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Macaulay2
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resultant.m2
R = QQ[a..d,x] for i to 11 do for j to 5 do assert ( resultant (c*(x-a)^i, d*(x-b)^j, x) == d^i * c^j * (a-b)^(i*j) ) R = QQ[p_0..p_3, q_0..q_4, x] P = sum (4, i -> p_i * x^i) Q = sum (5, i -> q_i * x^i) sylvesterMatrix (P,Q,x) assert( entries oo == {{p_3,p_2,p_1,p_0,0,0,0},{0,p_3,p_2,p_1,p_0,0,0},{0,0,p_3,p_2,p_1,p_0,0},{0,0,0,p_3,p_2,p_1,p_0},{q_4,q_3,q_2,q_1,q_0,0,0},{0,q_4,q_3,q_2,q_1,q_0,0},{0,0,q_4,q_3,q_2,q_1,q_0}} )