isReflexive(Ideal) -- whether an ideal or module is reflexive

Synopsis

Function: isReflexive
Usage:

isReflexive I
Inputs:
- I, an ideal or a module,
Optional inputs:
- Strategy => a symbol, default value NoStrategy, specify a strategy for the internal call to reflexify
- KnownDomain => a Boolean value, default value true, assume the ambient ring is a domain for the internal call to reflexify
Outputs:
- a Boolean value,

Description

This function returns true if the module or ideal is reflexive, otherwise it returns false. In other words this checks if $M \cong Hom(Hom(M, R))$. This function calls reflexify and passes the options Strategy and KnownDomain specified in its call.

i1 : R = QQ[x,y,z]/ideal(x^2-y*z);

i2 : m = ideal(x,y,z);

o2 : Ideal of R

i3 : isReflexive(m)

o3 = false

i4 : isReflexive(m*R^1)

o4 = false

i5 : I = ideal(x,y);

o5 : Ideal of R

i6 : isReflexive(I)

o6 = true

i7 : isReflexive(I*R^1)

o7 = true

Ways to use this method: