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discriminant --
the discriminant of a polynomial
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discriminant(F: RINGELEM): RINGELEM
discriminant(F: RINGELEM, X: RINGELEM): RINGELEM |
These functions compute the discriminant of a non-constant polynomial ``F``
with respect to the indeterminate ``X``; in the first form ``F`` must be
univariate, and ``X`` is taken to be its indeterminate.
The discriminant is defined as
(-1)^(N*(N-1)/2)*det(M)/M[1,1]
where
M := SylvesterMat(F, deriv(F,X), X)
and
N := deg(F, X).
/**/ 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
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