Usage:
<blowup0 J K
K is set to be the ideal with a standard basis defining the
ring R[t] as a quotient ring of a polynomial ring
S = R[t,y[1],...y[ncols(J)]]
under the map sending y[i] to the i th generator of J.
The ring R is the base ring of J. The variable "t" is the first
variable of S.
Parameters:
J = ideal to blow up
Output values:
K = standard basis of the ideal (y[i]-tJ[i], i=1..ncols(J)), where
J[i] stands for the i th generator of J, and K is an ideal in the
the ring S.
The ring S = R'[t, y[1], ..., y[ncols(J)]], where R' is
a copy of R, with variables named x[i], using the reverse
lexicographic order with three blocks of variables: the first block
consists of the variable "t", the second block contains the y[i], and
the last block contains the variables x[i] corresponding to the
variables of R.
The ring R may be a quotient ring.
This script is useful for computing blowup rings and associated graded
rings (normal cones). The ideal L defining the blowup ring R[tJ] is
obtained by eliminating "t" from K. The normal cone of J can be
obtained by adding the generators of J to the ideal L
(see the script "normalcone" for a different method).