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D.4.9.1 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; → // characteristic : 0 → // 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 |