Axel Vogt

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20 years, 228 days
Munich, Bavaria, Germany

MaplePrimes Activity


These are replies submitted by Axel Vogt

@Kitonum Just an idea: A very brute upper bound would be the hyper-rectangle, and a better (still brute one) would be the simplex 'defined' by the task. I do not know the formula, but for the unit simplex it is 1/n! (Wikipedia?) and transforming to that is by a diagonal matrix, having an easy determinant. Which - of course - does not replace the answer given in the linked replies.

 

In expanded and combined form? If not, then you have to do a bit more then in the already posted suggestions.

p:=x^n*x^r+x^m+y; 
a := convert(indets(p, `^`), list);
max(op(map2(op,2,indets(p,`^`(identical(x),anything)))));
                             max(m, n, r)
map(c ->`tools/symbolic_degree`(c, x), a);
                              [m, n, r]

For me it is not clear what do you mean by that? Importing a graphic file or the data? And which versions of Excel or Maple?

You should describe your task in more detail, an example may be good.

The following results in I = sqrt(-1):

eval(temp, [v=1,p=1,r=1,t=1]);
eval(%, [a=-1,b=-1]); # play with other values
simplify(%);

I do not speak Java (and have given up to play with Open Maple in C)

First I would test on a simple expression for that command. Then I would ponder whether the option 'tord' may disturb Java in understanding the string. And if it actually the length (which I can not understand), then one either can build it by substrings or use shorter names for the variables)

If I used that repeatedly (even after restart) there is no guaranteed order. And IIRC the help = specification does not state such.

But note that there is nothing like a 'natural' order for that, even for the 'natural' base using unit vectors (if ever you can say what norming should be used). For me a base is a set. And each isomorphism provieds one. Perhaps you expect an ordered set (which order?).

For me it is not clear what you want to achieve: an expression with thousands of characters id nothing which one wants to have be displayed (and it is certainly not more simple than your original one)

For m=0 you better use eval(eqn1, m=0), which gives 0. If you divide as you did, then in m=0 you have "0/0" and you need some extra twist

I always avoid indexed variables - do you mean partial derivatives of a function u = u(x,t) or what? In that case you would need to provide the function u (i.e. if you want to check a PDE)

BTW: there is no need to paste the code, it is unreadable in that length. A short sketch or just uploading a sheet is enough, something like

eqn1:= ... # as above 
b := eqn1/(1-exp(-m))^2;
c := subs(m = 0, b);
simplify(c);
  Error, numeric exception: division by zero

https://en.wikipedia.org/wiki/Least-upper-bound_property

It states "The least-upper-bound property is equivalent to other forms of the completeness axiom". It also contains your example (but not worked out).

Hm ... perhaps oune should try by something like "then least upper bound = supremum has to be rational"?

I remembered old stuff ... your setting is incomplete (covarianz matrix), no? The buzz word to search for may be "efficient frontier", if you mean the Markowitz Portfolio Model (it is not 'application of Markowitz optimization')

http://frank-oertel-math.de/markowtz.pdf, http://frank-oertel-math.de/Elem_StochFMSS02.html

Yes.
Choose r such that r^(1/2015) = 1 + eps and x < esp < j*eps.
Then x+j < j*eps + j = j*(1+eps) = j*r^(1/2015).
Thus 1 = x*Product(x+j) < x*Product(j*r^(1/2015)) = x * 2015! * r, so 1/2015! * 1/r < x.
r:= 1 + 1/2^32 should do (with Digits = 15) for ~ 12 leading decimals.
Or similar: Since j < x+j you have x * Product(j, 1 .. 2015) < 1, so x < 1/2015!

Strange ... might it be there is some policy on the server which prevents calling the NAG routines correctly?

You may try as test (which should give Pi):

Int(sqrt(4-x^2),x=0..2, method = _d01ajc); evalf(%);
Int(sqrt(4-x^2),x=0..2, method = _Dexp); evalf(%);

@Carl Love 

When I use IE 11 (on Win 7, no security settings) I also never see my 'reply'. And have to open aother browser

When I use FF I would have to use a profile with no security to let it work.

That is painful (and erduces my will to contribute), I never had such in any forum.

So I can imagine difficulties for others as well.

that will certainly happen

I would check the PDF first: is it what you expect? The CDF is the integral over the PDF.

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