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removeLowestDimension -- remove components of lowest dimension

Synopsis

Usage:
removeLowestDimension M
Inputs:
- M, an Ideal or a Module
Outputs:
- N, an Ideal, respectively a Module.

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

topComponents -- compute top dimensional component
saturate -- saturation of ideal or submodule
quotient -- quotient or division
radical -- the radical of an ideal
minimalPrimes -- minimal associated primes of an ideal

Ways to use `removeLowestDimension` :

removeLowestDimension(Ideal)
removeLowestDimension(Module)