/* DEMO FILE. */

/* until translated and compiled, use .MC file in DOE MACSYMA */
if get('vect,'version)=false then load("vect")$

/* First, we establish p, q, f, and g as vector entities:*/

declare([p, q, f, g], nonscalar) $
/* To attempt to prove the following vector identity:*/
(p~q).(f~g) + (q~f).(p~g) + (f~p).(q~g) = 0;
/* Evidently default simplifications are not drastic
enough, so let us try: */
vectorsimp(%), expandall;
/* Now, to determine the expansion of: */
example: laplacian(%pi*(s+h)) = div(3*s*p);
vectorsimp(example), expandall:true;
/* Now, suppose we wish to find the specific representation of this
equation in parabolic coordinates.  On MC, LOAD("SHARE;VECT ORTH");
gives access to numerous orthogonal curvilinear coordinate definitions.
On UNIX and VMS systems, load('vect_orth);.  One of
these is for parabolic coordinates:
*/

parabolic: [[(u^2-v^2)/2, u*v], u, v];

/*First, we use the function scalefactors to derive a set of global
scale factors, then we use the function express to express its
argument in the corresponding coordinate system:*/

scalefactors(parabolic) $
example:express(example);

/*Suppose that s is dependent upon both u and v, h is dependent upon
only u, and p is dependent only upon v.  To expand the above
derivatives, taking advantage of these simplifications:*/

depends([s,h],u, [s,p],v) $
example,diff,factor;

/* Now, suppose that we are given the following gradient, in parabolic
coordinates:*/
example: [(2*u*v**3+3*u**3*v)/(v**2+u**2),
   (2*u**2*v**2+u**4)/(u**2+v**2)];

/*To determine the corresponding scalar potential, relative to the
potential at point [0,0]:*/

potential(example);

/*There is an analagous function named VECTORPOTENTIAL that computes the
vector potential associated with a given curl vector.*/