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codim(ProjectiveVariety) -- codimension of the projective variety

Synopsis

Usage:
codim V
Function: codim
Inputs:
- V, a projective variety
Outputs:
- an integer

Description

Computes the codimension of the projective variety V.

i1 : R = ZZ/101[x_0..x_3];

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

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

             2       3
o2 : Matrix R  <--- R

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

i4 : codim V

o4 = 2

Caveat

The returned value is the usual codimension if the base graded ring is an integral domain or, more generally, equidimensional.

See also

codim(QuotientRing) -- compute the codimension