If CanonicalStrategy=>Katzman which is the default behavior, then the Frobenius action on the top local cohomology (bottom Ext) is computed via the method of Katzman. If it is set to anything else, it is simply brute forced in Macaulay2 using the fuctoriality of Ext. CanonicalStrategy=>Katzman typically is much faster.
i1 : R = ZZ/5[x,y,z]/ideal(y^2*z + x*y*z-x^3) o1 = R o1 : QuotientRing |
i2 : time isFinjective(R) -- used 0.0597287 seconds o2 = true |
i3 : time isFinjective(R, CanonicalStrategy=>null) -- used 3.55707 seconds o3 = true |