Usage: <blowup J T L L is set to be the ideal with standard basis defining the Rees ring R[tJ] as a quotient ring of a polynomial ring T over the base ring R of J. The variable "t" is the first variable of T. Parameters: J = ideal to blowup. T = a polynomial ring over R in variables whose weights are proportional to the degrees of the generators of J. Output values: L = the result ideal in T. The ring R may be a quotient ring. The ideal L defining the blowup ring R[tJ] is obtained by eliminating "t" from the ideal K produced by the script "blowup0". The situation is summarized by the following diagram: K ---> S = R[t,y] --->> R[t] (y[i] |--> tJ[i]) | | | L ---> T = R[y] --->> R[tJ] where the vertical lines represent inclusions. It is convenient to form the ring T by making a polynomial ring whose generators correspond to the generators of J, and then use ring-sum to tensor this ring with R. Caveats: If the ring T has more generators than needed, the correct initial subset is chosen.