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[MUG] Re: undefined limits
| [MUG] Re: undefined limits |
|
Author: Maple Group
Posted: 01/11/2000 15:06:44 GMT
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>> From: Maple Group
| >> From: Cesar Augusto de Freitas Anselmo
|
| If I need multiply the matrix
|
| a a^2 a^3 ... a^n
| b b^2 b^3 ... b^n
| c c^2 c^3 ... c^n
|
| by vector
|
| 1
| 2
| .
| .
| .
| n, how I put it in maple? Regards that n is undefined (n is positive
| integer).
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Date: Thu, 26 Oct 2000 16:45:12 -0400 (EDT)
From: Carl DeVore
To:
Subject: undefined limits
I doubt that you can do it in Maple as a matrix multiplication with an
arbitrary n. But with a very little work by hand (about 5 minutes) with
finite geometric series you can get this: Let a[k] be the generator of
the kth row of the matrix. Then the kth element of the product vector is
a[k]*(a[k]^n*(n*(a[k]-1)-1)+1)/(a[k]-1)^2, if a[k] <> 1
or
n*(n+1)/2, if a[k] = 1.
Carl Devore
University of Delaware
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Date: Fri, 27 Oct 2000 00:17:37 +0200
From: Theodore Kolokolnikov
To:
Subject: undefined limits
Maple can't deal with arbitrary-sized matrices, but Maple
can be useful to take arbitrary-length sums:
> sum(i*a^i, i=1..n);
(n + 1)
a ((n + 1) a - n - 1 - a) a
-------------------------------- + --------
2 2
(a - 1) (a - 1)
which gives the 1-st component of the solution (of course this is as
easily done by hand by noting that a+2*a^2+...+n*a^n =
a*diff(a+a^2+...+a^(n-1), a)
and summing up the resulting geometric series).
By the way the matrix you have is a well-known Vandermonde matrix.
Regards,
Theodore.
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From: "Willard, Daniel Dr DUSA-OR"
To:
Subject: matrix without defined limits
Date: Fri, 27 Oct 2000 08:45:16 -0400
In the case of the nth derivative or nth expansion coefficient, it may be
worth while to examine the programs you are most interested in. Bessel
fiunction series are restricted by maple to integer indices, but not by
mathematical rigor. A slight rerwrite fixes things. Unfortunately i have not
been able to teach maple to prefer my solutions.
-----Original Message-----
>> From: Barsuhn
Dear Cezar,
as far as I know, you cannot do that with present computer algera
programs. There are a lot of similar problems awaiting a solution in the
(far?) future, e.g.
- determine the n'th derivative of a function
- determine the n'th coefficient of a series expansion
for arbitrary n.
All the best Jurgen
--
-------------------
Prof. Dr. Jurgen Barsuhn
Fachhochschule Bielefeld
University of Applied Sciences
Fachbereich Elektrotechnik und Informationstechnik
Wilhelm-Bertelsmann-Str. 10
D-33602 Bielefeld
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