i1 : R=QQ[x_1..x_8]; |
i2 : m1=genericMatrix(R,x_1,2,2); m2=genericMatrix(R,x_5,2,2); 2 2 o2 : Matrix R <--- R 2 2 o3 : Matrix R <--- R |
i4 : m=m1*m2 o4 = | x_1x_5+x_3x_6 x_1x_7+x_3x_8 | | x_2x_5+x_4x_6 x_2x_7+x_4x_8 | 2 2 o4 : Matrix R <--- R |
i5 : i= ideal flatten m o5 = ideal (x x + x x , x x + x x , x x + x x , x x + x x ) 1 5 3 6 2 5 4 6 1 7 3 8 2 7 4 8 o5 : Ideal of R |
i6 : d1=minors(2,m1); d2=minors(2,m2); o6 : Ideal of R o7 : Ideal of R |
i8 : j=i+d1+d2 o8 = ideal (x x + x x , x x + x x , x x + x x , x x + x x , - x x + 1 5 3 6 2 5 4 6 1 7 3 8 2 7 4 8 2 3 ------------------------------------------------------------------------ x x , - x x + x x ) 1 4 6 7 5 8 o8 : Ideal of R |
i9 : M=matrix{{0,d1_0,m_(0,0),m_(0,1)}, {0,0,m_(1,0),m_(1,1)}, {0,0,0,d2_0}, {0,0,0,0}} o9 = | 0 -x_2x_3+x_1x_4 x_1x_5+x_3x_6 x_1x_7+x_3x_8 | | 0 0 x_2x_5+x_4x_6 x_2x_7+x_4x_8 | | 0 0 0 -x_6x_7+x_5x_8 | | 0 0 0 0 | 4 4 o9 : Matrix R <--- R |
i10 : M=M-(transpose M) o10 = | 0 -x_2x_3+x_1x_4 x_1x_5+x_3x_6 x_1x_7+x_3x_8 | | x_2x_3-x_1x_4 0 x_2x_5+x_4x_6 x_2x_7+x_4x_8 | | -x_1x_5-x_3x_6 -x_2x_5-x_4x_6 0 -x_6x_7+x_5x_8 | | -x_1x_7-x_3x_8 -x_2x_7-x_4x_8 x_6x_7-x_5x_8 0 | 4 4 o10 : Matrix R <--- R |
i11 : N=transpose (res coker transpose M).dd_2 o11 = {-4} | -x_2x_5-x_4x_6 x_2x_3-x_1x_4 -x_1x_5-x_3x_6 0 | {-4} | -x_2x_7-x_4x_8 0 -x_1x_7-x_3x_8 x_2x_3-x_1x_4 | {-4} | x_6x_7-x_5x_8 x_1x_7+x_3x_8 0 -x_1x_5-x_3x_6 | {-4} | 0 x_2x_7+x_4x_8 -x_6x_7+x_5x_8 -x_2x_5-x_4x_6 | 4 4 o11 : Matrix R <--- R |
i12 : uN=universalEmbedding -- (N) o12 = universalEmbedding o12 : MethodFunction |