/* vetor analysis */
/* vectanal.mac */
/* 1-st order differntial operators */

prefix("Grad", 142, expr, expr)$
prefix("Div", 142, expr, expr)$
prefix("Rot", 142 , expr, expr)$

"Grad"(f) := block([gv],
  gv : zeromatrix(3,1),
  gv[1][1] : diff(f, x),
  gv[2][1] : diff(f, y),
  gv[3][1] : diff(f, z),
  return(gv)
)$

"Div"(v) := block([f],
  f : diff(v[1][1], x) + diff(v[2][1], y) + diff(v[3][1], z),
  return(f)
)$

"Rot"(v) := block([w],
  w : zeromatrix(3,1),
  w[1][1] : diff(v[3][1], y) - diff(v[2][1], z),
  w[2][1] : diff(v[1][1], z) - diff(v[3][1], x),
  w[3][1] : diff(v[2][1], x) - diff(v[1][1], y),
  return(w)
)$

Laplacian(f) := div (grad (f))$

/* inner and outer products */

infix("@*")$
infix("@x")$

v @* w := block([val],
  val : v[1][1] * w[1][1] + v[2][1] * w[2][1] + v[3][1] * w[3][1] ,
  return(val)
)$

v @x w := block([valvec],
  valvec : zeromatrix(3,1),
  valvec[1][1] : v[2][1] * w[3][1] - v[3][1] * w[2][1] ,
  valvec[2][1] : v[3][1] * w[1][1] - v[1][1] * w[3][1] ,
  valvec[3][1] : v[1][1] * w[2][1] - v[2][1] * w[1][1] ,
  return(valvec)
)$