Suppose ( g1, ..., gm ) = J ⊆R is an ideal in a ring R. We form the Rees algebra R[Jt] = R[Y1, ..., Ym]/K where the Yi map to the gi. This function returns the maximum Y-degree of the generators of K. For more information, see page 22 of Vasconcelos, Rees algebras, multiplicities, algorithms. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2005.
i1 : R = QQ[x_0..x_8]; |
i2 : M = genericMatrix(R,x_0,3,3) o2 = | x_0 x_3 x_6 | | x_1 x_4 x_7 | | x_2 x_5 x_8 | 3 3 o2 : Matrix R <--- R |
i3 : J = minors (2,M) o3 = ideal (- x x + x x , - x x + x x , - x x + x x , - x x + x x , - 1 3 0 4 2 3 0 5 2 4 1 5 1 6 0 7 ------------------------------------------------------------------------ x x + x x , - x x + x x , - x x + x x , - x x + x x , - x x + x x ) 2 6 0 8 2 7 1 8 4 6 3 7 5 6 3 8 5 7 4 8 o3 : Ideal of R |
i4 : relationType(R,J) blowUpIdeals computed. o4 = 1 |