Usage:
<l_homog0 I v J
Homogenize the columns of the matrix "I" using the new variable "v",
producing a matrix "J" over a new ring. The monomial order for
this new ring is "elimination w.r.t. the variable v", which is
useful for many operations over local rings.
Parameters:
I = mxn matrix over a ring R
v = a variable name not occuring in R, such as t[-100].
Output values:
J = mxn matrix over the ring R[v], whose columns are now homogenious.
This script is used by those scripts which compute over a local ring.
Let R_m be the localization of R at the homogeneous maximal ideal.
The lead terms of a polynomial of R_m are the terms of LOWEST degree.
The elimination order above has the property that the lead term
of the homogenization of a polynomial f corresponds to the term of lowest
total degree.
Caveats: the variable v must be distinct from the variables of the
ring R.