CoCoA:EquiIsoDec

EquiIsoDec

equidimensional isoradical decomposition

Description

This function computes an equidimensional isoradical decomposition of

I, i.e. a list of unmixed ideals <formula>I_1,...,I_k</formula> such that the radical of I

is the intersection of the radicals of <formula>I_1,...,I_k</formula>. Redundancies are possible.

NOTE: at the moment, this implementation works only if the coefficient

ring is the rationals or has large enough characteristic.

Example

  Use R ::= Q[x,y,z];
  I := Intersection(Ideal(x-1,y-1,z-1),Ideal(x-2,y-2)^2,Ideal(x)^3);
  H := EquiIsoDec(I);
  H;
[Ideal(x), Ideal(z - 1, y - 1, x - 1), Ideal(xy - y^2 - 2x + 2y, x^2 -
y^2 - 4x + 4y, y^2z - y^2 - 4yz + 4y + 4z - 4, y^3 - 5y^2 + 8y - 4, x
- 2)]
-------------------------------
  T := [Radical(J)|J In H];
  S := IntersectionList(T);
  Radical(I) = S;
TRUE
-------------------------------

Syntax

EquiIsoDec(I:IDEAL):LIST of IDEAL

PrimaryDecomposition

Radical

RadicalOfUnmixed

   <type>groebner</type>
   <type>ideal</type>