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

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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