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discriminant

the discriminant of a polynomial

Syntax
discriminant(F: RINGELEM): RINGELEM
discriminant(F: RINGELEM, X: RINGELEM): RINGELEM

Description
This function computes the discriminant of a polynomial F (with respect to a given indeterminate X, if the polynomial is multivariate). If the polynomial is univariate then there is no need to specify which indeterminate to use.

The discriminant is defined as
(-1)^(N*(N-1)/2)*det(M)/M[1,1]
where M := Sylvester(F, deriv(F,X), X) and N := deg(F, X) .

Example
/**/  Use R ::= QQ[x,y];
/**/  discriminant(x^2+3*y^2, x);
-12*y^2

/**/  discriminant(x^2+3*y^2, y);
-12*x^2

/**/  discriminant((x+1)^20+2);
54975581388800000000000000000000

See Also