#### UserFunction Radical

`Radical(u:DPOLID(C,v,O))`

The single argument $u$ has the type $DPOLID$ which abbreviates

*Distributive Polynomial Ideal*, it must represent a zero-dimensional ideal. The meaning

of its parameters is as follows.

$C$: Coefficient type.

$v=\{v_1,v_2,\ldots \}$: Distributive variables in decreasing order.

$O:LEX|GRLEX|GREVLEX$: Term ordering.

**Specification.**

Generators for the radical of the input ideal $u$ are returned.

**Examples.** The input is given in *Reduce* algebraic mode syntax. The output for each minisession

is returned in a separate window.

`I:={x**2*z**2+x**3,x*z**4+2*x**2*z**2+x**3,
y**2*z-2*y*z**2+z**3,x**2*y+y**3};`

`Radical(I|DPOLID(Q,{x,y,z},GRLEX)|);`

$<x^2z^2+x^3,xz^4+2x^2z^2+x^3,y^2z-2yz^2+z^3,x^2y+y^3>$

The radical: $<x^2-x,xz-z,z^2+x,y-z>$

**Related Functions.**RadicalMembership.

**References.**

W.W. Adams, P. Loustaunau, * An Introduction to Groebner Bases*, American Mathematical Society, 1994.

D. Cox, J. Little, D. O'Shea, * Ideals, Varieties and Algorithms Using Algebraic Geometry*,

Undergraduate Texts in Mathematics, Springer, 1992 and 1998.

G.M. Greuel, G. Pfister, *A Singular Introduction to Commutative Algebra*, Springer, 2002.

M. Kreuzer, L. Robbiano, *Using Computational Commutative Algebra I and II*, Springer, 2000.