codim(Ideal) -- compute the codimension

Synopsis

Function: codim
Usage:

codim I
Inputs:
- I
Optional inputs:
- Generic => ..., default value false,
Outputs:
- an integer, dim(R) - dim(R/I), where R is the ring containing I.

Description

When R is equidimensional, this quantity is the codimension of the ideal I.

i1 : R = ZZ/101[a..e];

i2 : I = monomialCurveIdeal(R,{2,3,5,7})

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

o2 : Ideal of R

i3 : J = ideal presentation singularLocus(R/I);

o3 : Ideal of R

i4 : codim J

o4 = 4

i5 : radical J

o5 = ideal (d, c, b, a*e)

o5 : Ideal of R

The following may not be the expected result, because the ring is not equidimensional.

i6 : R = QQ[x,y]/(ideal(x,y) * ideal(x-1))

o6 = R

o6 : QuotientRing

i7 : codim ideal(x,y)

o7 = 1

Ways to use this method: