Description
Let R be a polynomial ring in two groups of variables $X_1,...,X_{n-1}$ and $a_1,...,a_s$. The variables $a_1,...,a_s$ are seen as parameters and the variables $X_1,...,X_{n-1}$ are to be eliminated. Being given a row matrix $f_1,...,f_n$ where each $f_i$ is a polynomial in $X_1,...,X_{n-1}$ and $a_1,...,a_s$, this function returns an elimination matrix that only depends on the parameters $a_1,...,a_s$ and whose maximal nonzero minor yields a multiple of the generalized resultant associated to $f_1,...,f_n$
i1 : R=QQ[a..i,x,y]
o1 = R
o1 : PolynomialRing
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i2 : f1 = a*x+b*y+c
o2 = a*x + b*y + c
o2 : R
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i3 : f2 = d*x+e*y+f
o3 = d*x + e*y + f
o3 : R
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i4 : f3 = g*x+h*y+i
o4 = g*x + h*y + i
o4 : R
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i5 : M = matrix{{f1,f2,f3}}
o5 = | ax+by+c dx+ey+f gx+hy+i |
1 3
o5 : Matrix R <-- R
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i6 : l = {x,y}
o6 = {x, y}
o6 : List
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i7 : MR = bezoutianMatrix (l,M)
o7 = | -ceg+bfg+cdh-afh-bdi+aei |
1 1
o7 : Matrix R <-- R
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