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EliminationMatrices :: eliminationMatrix(List,Matrix)

eliminationMatrix(List,Matrix) -- returns a matrix associated to the Macaulay resultant

Synopsis

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 a matrix which is generically (in terms of the parameters $a_1,...,a_s$) surjective such that the gcd of its maximal minors is the Macaulay resultant of $f_1,...,f_n$

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 = eliminationMatrix (l,M)

o7 = {1} | a d g |
     {1} | b e h |
     {1} | c f i |

             3       3
o7 : Matrix R  <--- R