# SparseResultant Thing -- evaluate a sparse resultant

## Synopsis

• Operator: SPACE
• Usage:
R(f)
• Inputs:
• R, an instance of the type SparseResultant, associated to $n+1$ integral matrices $A_0,\ldots,A_n$ with $n$ rows.
• , $n+1$ Laurent polynomials $f = (f_0,\ldots,f_n)$ in $n$ variables $x=(x_1,\ldots,x_n)$, with $f_i = \sum_{\omega\in \{columns\ of\ A_i\}} a_{i,\omega} x^{\omega}$.
• Outputs:
• , the $(A_0,\ldots,A_n)$-resultant of $f_0,\ldots,f_n$.

## Description

 i1 : R = denseResultant(2,3); o1 : SparseResultant (sparse mixed resultant associated to {| 0 1 2 |, | 0 1 2 3 |}) i2 : f = genericLaurentPolynomials(2,3) 2 3 2 o2 = (a x + a x + a , b x + b x + b x + b ) 2 1 1 1 0 3 1 2 1 1 1 0 o2 : Sequence i3 : R(f) 3 2 2 2 2 2 2 2 2 o3 = a b - a a b b + a a b + a a b b - 2a a b b - a a a b b + a a b - 2 0 1 2 0 1 0 2 1 1 2 0 2 0 2 0 2 0 1 2 1 2 0 2 2 ------------------------------------------------------------------------ 3 2 2 2 3 2 a b b + 3a a a b b + a a b b - 2a a b b - a a b b + a b 1 0 3 0 1 2 0 3 0 1 1 3 0 2 1 3 0 1 2 3 0 3 o3 : ZZ[a ..a , b ..b ] 0 2 0 3