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D.15.33.6 projectiveSpace

Procedure from library schubert.lib (see schubert_lib).

Usage:
projectiveSpace(n); n int

Return:
variety

Theory:
create a projective space of dimension n as an abstract variety. Its Chow ring is a quotient ring in one variable h modulo the ideal generated by h^(n+1).

Example:
 
LIB "schubert.lib";
variety P = projectiveSpace(3);
P;
==> A variety of dimension 3
==> 
P.dimension;
==> 3
def r = P.baseRing;
setring r;
P.relations;
==> _[1]=h4
ChowRing(P);
==> // coefficients: QQ
==> // number of vars : 1
==> //        block   1 : ordering wp
==> //                  : names    h
==> //                  : weights  1
==> //        block   2 : ordering C
==> // quotient ring from ideal ...
See also: Grassmannian; projectiveBundle.