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+yz+x xy-yz+x | 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 : bracket = ideal flatten (X*Y - Y*X); o14 : Ideal of A |
i15 : B = A/bracket; |
i16 : m = ideal gens B; o16 : Ideal of B |
i17 : regularSequence(m,B,Attempts=>1,Maximal=>false) o17 = | -x_(1,2)+x_(2,2)-y_(1,1)-y_(2,2) ----------------------------------------------------------------------- -x_(1,2)+x_(2,1)-y_(1,2)-y_(2,1)+y_(2,2) ----------------------------------------------------------------------- -x_(2,2)-y_(1,1)-y_(2,1)-y_(2,2) -x_(2,2)-y_(2,2) ----------------------------------------------------------------------- x_(2,1)+x_(2,2)+y_(1,1)-y_(2,1)+y_(2,2) -x_(1,1)-x_(2,1)+y_(2,1) | 1 6 o17 : Matrix B <--- B |
i18 : n = 2; |
i19 : A = ZZ/101[x_(1,1)..x_(n,n),y_(1,1)..y_(n,n)]; |
i20 : X = transpose genericMatrix(A,n,n); 2 2 o20 : Matrix A <--- A |
i21 : Y = transpose genericMatrix(A,y_(1,1),n,n); 2 2 o21 : Matrix A <--- A |
i22 : bracket = ideal flatten (X*Y - Y*X); o22 : Ideal of A |
i23 : B = A/bracket; |
i24 : m = ideal gens B; o24 : Ideal of B |
i25 : time regularSequence(m,B) -- used 0.014998 seconds o25 = | y_(1,1)+y_(2,2) -x_(1,2)-x_(2,2)+y_(1,1)-y_(2,1) ----------------------------------------------------------------------- -x_(2,1)+y_(2,1)+y_(2,2) x_(1,1)-x_(1,2)+x_(2,2)-y_(1,2)+y_(2,2) ----------------------------------------------------------------------- x_(1,1)-x_(1,2)-y_(2,2) -x_(2,2)+y_(2,1) | 1 6 o25 : Matrix B <--- B |
i26 : time depth(m,B) -- used 1.52277 seconds o26 = 6 |
This symbol is provided by the package Depth.