gfanKrullDimension -- krull dimension

Synopsis

Usage:

D = gfanKrullDimension(M)

D = gfanKrullDimension(L)

D = gfanKrullDimension(I)
Inputs:
- M, a marked polynomial list, a marked Groebner basis
- L, a list,
- I, an ideal,
Outputs:
- D, an integer, the Krull dimension of the polynomial ring modulo the ideal generated by M or L or the ideal I.

Description

This method returns the Krull dimension of the quotient of the polynomial ring by the ideal generated by M or L or the ideal I.

Note that Macaulay 2 already provides this functionality (see dim).

i1 : QQ[x,y,z,u,v];

i2 : L = {x^3, y^2};

i3 : gfanKrullDimension(L)

o3 = 3

i4 : dim ideal L

o4 = 3

gfan Documentation Takes an ideal $I$ and computes the Krull dimension of R/I where R is the polynomial ring. This is done by first computing a Groebner basis.Options:-g: Tell the program that the input is already a reduced Groebner basis.

Ways to use gfanKrullDimension :

"gfanKrullDimension(Ideal)"
"gfanKrullDimension(List)"
"gfanKrullDimension(MarkedPolynomialList)"

For the programmer

The object gfanKrullDimension is a method function with options.