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D.4.17.1 nonMonomials

Procedure from library pointid.lib (see pointid_lib).

Usage:
nonMonomials(id); id = <list of vectors> or <list of lists> or <module> or <matrix>.
Let A= {a1,...,as} be a set of points in K^n, ai:=(ai1,...,ain), then A can be given as
- a list of vectors (the ai are vectors) or
- a list of lists (the ai are lists of numbers) or
- a module s.t. the ai are generators or
- a matrix s.t. the ai are columns

Assume:
basering must have ordering rp, i.e., be of the form 0,x(1..n),rp; (the first entry of a point belongs to the lex-smallest variable, etc.)

Return:
ideal, the non-monomials of the vanishing ideal I(A) of A

Purpose:
compute the set of non-monomials Mon(x(1),...,x(n)) \ {LM(f)|f in I(A)} of the vanishing ideal I(A) of the given set of points A in K^n, where K[x(1),...,x(n)] is equipped with the lexicographical ordering induced by x(1)<...<x(n) by using the algorithm of Cerlienco-Mureddu

Example:
 


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