dim(ProjectiveVariety) -- dimension of the projective variety

Synopsis

Computes the dimension of the projective algebraic set from the Krull dimension of its homogeneous coordinate ring.

i1 : R = ZZ/101[x_0..x_4];

i2 : M = matrix{{x_0,x_1,x_2,x_3},{x_1,x_2,x_3,x_4}}

o2 = | x_0 x_1 x_2 x_3 |
     | x_1 x_2 x_3 x_4 |

             2       4
o2 : Matrix R  <--- R

i3 : V = Proj(R/minors(2,M));

i4 : degree V

o4 = 4

i5 : dim V

o5 = 1

i6 : dim minors(2,M)

o6 = 2