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D.4.25.1 ReesAlgebra

Procedure from library reesclos.lib (see reesclos_lib).

ReesAlgebra (I); I = ideal

The Rees algebra R[It] as an affine ring, where I is an ideal in R. The procedure returns a list containing two rings:
[1]: a ring, say RR; in the ring an ideal ker such that R[It]=RR/ker

[2]: a ring, say Kxt; the basering with additional variable t containing an ideal mapI that defines the map RR-->Kxt

LIB "reesclos.lib";
ring R = 0,(x,y),dp;
ideal I = x2,xy4,y5;
list L = ReesAlgebra(I);
def Rees = L[1];       // defines the ring Rees, containing the ideal ker
setring Rees;          // passes to the ring Rees
==> // coefficients: QQ
==> // number of vars : 5
==> //        block   1 : ordering dp
==> //                  : names    x y U(1) U(2) U(3)
==> //        block   2 : ordering C
ker;                   // R[It] is isomorphic to Rees/ker
==> ker[1]=y*U(2)-x*U(3)
==> ker[2]=y^3*U(1)*U(3)-U(2)^2
==> ker[3]=y^4*U(1)-x*U(2)
==> ker[4]=x*y^2*U(1)*U(3)^2-U(2)^3
==> ker[5]=x^2*y*U(1)*U(3)^3-U(2)^4
==> ker[6]=x^3*U(1)*U(3)^4-U(2)^5