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idealPower -- compute the ideal generated by the generators of the ideal raised to a power

Synopsis

Description

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

See also

Ways to use idealPower :

For the programmer

The object idealPower is a method function.