# Singular

#### D.4.25.1 ReesAlgebra

Procedure from library `reesclos.lib` (see reesclos_lib).

Usage:
ReesAlgebra (I); I = ideal

Return:
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

Example:
 ```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 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 ```