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)|);

The given ideal:
$<x^2z^2+x^3,xz^4+2x^2z^2+x^3,y^2z-2yz^2+z^3,x^2y+y^3>$
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.