Let $f_1,...,f_n$ be a polynomials two groups of variables $X_1,...,X_n$ and $a_1,...,a_s$ and such that $f_1,...,f_n$ are homogeneous polynomials with respect to the variables $X_1,...,X_n$. This function returns two matrices M1 and M2 such that $det(D_1)/det(D_2)$ is the Macaulay resultant of $f_1,...,f_n$ providing det(D_2) is nonzero.
Remark: if D2 is the empty matrix, its determinant has to be understood as 1 (and not zero, which is the case in Macaulay2 since the empty matrix is identified to the zero.
i1 : R=QQ[a..i,x,y,z] o1 = R o1 : PolynomialRing |
i2 : f1 = a*x+b*y+c*z o2 = a*x + b*y + c*z o2 : R |
i3 : f2 = d*x+e*y+f*z o3 = d*x + e*y + f*z o3 : R |
i4 : f3 = g*x+h*y+i*z o4 = g*x + h*y + i*z o4 : R |
i5 : M = matrix{{f1,f2,f3}} o5 = | ax+by+cz dx+ey+fz gx+hy+iz | 1 3 o5 : Matrix R <--- R |
i6 : l = {x,y,z} o6 = {x, y, z} o6 : List |
i7 : MR = macaulayFormula (l,M) o7 = ({1} | a d g |, 0) {1} | b e h | {1} | c f i | o7 : Sequence |
The object macaulayFormula is a method function.