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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