By default (when AscentCount => true), ascendIdeal just returns the stable (ascended) ideal. If instead you set AscentCount=>true then it returns a list. The first value is the stable ideal. The second is how many steps it took to reach that ideal.
i1 : R = ZZ/5[x,y,z]; |
i2 : J = ideal(x^12,y^15,z^21); o2 : Ideal of R |
i3 : f = y^2+x^3-z^5; |
i4 : ascendIdeal(1, f^4, J) o4 = ideal (z, y, x) o4 : Ideal of R |
i5 : ascendIdeal(1, f^4, J, AscentCount=>true) o5 = {ideal (z, y, x), 3} o5 : List |