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/* Original version of this file copyright 1999 by Michael Wester,
* and retrieved from http://www.math.unm.edu/~wester/demos/Programming/dif.macsyma
* circa 2006-10-23.
*
* Released under the terms of the GNU General Public License, version 2,
* per message dated 2007-06-03 from Michael Wester to Robert Dodier
* (contained in the file wester-gpl-permission-message.txt).
*
* See: "A Critique of the Mathematical Abilities of CA Systems"
* by Michael Wester, pp 25--60 in
* "Computer Algebra Systems: A Practical Guide", edited by Michael J. Wester
* and published by John Wiley and Sons, Chichester, United Kingdom, 1999.
*/
/* ----------[ M a c s y m a ]---------- */
/* ---------- Initialization ---------- */
showtime: all$
prederror: false$
/* ---------- Programming and Miscellaneous ---------- */
/* Define a simple differentiation operator. This is most easily done with
pattern matching. Here is an expression that we ultimately hope to be able
to differentiate. */
expr: a + b*u + c*u^2 + d*(e*u + f)^3 + g*u*exp(h*u);
dif(e, x):= block([oper, n],
if not atom(e) then
oper: part(e, 0),
n: length(e),
/* Start by making the derivative of a sum to be the sum of the derivatives. */
if oper = "+" then
map(lambda([z], dif(z, x)), e)
/* Add the product rule. */
else if oper = "*" then
dif(part(e, 1), x) * part(e, 2..n) + part(e, 1) * dif(part(e, 2..n), x)
/* Now, make the derivative of a constant (with respect to x) zero. */
else if freeof(x, e) then
0
/* Define the derivative of x with respect to x to be one. */
else if e = x then
1
/* Enter the generalized power rule. */
else if oper = "^" and not freeof(x, part(e, 1)) then
part(e, 2)*part(e, 1)^(part(e, 2) - 1)*dif(part(e, 1), x)
/* To get that last term, add in the exponential rule. */
else if oper = "^" and part(e, 1) = %e then
e*dif(part(e, 2), x)
);
/* Now, try it out! => b + 2 c u + 3 d e (e u + f)^2 + g exp(h u) (1 + h u) */
dif(expr, u);
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