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

Synopsis

Usage:
eliminationMatrix(v,m)
Function: eliminationMatrix
Inputs:
- v, a list, a list of n variables such that the polynomials f₁,...,f_n are homogeneous with respect to these variables
- m, a matrix, a single row matrix with polynomials f₁,...,f_n
Optional inputs:
- Strategy => ..., -- returns a matrix that represents the image of the map
Outputs:
- a matrix, a generically surjective matrix such that the gcd of its maximal minors if the Macaulay resultant of f1,...,fn with respect to the variables 'varList'

Description

Let f₁,...,f_n be a polynomials two groups of variables X₁,...,X_n and a₁,...,a_s and such that f₁,...,f_n are homogeneous polynomials with respect to the variables X₁,...,X_n. This function returns a matrix which is generically (in terms of the parameters a₁,...,a_s) surjective such that the gcd of its maximal minors is the Macaulay resultant of f₁,...,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