# affineResultant -- affine resultant

## Synopsis

• Usage:
affineResultant f
• Inputs:
• f, , a row matrix whose entries are $n+1$ polynomials $f_0,\ldots,f_n$ in $n$ variables (or a list to be interpreted as such a matrix)
• Optional inputs:
• Outputs:
• , the resultant of the polynomials obtained by homogenizing $f_0,\ldots,f_n$ with respect to a new variable

## Description

 i1 : ZZ[t,u][y,z] o1 = ZZ[t..u][y..z] o1 : PolynomialRing i2 : f = {3*t*y*z-u*z^2+1, -y+t+3*u-1, u*z^4-t*y^3+t*y*z} 2 4 3 o2 = {3t*y*z - u*z + 1, - y + t + 3u - 1, u*z - t*y + t*y*z} o2 : List i3 : affineResultant f 12 11 2 10 3 9 4 8 5 7 6 o3 = - 81t u - 1701t u - 15309t u - 76545t u - 229635t u - 413343t u ------------------------------------------------------------------------ 6 7 5 8 11 10 2 9 3 - 413343t u - 177147t u + 567t u + 10206t u + 76545t u + ------------------------------------------------------------------------ 8 4 7 5 6 6 5 7 4 8 3 9 306181t u + 688923t u + 826821t u + 413883t u + 1215t u + 1458t u ------------------------------------------------------------------------ 2 10 10 9 2 8 3 7 4 6 5 + 729t u - 1701t u - 25515t u - 153093t u - 459321t u - 689265t u ------------------------------------------------------------------------ 5 6 4 7 3 8 2 9 9 8 2 - 414693t u - 2835t u - 3159t u - 1458t u + 2835t u + 33984t u + ------------------------------------------------------------------------ 7 3 6 4 5 5 4 6 3 7 2 8 152565t u + 303135t u + 220905t u - 12150t u - 5913t u + 1215t u - ------------------------------------------------------------------------ 8 7 2 6 3 5 4 4 5 3 6 2862t u - 25659t u - 75873t u - 70031t u + 16263t u + 13230t u - ------------------------------------------------------------------------ 2 7 7 6 2 5 3 4 4 3 5 540t u + 1809t u + 10818t u + 15015t u - 6609t u - 9360t u + ------------------------------------------------------------------------ 2 6 6 5 2 4 3 3 4 2 5 6 135t u - 729t u - 2313t u + 684t u + 3165t u - 81t u - 54t*u + ------------------------------------------------------------------------ 5 4 2 3 3 2 4 5 4 3 2 2 3 189t u + 135t u - 583t u - 38t u + 54t*u - 27t u + 54t u + 47t u - ------------------------------------------------------------------------ 4 2 2 3 2 18t*u - 9t u + 2t*u + u o3 : ZZ[t..u]