(* $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"
}