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.
- a thing, $n+1$ 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:
- a ring element, 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

Ways to use this method: