Carl Love

## 26862 Reputation

11 years, 303 days
Himself
Wayland, Massachusetts, United States
My name was formerly Carl Devore.

## I think the bug is in limit...

@Markiyan Hirnyk Plots show that all forms of the function presented in this thread---LommelS1, both hypergeoms, conversion to rational, and the results of simplifying those to BesselJ times Gamma---are equivalent and that the limit is 1/4/a ~ 0.06188. Series expansions at z=0---when they work at all---also show equivalence. So I think that the bug is in limit.

## I think the bug is in limit...

@Markiyan Hirnyk Plots show that all forms of the function presented in this thread---LommelS1, both hypergeoms, conversion to rational, and the results of simplifying those to BesselJ times Gamma---are equivalent and that the limit is 1/4/a ~ 0.06188. Series expansions at z=0---when they work at all---also show equivalence. So I think that the bug is in limit.

## galois group...

`eval(%, [sc= 1, t= 1, a= 1, k1= 1]);  1       6   2       5         4            2                 - - lambda  - - lambda  + lambda  + 32 lambda  + 64 lambda + 96  9           9                                                galois(%, lambda);        "6T16", {"S(6)"}, "-", 720,           {"(1 6)", "(2 6)", "(3 6)", "(4 6)", "(5 6)"}The galois group being S(6), the polynomial is not solvable.`

## galois group...

`eval(%, [sc= 1, t= 1, a= 1, k1= 1]);  1       6   2       5         4            2                 - - lambda  - - lambda  + lambda  + 32 lambda  + 64 lambda + 96  9           9                                                galois(%, lambda);        "6T16", {"S(6)"}, "-", 720,           {"(1 6)", "(2 6)", "(3 6)", "(4 6)", "(5 6)"}The galois group being S(6), the polynomial is not solvable.`

## Try it...

Why don't you try it yourself first? Then, if you have any problems, post a Reply.

By the way, you should remove with(linalg). That is a very old package that is not meant to be used anymore.

## No need to apologize...

There's no need to apologize. I realize that there's no easy way to avoid multiple answering, and I enjoy seeing a different presentation of essentially the same answer. Anyway, you have the additional information about Explore, which was educational for me.

If someone simul-posts an Answer that seems significantly better than mine, I usually delete mine.

## No need to apologize...

There's no need to apologize. I realize that there's no easy way to avoid multiple answering, and I enjoy seeing a different presentation of essentially the same answer. Anyway, you have the additional information about Explore, which was educational for me.

If someone simul-posts an Answer that seems significantly better than mine, I usually delete mine.

## Warning: long expression...

Warning: The worksheet attached to the Question has a single expression that is 3753 pages long.

## Two solutions...

@maplelearner Note that your variable RootOfLambda has two parts. One of the roots is 0. Your eval statement should be eval(P, lambda= RootOfLambda[2]) so that you select only the second root. At this point, you can continue working with the P expression, even though it contains RootOfs. For example, you can set it to 0 and solve it, getting three simple solutions with no RootOfs.

Numerical solution will not be possible because of your four symbolic constants.

The RootOf is a degree 6 polynomial with symbolic coefficients. Since it's polynomial, it is not considered transcendental, for whatever that's worth. Still, I don't have much hope for simplifying it.

## Two solutions...

@maplelearner Note that your variable RootOfLambda has two parts. One of the roots is 0. Your eval statement should be eval(P, lambda= RootOfLambda[2]) so that you select only the second root. At this point, you can continue working with the P expression, even though it contains RootOfs. For example, you can set it to 0 and solve it, getting three simple solutions with no RootOfs.

Numerical solution will not be possible because of your four symbolic constants.

The RootOf is a degree 6 polynomial with symbolic coefficients. Since it's polynomial, it is not considered transcendental, for whatever that's worth. Still, I don't have much hope for simplifying it.

## Found it...

@acer Thanks, I found it.

## Found it...

@acer Thanks, I found it.

## Still having trouble finding it...

Thank you for your response. Let's consider the worksheet with embedded components that was under discussion on this forum yesterday, which I include here for convenience: test.mw

When I do as you suggest on the slider in the upper left, the only code that I see is test:-suwak();. I can't find any other spot on the worksheet that has a context menu with the entry Edit Value Changed Action. Where am I going wrong?

And how does one access the Startup and/or Code Edit Regions?

## Still having trouble finding it...

Thank you for your response. Let's consider the worksheet with embedded components that was under discussion on this forum yesterday, which I include here for convenience: test.mw

When I do as you suggest on the slider in the upper left, the only code that I see is test:-suwak();. I can't find any other spot on the worksheet that has a context menu with the entry Edit Value Changed Action. Where am I going wrong?

And how does one access the Startup and/or Code Edit Regions?

## Many possible causes...

There are many possible causes for this error. It just means that Maple's kernel process has died. For me, it usually seems related to a computation getting too large or out of control. Unless the message occurs within a few seconds of opening Maple, I seriously doubt that it has anything to do with firewalls.

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