-- -*- M2-comint -*- {* hash: 89791885 *} i1 : A = ZZ/5051[x, y, z]; i2 : I = ideal (x, x*y, y*z); o2 : Ideal of A i3 : X = regularSequence(I,A) o3 = | xy-x -xy+yz | 1 2 o3 : Matrix A <--- A i4 : isRegularSequence(X,A) o4 = true i5 : A = ZZ/5051[x, y, z]; i6 : I = ideal (x, x*y, y*z); o6 : Ideal of A i7 : regularSequence(I,A,Attempts=>1,Bound=>100,Sparseness=>.9) --warning: no maximal regular sequence found o7 = 0 1 o7 : Matrix A <--- 0 i8 : x = symbol x; y = symbol y; i10 : n = 2; i11 : A = ZZ/101[x_(1,1)..x_(n,n),y_(1,1)..y_(n,n)]; i12 : X = transpose genericMatrix(A,n,n); 2 2 o12 : Matrix A <--- A i13 : Y = transpose genericMatrix(A,y_(1,1),n,n); 2 2 o13 : Matrix A <--- A i14 : b = ideal(X*Y - Y*X); o14 : Ideal of A i15 : B = A/b; i16 : regularSequence(B,Attempts=>1,Maximal=>false) o16 = | -y_(2,1) -x_(2,2)-y_(1,1) x_(1,2)+y_(1,1) ----------------------------------------------------------------------- x_(1,2)-x_(2,1)-x_(2,2)-y_(1,2)-y_(2,2) x_(1,1) ----------------------------------------------------------------------- -x_(2,2)-y_(1,1)+y_(1,2)-y_(2,2) | 1 6 o16 : Matrix B <--- B i17 :