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Sylvester
Syntax
Sylvester(F:POLY,G:POLY,X:INDET)
Summary
the Sylvester matrix of two polynomials
Description
This function returns the Sylvester matrix of the polynomials F and G
with respect to the indeterminate X. This is the matrix used to
calculate the resultant.
example
Use R ::= Q[p,q,x];
F := x^3+px-q; G := Der(F,x);
Sylvester(F,G,x);
Mat[
[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]
]
-------------------------------
Det(Sylvester(F,G,x)) = Resultant(F,G,x);
TRUE
-------------------------------
See Also