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RationalMaps :: relationType

relationType -- Given an ideal in a ring this computes the maximum degree, of the new variables, of the minimal generators of the defining ideal of the associated Rees algebra.

Synopsis

Description

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

Ways to use relationType :