-- -*- M2-comint -*- hash: 16417234212823519011

i1 : R = QQ[a..i];

i2 : M = genericMatrix(R,a,3,3)

o2 = | a d g |
     | b e h |
     | c f i |

             3      3
o2 : Matrix R  <-- R

i3 : I = ideal(M^3);

o3 : Ideal of R

i4 : f = trace M

o4 = a + e + i

o4 : R

i5 : G = gb(I, DegreeLimit=>3)

o5 = GroebnerBasis[status: DegreeLimit; all S-pairs handled up to degree 3]

o5 : GroebnerBasis

i6 : f^7 % G == 0

o6 = false

i7 : gb(I, DegreeLimit=>7)

o7 = GroebnerBasis[status: DegreeLimit; all S-pairs handled up to degree 7]

o7 : GroebnerBasis

i8 : f^7 % G

o8 = 0

o8 : R

i9 : gb I

o9 = GroebnerBasis[status: done; S-pairs encountered up to degree 9]

o9 : GroebnerBasis

i10 : I = ideal(M^3);

o10 : Ideal of R

i11 : G = gb(I, StopBeforeComputation=>true)

o11 = GroebnerBasis[status: not started; all S-pairs handled up to degree -1]

o11 : GroebnerBasis

i12 : f^7 % I

o12 = 0

o12 : R

i13 : status G

o13 = status: DegreeLimit; all S-pairs handled up to degree 7

i14 : 
