** suivant:** Resultant of two polynomials
** monter:** Arithmetic and polynomials
** précédent:** Sturm sequences : sturmseq
** Table des matières**
** Index**

##

Sylvester matrix of two polynomials : `sylvester`

`sylvester` takes two polynomials as arguments.

`sylvester` returns the Sylvester matrix *S* of these polynomials.

If
*A*(*x*) = *a*_{i}*x*^{i} and
*B*(*x*) = *b*_{i}*x*^{i} are 2 polynomials, their Sylvester matrix
*S* is a squared matrix of size `m+n` where `m=degree(B(x))` and
`n=degree(A(x))`. The `m` first lines are made with the *A*(*x*)
coefficients, so that :

and the `n` further lines are made with the *B*(*x*)
coefficients, so that :

Input :
`sylvester(x``^`

3-p*x+q,3*x`^`

2-p,x)

Output :
`[[1,0,-p,q,0],[0,1,0,-p,q],[3,0,-p,0,0], [0,3,0,-p,0],[0,0,3,0,-p]]`

Input :
`det([[1,0,-p,q,0],[0,1,0,-p,q],[3,0,-p,0,0], [0,3,0,-p,0],[0,0,3,0,-p]])`

Output :
`-4*p``^`

3-27*q`^`

2

giac documentation written by Renée De Graeve and Bernard Parisse