[MUG] undefined limits

[MUG] Re: undefined limits
Author: Maple Group    Posted: 01/11/2000 15:06:44 GMT
>> 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). -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- 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 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- 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. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- 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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