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) = aixi and
B(x) = bixi 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