phi N.sagews

R.<T1,A12,A13,A14,A15,T2,A23,A24,A25,T3,A34,A35,T4,A45,T5,B12,B13,B14,B15,B23,B24,B25,B34,B35,B45>=QQ['T1,A12,A13,A14,A15,T2,A23,A24,A25,T3,A34,A35,T4,A45,T5,B12,B13,B14,B15,B23,B24,B25,B34,B35,B45'];R 
G=GL(5,R);G
M=MatrixSpace(R,5,5); M 
P=G([T1,A12,A13,A14,A15,0,T2,A23,A24,A25,0,0,T3,A34,A35,0,0,0,T4,A45,0,0,0,0,T5]); P 
Q=M([0,B12,B13,B14,B15,0,0,B23,B24,B25,0,0,0,B34,B35,0,0,0,0,B45,0,0,0,0,0]); Q 
S=Q*P-P*Q*5;S
I=Ideal(S[0][1],S[0][2],S[0][3],S[0][4],S[1][2],S[1][3],S[1][4],S[2][3],S[2][4],S[3][4]); I 
L=I.minimal_associated_primes();L

Multivariate Polynomial Ring in T1, A12, A13, A14, A15, T2, A23, A24, A25, T3, A34, A35, T4, A45, T5, B12, B13, B14, B15, B23, B24, B25, B34, B35, B45 over Rational Field General Linear Group of degree 5 over Multivariate Polynomial Ring in T1, A12, A13, A14, A15, T2, A23, A24, A25, T3, A34, A35, T4, A45, T5, B12, B13, B14, B15, B23, B24, B25, B34, B35, B45 over Rational Field Full MatrixSpace of 5 by 5 dense matrices over Multivariate Polynomial Ring in T1, A12, A13, A14, A15, T2, A23, A24, A25, T3, A34, A35, T4, A45, T5, B12, B13, B14, B15, B23, B24, B25, B34, B35, B45 over Rational Field [ T1 A12 A13 A14 A15] [ 0 T2 A23 A24 A25] [ 0 0 T3 A34 A35] [ 0 0 0 T4 A45] [ 0 0 0 0 T5] [ 0 B12 B13 B14 B15] [ 0 0 B23 B24 B25] [ 0 0 0 B34 B35] [ 0 0 0 0 B45] [ 0 0 0 0 0] [ 0 -5*T1*B12 + T2*B12 A23*B12 - 5*T1*B13 + T3*B13 - 5*A12*B23 A24*B12 + A34*B13 - 5*T1*B14 + T4*B14 - 5*A12*B24 - 5*A13*B34 A25*B12 + A35*B13 + A45*B14 - 5*T1*B15 + T5*B15 - 5*A12*B25 - 5*A13*B35 - 5*A14*B45] [ 0 0 -5*T2*B23 + T3*B23 A34*B23 - 5*T2*B24 + T4*B24 - 5*A23*B34 A35*B23 + A45*B24 - 5*T2*B25 + T5*B25 - 5*A23*B35 - 5*A24*B45] [ 0 0 0 -5*T3*B34 + T4*B34 A45*B34 - 5*T3*B35 + T5*B35 - 5*A34*B45] [ 0 0 0 0 -5*T4*B45 + T5*B45] [ 0 0 0 0 0] Ideal (-5*T1*B12 + T2*B12, A23*B12 - 5*T1*B13 + T3*B13 - 5*A12*B23, A24*B12 + A34*B13 - 5*T1*B14 + T4*B14 - 5*A12*B24 - 5*A13*B34, A25*B12 + A35*B13 + A45*B14 - 5*T1*B15 + T5*B15 - 5*A12*B25 - 5*A13*B35 - 5*A14*B45, -5*T2*B23 + T3*B23, A34*B23 - 5*T2*B24 + T4*B24 - 5*A23*B34, A35*B23 + A45*B24 - 5*T2*B25 + T5*B25 - 5*A23*B35 - 5*A24*B45, -5*T3*B34 + T4*B34, A45*B34 - 5*T3*B35 + T5*B35 - 5*A34*B45, -5*T4*B45 + T5*B45) of Multivariate Polynomial Ring in T1, A12, A13, A14, A15, T2, A23, A24, A25, T3, A34, A35, T4, A45, T5, B12, B13, B14, B15, B23, B24, B25, B34, B35, B45 over Rational Field