resolvent

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12 years, 85 days

MaplePrimes Activity


These are answers submitted by resolvent

I did not know that ?command_name brings up the help menu for that command.

Problem is - one would already have to know the name of command_name in order to call up its help menu.

Thank you. However, I should have asked: how do I show group action?  How do I show [1,2] * [1,3] = [2, 3, 1]  ?

Thank you, Alec.

How do I convert G to a set?  That is what I need. I don't need just the size of G. I need to be able to do things (e.g. sum) over all elements of G.

That is the stupidest feature I have ever heard of: not allowing one to delete uploaded files if one chooses.

No - setting them to private is not sufficient.

I need to be able to put more than 1 conditional statements within a for loop.

Specifically, in pseudocode, I need to be able to do things such as

for j from 1 to size(ListThing) do

if j=1, then Left[1]:= InitialSet

if j>1, then Left[j]:=Left[j-1] minus OtherSet[IndexingSet[j]]:

end do

Absolutely none of the examples in any of the Maple Help menus ever show how to contain multiple conditional statements within

a for or do loop.

Thank you for the response.  The theorems you cite are what I had in mind.

Here is the specific thing on which I am working:

z^a + c*z = w    where c and w are fixed nonzero complex numbers, preferably chosen generically so that we can avoid special cases.

My goal: find all infinitely many solutions z=F(a,c,w,k), where k indexes the solutions.

z is an analytic function of complex variable 'a' as long as we avoid the essential singularity at a=0.

The case with c=0 is already known. We already all infinitely many solution,

z=G(a,w,k) of z^a = w.  Writing w=exp(u+(v+2*pi*k)*i)  for real numbers x and y, we have

G(a,w,k) = exp((u+(v+2*pi*k)*i) / a ) .  Writing a = x+y*i for real numbers, x and y we can break apart the real and imaginary parts of G(a,w,k).

But, here is the problem. Knowing all infinitely many solutions, G(a,w,k) of z^a=w, we can compute the Taylor series for z as a function of 'a' around any nonzero complex number, p. The radius of convergence of that series will be the distance from p to the essential singularity, a=0, in other words, abs(p).  So, let's created two different Taylor series expansions for z as a function of 'a' with two real centers, say, p and q.

Since we know a priori that z=w^(1/a) - a multivalued function - we can compute the Taylor coefficients, d^m z/d a^m = P(m,1/a)*w^1/a where P(m,t) is a polynomial in the variable, t, with integer coefficients. Hence, when we set a = p, our chosen center of the Taylor series, we get d^m z/ d a^m at a=p = P(m,1/p)*p^(1/a) where, P(m,1/p) is single-valued, but p^1/a depends upon an index, k, in other words, p^1/a = G(a,p,k)

So, the k-th Taylor series for z as a function of 'a' centered at a=p is

sum of 1/m! * P(m,1/p)*G(a,p,k) * ( a-p)^m,  indexed by k

Similarly, the Taylor series for z as a function of 'a' centered at a=q is

sum of 1/m! * P(m,1/q)*G(a,q,k')*(a-q)^m, indexed by k'

If we choose the centers p & q of these two infinite collections of Taylor series close enough, such that the abs(p - q) is less than the radius of convergence of either, these two Taylor series must coincide, i.e. they must be equal for all complex values of 'a' in some sufficiently small disk situated between p and q

But, which k of the first infinite collection of Taylor series matches up with which k' of the second infinite collection of Taylor series?

Now, apparently, the G(a,p,k) and G(a,q,k') factor out of each series, separately. But, nevertheless, G(a,p,k)*(a power series in 'a' that does not depend upon k) still has to equal G(a,q,k')*(a power series in 'a' that does not depend upon k'). So, we still have to match two power series which each depend upon which "root" of z^a = w we are taking.

This is what confuses me. It becomes more complicated with z^a + c*z=w.

Just letting you know: Maple 11 did not understand these commands.

Statistics:-Mean(L);

etc.

Sorry. None of these ideas worked.

I keep forgetting that Excel has a linear regression routine that works. I've used it before. However, for the little assignments in my Biotech class, I used Maple anyway. I just typed the data into Maple manually and computed the mean and least squares by typing the formulae into Maple, also.

Unfortunately, Excel does not fit data to any curves other than simple linear curves.

 

Ok. I will give this a try.

Wow! I had never heard of the LerchPhi function before. I knew in my heart that SOMEBODY must have given this function a special name. Thank you.

Thank you for this reference.  I have no idea how to retrieve these papers. But I will ask someone at Arxiv.org.

I know that that file extension name change trick works in many situation. But not this one.  If I recall, when one changes .txt to .mw, a > is inserted at the start of every line, each of which must be removed manually. Very tedious for large files.

Thank you. I did made a test file as you and another suggested. I successfully read that into my Maple document. I find it odd that the syntax is

read "C:/directory/filename.txt":

or whatever, with the forward slashes, even though everywhere else directories use backslashes.  Both single quotes and double quotes worked.  I said "sort of", in the subject line above, because even though I successfully "read in" the particular free Maple programs I had downloaded from a particular math researcher's website, I cannot get his programs to run. Only the "header" is printed it out.  It takes too long to explain here

Exactly as happens ONLY after I post my question,

I fixed the problem by myself. I fixed it by more carefully copying the sample Maplets. However, I still do NOT understand their logic - i.e. the logic of the nests within nests.

Here is the program which did not work - it did not display the output TextBox.

DoubleX:=Maplet(Window('title'="DoubleX",

["Enter X",TextField['TF']()],

TextBox['XDoubled']('editable'='true'),

Button("XDoubled",Evaluate('XDoubled'=2*''TF'))

)):

Maplets[Display](DoubleX);

 

Here is the program which did display the output TextBox

 

DoubleX:=Maplet(Window('title'="DoubleX",[

["Enter X",TextField['TF']()],

TextBox['XDoubled']('editable'='true'),

Button("XDoubled",Evaluate('XDoubled'=2*''TF'))

] )):

Maplets[Display](DoubleX);

Somehow, that extra embedded square bracket made the difference.

I do not know why.

Thank you. I didn't realize I was supposed to type, literally, "?Maplets", into the command line of my Maple program. I've never used the ? key symbol or command before. I figured that out just now.

 

By the way: I do NOT really want to start another thread with this,

since the moderators may (rightfully) consider it to be off-topic,

being a philosophical, rather than technical question, but,

I have wondered: has anyone felt that they have gotten a paid job

because of some Maple program they wrote? Obviously, one can never prove

how one got a job. But, sometimes, one can suspect strongly.

(e.g. I believe my Masters degree in math got me my math-teaching gigs

at Mercer County Community College in New Jersey. Actually, my employer explicitly told me that one. I suspect my passing 2 actuarial exams got me a 1-week job

at Gaming Laboratories International in NJ.  In general, I know, there is absolutely NO logic to how employers hire people. I am not claiming negative correlation between good potential employee and getting hired, but I do knowit is zero correlation - independence - between good potential employee and getting hired)

And - if a Maple program you wrote impressed anyone, did that someone ask you to convert it to Java - or some other more common, non-licensed, language?

Thank you for your response.

I see the blogs discussing Maplets. So, I conclude Maplets (Maple applets) exist.

Next question: How? How do I create one?

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