# dim(ProjectiveVariety) -- dimension of the projective variety

## Synopsis

• Function: dim
• Usage:
dim V
• Inputs:
• Outputs:

## Description

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