Macaulay2 » Documentation
Packages » PrimaryDecomposition :: removeLowestDimension
next | previous | forward | backward | up | index | toc

removeLowestDimension -- remove components of lowest dimension

Synopsis

Description

This function yields the intersection of the primary components of M except those of lowest dimension, and thus returns the ambient free module of M (or unit ideal) if M is pure dimensional. For a very brief description of the method used, see topComponents.

As an example we remove the lowest dimensional component of an ideal I:

i1 : R = ZZ/32003[a..d];
 
i2 : I = intersect(ideal(a*b+a^2,b^2), ideal(a^2,b^2,c^2), ideal(b^3,c^3,d^3))

             3   2 3   2 3   2 3        3   2   3   3 3   2 2 3        2 3
o2 = ideal (b , b d , b c , a c  + a*b*c , a b*d , a d , a c d  + a*b*c d )

o2 : Ideal of R
 
i3 : removeLowestDimension I

             2   2
o3 = ideal (b , a  + a*b)

o3 : Ideal of R

See also

Ways to use removeLowestDimension :

For the programmer

The object removeLowestDimension is a method function.