Resultant of two polynomials

The determinant of the Sylvester matrix, taken with the Bareiss fraction-free algorithm so integer coefficients give an exact integer answer. It vanishes exactly when the two polynomials share a root, which is what makes it the standard elimination tool.

Usage

Resaln(p, q)

Arguments

p, q

Coefficients, lowest degree first.

Value

Named list with estimate, resultant, sylvester, deg_p, deg_q, share_root, method.

References

Classical algebra; no single owning source.

Examples

Resaln(c(2, -3, 1), c(6, -5, 1))
#> $estimate
#> [1] 0
#> 
#> $resultant
#> [1] 0
#> 
#> $sylvester
#>      [,1] [,2] [,3] [,4]
#> [1,]    1   -3    2    0
#> [2,]    0    1   -3    2
#> [3,]    1   -5    6    0
#> [4,]    0    1   -5    6
#> 
#> $deg_p
#> [1] 2
#> 
#> $deg_q
#> [1] 2
#> 
#> $share_root
#> [1] TRUE
#> 
#> $method
#> [1] "resultant via the Sylvester matrix (Bareiss)"
#>