very deep well.  I get a rush when you talk like that.

I read this: http://en.wikipedia.org/wiki/Gelfond's_theorem

and the Maple help page ?LambertW

and I plotted a few things: View 4937_Lambert W function.mw on MapleNet or Download 4937_Lambert W function.mw
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