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radical

radical of an ideal

Syntax
radical(N: INT): INT
radical(X: RINGELEM): RINGELEM
radical(I: IDEAL): IDEAL

Description
This function computes the radical of its argument. For integers and ring elements this means the product of the distinct irreducibles dividing the argument (sometimes called "square-free"). For ideals it computes the radical ideal using the algorithm described in the paper

M. Caboara, P. Conti and C. Traverso: Yet Another Ideal Decomposition Algorithm. Proc. AAECC-12, pp 39-54, 1997, Lecture Notes in Computer Science, n.1255 Springer-Verlag.

NOTE: at the moment, this implementation works only if the coefficient ring is the rationals or has large enough characteristic.

Example
/**/  radical(99);
33
/**/  use R ::= QQ[x,y];
/**/  radical((x -y)^3 * (x +y));
x^2 -y^2
/**/  I := ideal(x,y)^3;
/**/  radical(I);
ideal(y, x)

See Also