(*  $Log: euclid3.m%v $
# Revision 1.4  1995/02/07  14:08:28  bill
# corrected mistake, was not returning sorted forms
#
# Revision 1.3  1995/02/07  05:29:14  bill
# changed over to the forms version 3 style of tree
#
# Revision 1.2  1995/02/07  01:15:00  bill
# added basis vectors, px, etc.
#
# Revision 1.1  1995/02/06  20:18:08  bill
# Initial revision
#  *)
(*  Special definitions for Euclidean 3-space for use with forms.m  *)


Print["   --   Euclidean 3-Space Basis Forms   -- "]
Print["$Header: d:/math/bb/forms/euclid3.m%v 1.4 1995/02/07 14:08:28 bill Exp bill $"]

px = Vector[x]
py = Vector[y]
pz = Vector[z]

dx = Form[x]
dy = Form[y]
dz = Form[z]

dxdy =  Form[x, y]
dydz =  Form[y, z]
dzdx = -Form[x,z]
dxdz =  Form[x,z]

dxdydz = Form[x, y, z]

wx = WForm[x]
wy = WForm[y]
wz = WForm[z]

wxwy =  WForm[x, y]
wywz =  WForm[y, z]
wzwx = -WForm[x, z]
wxwz =  WForm[x, z]

wxwywz = WForm[x, y, z];

Efilter[zzz_] := zzz /.
  { Form[x] -> "dx",
    Form[y] -> "dy",
    Form[z] -> "dz",
    WForm[x] -> "wx",
    WForm[y] -> "wy",
    WForm[z] -> "wz",
    Form[x,y] -> "dxdy",
    Form[y,z] -> "dydz",
    Form[x,z] -> "dxdz",
    WForm[x,y] -> "wxwy",
    WForm[y,z] -> "wywz",
    WForm[x,z] -> "wxwz",
    Form[x,y,z] -> "dxdydz",
    Form[x,y,z] -> "wxwywz",
    Form[] -> "",
    WForm[] -> "^1"
}