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[MUG] Kronecker delta

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[MUG] Kronecker delta
Author: Willard, Daniel Dr DUSA-OR    Posted: 10/11/2000 13:50:52 GMT
>> From: "Willard, Daniel Dr DUSA-OR" Does Maple V know how to give you a fast Kronecker delta (discrete form of Dirac delta)? Sample: >kron:= proc(i::integer, j::integer, x) >if i <> j then >x:=0 else >x=1 fi end; Daniel Willard Special Assistant for Air and Missile Defense Office, Deputy Under Secretary of the Army (Operations Research) 102 Army Pentagon ATTN: SAUS-OR Washington, DC 20310-0102 Phone: 703-697-6742 (DSN 227) Fax: 703-693-3897 (DSN 223) E-mail:

[MUG] Re: Kronecker delta
Author: Maple Group    Posted: 15/11/2000 20:58:20 GMT
>> From: Maple Group | >> From: "Willard, Daniel Dr DUSA-OR" | Does Maple V know how to give you a fast Kronecker delta (discrete | form of Dirac delta)? -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Mon, 13 Nov 2000 19:32:14 -0500 (EST) From: Carl DeVore To: Subject: Kronecker delta I'm not sure what you mean by fast when it comes to Maple. But, anyway, here's the fastest that I could come up with: > kron:= proc(x,y) option inline; `if`(x=y, 1, 0) end; I did 100,000 evaluations in 1.1 seconds on a Sparc Ultra 1 (not a particularly fast computer). About half of that time is just incrementing the loop counter. Carl Devore University of Delaware -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Dr. Ferdinand Gleisberg" To: Subject: Kronecker delta Date: Tue, 14 Nov 2000 09:37:31 +0100 Hello, I'm always using BesselJ(i-j,0) for Kronecker(i,j) . Ferdinand Gleisberg -- Dr. Ferdinand Gleisberg Abteilung fuer Mathematische Physik Universitaet Ulm D-89069 Ulm Tel. +49-731-50-23000 Fax +49-731-50-23003 e-mail: -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 14 Nov 2000 10:46:34 -0800 (PST) From: Robert Israel To: Subject: Kronecker delta This came up about 5 years ago in MUG. It's easy to do if i and j are to be integers: I would just say delta:= proc(i::integer, j::integer) if i=j then 1 else 0 fi end; The tricky part is that you usually want to give delta symbolic arguments and use it in sums. Here's one version from Holger Friedrich's posting of 10 Nov 1995: > delta := proc(j, k) > option `Workaround avoiding sum/hgpossib2 suggested by Michael Monagan`; > if type([j, k], [numeric, numeric]) > then if j = k then 1 else 0 fi > else 'delta'(args) > fi end: `sum/delta` := proc() > local x, s; > if isdelta(args[1]) then > x := solve(op(1, args[1]) = op(2, args[1]), args[2]); > RETURN(Heaviside(args[2] - x - 1)) > fi; > if isproductwithdelta(args[1], 's') then > x := solve(op(1, op(s, args[1])) = op(2, op(s, args[1])), args[2]); > RETURN(Heaviside(args[2] - x - 1) * subs(args[2]=x, args[1])) > fi; > ERROR(`sorry, input expression too complicated :-(`) end: isdelta > := proc(expr) > local i; > if not has(expr, delta) then RETURN(false) fi; > for i to nops(expr) do if has(op(i, expr), delta) then RETURN(false) fi od; > true; end: isproductwithdelta := proc(expr, j) > local i; > j := `nowhere`; > if not type(expr, `*`) then RETURN(false) fi; > for i to nops(expr) do if isdelta(op(i, expr)) then j := i; RETURN(true) fi od; > false end: I would make one change to this: the test in line 3 should not be if type([j, k], [numeric, numeric]) but rather if type(j-k, numeric) Robert Israel Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2

[MUG] Re: Kronecker delta
Author: Willard, Daniel Dr DUSA-OR    Posted: 23/11/2000 13:38:57 GMT
>> From: "Willard, Daniel Dr DUSA-OR" Thanks. But how about: > kron:=proc(i::integer,j::integer)`if`(i<>j, 0, 1) end: With Windows 98 and Maple V rel 5.1 "inline" is defined only for plotting. And since mostly i<>j no branching would then occur. Dan Willard >> From: Maple Group | >> From: "Willard, Daniel Dr DUSA-OR" | Does Maple V know how to give you a fast Kronecker delta (discrete | form of Dirac delta)? -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*= - Date: Mon, 13 Nov 2000 19:32:14 -0500 (EST) From: Carl DeVore To: Subject: Kronecker delta I'm not sure what you mean by fast when it comes to Maple. But, anyway, here's the fastest that I could come up with: > kron:= proc(x,y) option inline; `if`(x=y, 1, 0) end; I did 100,000 evaluations in 1.1 seconds on a Sparc Ultra 1 (not a particularly fast computer). About half of that time is just incrementing the loop counter. Carl Devore University of Delaware

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