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IsStable, IsStronglyStable, IsLexSegment

Syntax

IsStable(I: MONOMIAL IDEAL): BOOL
IsStronglyStable(I: MONOMIAL IDEAL): BOOL
IsLexSegment(I: MONOMIAL IDEAL): BOOL
    

Summary

checks if an ideal is stable (resp. strongly stable or a lex-segment)

Description

These functions return whether the monomial ideal I is stable, strongly stable (Borel-fixed in characteristic 0), or a lex-segment ideal.

example

    
Use R ::= Q[x,y,z];
I := Ideal(xy^3, y^4, x^3, x^2y, x^2z);
IsStable(I);
TRUE
-------------------------------
IsStronglyStable(I);
TRUE
-------------------------------
IsLexSegment(I);
FALSE
-------------------------------