Singular Manual: EulerProj

| #### D.15.4.61 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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