Description
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
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i2 : f1 = a*x+b*y+c*z
o2 = a*x + b*y + c*z
o2 : R
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i3 : f2 = d*x+e*y+f*z
o3 = d*x + e*y + f*z
o3 : R
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i4 : f3 = g*x+h*y+i*z
o4 = g*x + h*y + i*z
o4 : R
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i5 : M = matrix{{f1,f2,f3}}
o5 = | ax+by+cz dx+ey+fz gx+hy+iz |
1 3
o5 : Matrix R <-- R
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i6 : l = {x,y,z}
o6 = {x, y, z}
o6 : List
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i7 : MR = macaulayFormula (l,M)
o7 = ({1} | a d g |, 0)
{1} | b e h |
{1} | c f i |
o7 : Sequence
|