Merge pull request oscar-system#402 from hannes14/saturation

saturation: also return number of iterations

src/ideal/ideal.jl

@@ -327,19 +327,21 @@ end
     saturation{T <: Nemo.RingElem}(I::sideal{T}, J::sideal{T})
 
 Returns the saturation of the ideal $I$ with respect to $J$, i.e. returns
-the quotient ideal $(I:J^\infty)$.
+the quotient ideal $(I:J^\infty)$ and the number of iterations.
 """
 function saturation(I::sideal{T}, J::sideal{T}) where T <: Nemo.RingElem
    check_parent(I, J)
    R = base_ring(I)
    !has_global_ordering(R) && error("Must be over a ring with global ordering")
    Q = quotient(I, J)
    # we already have contains(Q, I) automatically
+   k = 0
    while !contains(I, Q)
       I = Q
       Q = quotient(I, J)
+      k = k + 1
    end
-   return I
+   return I,k
 end
 
 ###############################################################################

test/ideal/sideal-test.jl

@@ -161,12 +161,14 @@ end
    I = Ideal(R, (x^2 + x*y + 1)*(2y^2+1)^3, (2y^2 + 3)*(2y^2+1)^2)
    J = Ideal(R, 2y^2 + 1)
 
-   @test equal(saturation(I, J), Ideal(R, 2y^2 + 3, x^2 + x*y + 1))
+   S,k = saturation(I, J)
+   @test equal(S, Ideal(R, 2y^2 + 3, x^2 + x*y + 1))
 
    I = Ideal(R, (x*y + 1)*(2x^2*y^2 + x*y - 2) + 2x*y^2 + x, 2x*y + 1)
    J = Ideal(R, x)
 
-   @test equal(satstd(I, J), std(saturation(I, J)))
+   S,k = saturation(I, J)
+   @test equal(satstd(I, J), std(S))
 end
 
 @testset "sideal.slimgb" begin