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From: Joe Riel <joer@san.rr.com>
Newsgroups: comp.soft-sys.math.maple
Subject: Re: Simplify Difficulty
Date: Sun, 10 May 2015 08:50:05 -0700
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"Thomas D. Dean" <tomdean@speakeasy.org> writes:

About a dozen years ago I wrote a Maple package using many of the
inductance formulas in Grover and elsewhere.  Never got around to
pushing it to the web.  I should try to hunt it down.

Joe

> I want to get a simpler expression for a function from C code.
>
> I have the inductance calculations from the National Bureau of
> Standards, developed by Grover.
>
> I copied the C function to a proc, with some minor edits, such as
> making variable declarations local, changing = to :=, asinh to
> arcsinh, etc. with evalf, Maple 15 produces the same result as the C
> code, so my edits were correct.
>
> If I call the proc as
>   rectangle(ht, wd, len, turns)
> I get a very complicated expression, as expected.
>
> I have been attempting, unsuccessfully to simplify this and am about
> to try manually.  Simple is 10 to 12 terms.
>
> Before I do this, will Maple do it?
>
> Tom Dean
>
> rectangle := proc(a, a1, b, N)
>   local p, q, r, s, t, L;
>   local aob, a1ob, g2, b2, a2ob2, aa1, b2oaa1;
>
>   a1ob := a1 / b;
>   aob := a / b;
>
>   t := ((1/2) / a1ob) * arcsinh (aob);
>   L := t;
>
>   t := ((1/2) / aob) * arcsinh (a1ob);
>   L := L + t;
>
>   q := a1ob * a1ob;
>   r := (1/2) * (1 - q) / a1ob;
>   s := a / (b * sqrt (1 + q));
>   t := -r * arcsinh (s);
>   L := L + t;
>
>   a2ob2 := aob * aob;
>   r := (1/2) * (1 - a2ob2) / aob;
>   s := a1 / (b * sqrt (1 + a2ob2));
>   t := -r * arcsinh (s);
>   L := L + t;
>
>   t := -(1/2) * a1ob * arcsinh (a / a1);
>   L := L + t;
>
>   t := -(1/2) * aob * arcsinh (a1 / a);
>   L := L + t;
>
>   b2 := b * b;
>   g2 := a * a + a1 * a1;
>   q := sqrt (1 + g2 / b2);
>   aa1 := a * a1;
>   b2oaa1 := b2 / aa1;
>   s := 1 / (b2oaa1 * q);
>   t := ((1/2) * Pi - arctan (s));
>   L := L + t;
>
>   r := b2oaa1 / 3;
>   t := r * q * (1 - ((1/2) * g2) / b2);
>   L := L + t;
>
>   t := r;
>   L := L + t;
>
>   t := -r * sqrt (1 + a2ob2) * (1 - (1/2) * a2ob2);
>   L := L + t;
>
>   q := (a1 * a1) / b2;
>   p := sqrt (1 + q);
>   t := -r * p * (1 - (1/2) * q);
>   L := L + t;
>
>   p := b / (6 * aa1);
>   q := g2 * sqrt(g2);  ## g^2 := a^2 + a1^2 */
>   q := (q - (a * a * a) - (a1 * a1 * a1)) / b2;
>   t := p * q;
>   L := L + t;
>   L := 8*(10^(-7)) * N * N * L * aa1 / b
> end proc;

-- 
Joe Riel