Let R be a polynomial ring in two groups of variables X1,...,Xn-1 and a1,...,as. The variables a_1,..,as are seen as parameters and the variables X1,...,Xn-1 are to be eliminated. Being given a row matrix [f1,...,fn] where each fi is a polynomial in X1,...,Xn-1 and a1,...,ar, this function returns an elimination matrix that only depends on the parameters a1,...,as and whose maximal nonzero minor yields a multiple of the generalized resultant associated to f1,...,fn.
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 (M,l)
o7 = | -ceg+bfg+cdh-afh-bdi+aei |
1 1
o7 : Matrix R <--- R
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