2.3.2 Elimination

Lemma 2..7   Let < be an elimination order for $y_1, \ldots, y_n$, $R = K [ x_1, \ldots, x_r,y_1, \ldots, y_n ]$. Then $std(I) \cap K [ x_1, \ldots, x_r] = std (I \cap K[x_1, \ldots, x_r] )$.

SINGULAR example:

// find the equations from a parametrization t->(t^3,t^4,t^5)
ring R=0,(x,y,z,t),dp;
ideal i=x-t^3,
        y-t^4,
        z-t^5;
ideal j=eliminate(i,t);        
j;