isInvertibleIdeal -- checks whether an ideal is locally principal (invertible)

Usage:

b = isInvertibleIdeal(I)
Inputs:
- I, an ideal,
Outputs:
- b, a Boolean value,

Description

Given an ideal $I$, this function returns true if $I$ is locally principal, and false otherwise. It will work in a normal domain (or more generally a G1 + S2 domain reduced equidimensional ring).

i1 : R = QQ[x,y]/(y^2-x*(x-1)*(x+1)); --an elliptic curve

i2 : I = ideal(x,y); --corresponding to a point, should be invertible, even if not principal

o2 : Ideal of R

i3 : isInvertibleIdeal(I)--should be true

o3 = true

i4 : S = QQ[u,v];

i5 : J = ideal(u,v);

o5 : Ideal of S

i6 : isInvertibleIdeal(J) --should be false

o6 = false

This frequently also works in non-domains.

i7 : R = QQ[w..z]/ideal(x*y,x*z,y*z,x^2-y^2,x^2-z^2);

i8 : isInvertibleIdeal(ideal(w,x)) -- should be false

o8 = false

i9 : isInvertibleIdeal(ideal(x,y,z)) -- should be true

o9 = true

Ways to use isInvertibleIdeal:

isInvertibleIdeal(Ideal)

For the programmer

The object isInvertibleIdeal is a method function with options.

The source of this document is in NonPrincipalTestIdeals.m2:1208:0.