If I is generated by $(f1, ..., fk)$ then idealPower(n, I) is the ideal generated by $(f1^n, ..., fk^n)$. This is relevant because idealPower(n, I) and I^n have the same reflexification, but idealPower(n, I) can be much faster to compute with since it has fewer generators typically.
i1 : R = QQ[x, y, u, v] / ideal(x * y - u * v); |
i2 : I = ideal(x, u); o2 : Ideal of R |
i3 : idealPower(5, I) 5 5 o3 = ideal (x , u ) o3 : Ideal of R |
i4 : I^5 5 4 3 2 2 3 4 5 o4 = ideal (x , x u, x u , x u , x*u , u ) o4 : Ideal of R |
The object idealPower is a method function.