This is mostly an internal function which is used when checking if a map is birational and when computing the inverse map. If the AssumeDominant option is set to true, it assumes that the kernel of the associated ring map is zero (default value is false). Valid values for the Strategy option are ReesStrategy and SaturationStrategy. For more information, see Doria, Hassanzadeh, Simis, A characteristic-free criterion of birationality. Adv. Math. 230 (2012), no. 1, 390–413.
i1 : R=QQ[x,y]; |
i2 : S=QQ[a,b,c,d]; |
i3 : Pi = map(R, S, {x^3, x^2*y, x*y^2, y^3}); o3 : RingMap R <--- S |
i4 : jacobianDualMatrix(Pi, Strategy=>SaturationStrategy) o4 = | -d -c -b | | c b a | / S \2 / S \3 o4 : Matrix |-------------------------------| <--- |-------------------------------| | 2 2 | | 2 2 | \(c - b*d, b*c - a*d, b - a*c)/ \(c - b*d, b*c - a*d, b - a*c)/ |
The object jacobianDualMatrix is a method function with options.