rcorless

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1 years, 58 days

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Editor-in-Chief of Maple Transactions (www.mapletransactions.org), longtime Maple user (1st use 1981, before Maple was even released). Most obscure piece of the library that I wrote? Probably `convert/MatrixPolynomialObject` which is called by LinearAlgebra[CompanionMatrix] to compute linearizations of matrix polynomials in several different bases. Do not look at the code. Seriously. Do not look. You have been warned.

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These are questions asked by rcorless

Consider F := Int( 1/(1+x^n), x=0..1 ).  Once upon a time in Maple ("when tigers smoked pipes") I got it to tell me that F = hypergeom( [1,1/n], [1+1/n], -1 ).  This is true, compact, and very helpful.   n is a positive integer.

I don't seem to be able to do this any more; the combinations of Int, Sum, int, sum, convert/hypergeom, etc are not working for me. I am probably forgetting just which trick I used---I don't think that Maple's capabilities have changed, except that now sometimes I get a finite sum for the integral going from k=0 to k=floor(n/2) which I don't remember seeing before.

Any ideas?

BTW "recusant" is an old word, religious in origin, for someone who refuses to do what they're told, or believe what they're told to believe.

Here's my problem:

phi := (1+sqrt(5))/2;

plots[pointplot]([seq([n, sin(n*phi)], n = 1000 .. 2000)], symbol = point, axes = boxed, labels = [n, typeset('sin(n*phi)')], labeldirections = [horizontal, vertical])

produces a label sin( n phi ).  I want it to say sin( phi n ). 

I've tried the noncommuting times &*  (which prints &*) and the matrix product . (which prints as a function call).

Is there a way to typeset this product in the order that I want?  Here "n" is the variable and "phi" is the constant (yes that looks weird, but so does the graph).  I suspect that there is; I think "typeset" is probably much more powerful than I have been kludging it as.  Help?

screenshot:

maxcharheight.mw

The above worksheet contains some computations I needed for a paper I am writing for the next issue of Maple Transactions.  The computations are within reach of hand computation (which is why I know the right answers).  I wanted Maple to be able to do them, however.

I couldn't make Maple do anything but verify that I was right (this is useful, I will admit).  But can anyone find any artful ways to simplify or solve any of those steps?  I suspect that this is quite hard in general, but with these things involving phi = (1+sqrt(5))/2 it's likely that others would find some "art" useful.  By the way, phi is not built-in to Maple, as far as I know.  Any more votes for including it?

There is an undocumented feature reported here that is useful: asympt works with "leadterm" and this turns out to be necessary.  I forget how I found out that leadterm works with asympt.  It's not in ?asympt, though I think that it should be.

-r

cyclebasis.mw contains a computation of a graph on 14 vertices which has a two-cycle.  I was expecting CycleBasis to find this two-cycle, but it does not.  Anybody know why not?

I was also expecting CycleBasis to work on the original directed graph, but it did not, for reasons that I do not understand.

I think the issue is that the writer of this package had a different mental model of what graphs were; I freely admit that I am a novice with regard to graphs.

Comments welcome.

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