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NmzIntClosureMonIdeal

integral closure of a monomial ideal

Syntax
NmzIntClosureMonIdeal(L: LIST of RINGELEM): LIST of RINGELEM
NmzIntClosureMonIdeal(L: LIST of RINGELEM, s: RINGELEM): LIST of RINGELEM,

Description
Given a list L of power-products in a ring R , the function returns the generators of the integral closure of the ideal generated by L . As second argument you can specify an indeterminate of the ring which is not used in the power-products. In this case the result is the normalisation of its Rees algebra (or Rees ring); see Bruns and Herzog, Cohen-Macaulay Rings, Cambridge University Press 1998, p. 182.

Example
/**/     use R::=QQ[x,y,z,t];
/**/     NmzIntClosureMonIdeal([x^2,y^2,z^3]);
-- the integral closure of the ideal generated by x^2,y^2 and z^3 is...
[y^2, x^2, x*y, z^3, y*z^2, x*z^2]
-- ...the ideal generated by y^2, x^2, x*y, z^3, y*z^2 and x*z^2
/**/     NmzIntClosureMonIdeal([x^2,y^2,z^3],t);
-- and the complete rees algebra is generated by
[z, z^3*t, y, y*z^2*t, y^2*t, x, x*z^2*t, x*y*t, x^2*t]

See Also