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D.5.2.61 EulerProj
Procedure from library chern.lib (see chern_lib).
- Usage:
- EulerProj(I); I an ideal
- Return:
- integer
- Purpose:
- computes the highest degree term of the Chern-Schwartz-MacPherson class
of the variety defined by I, which equals the Euler characteristic
- Note:
- uses CSMA(...)
Example:
| | LIB "chern.lib";
// consider the projective plane with homogeneous coordinates x, y, z
ring r = 0, (x, y, z), dp;
// Euler characteristic of a smooth cubic:
ideal I=x3+y3+z3;
I;
==> I[1]=x3+y3+z3
EulerProj(I);
==> 0
// Euler characteritic of 3 non-collinear lines:
ideal J=x*y*z;
J;
==> J[1]=xyz
EulerProj(J);
==> 3
// Euler characteristic of 3 lines passing through one point
ideal K=x*y*(x+y);
K;
==> K[1]=x2y+xy2
EulerProj(K);
==> 4
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