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Gin

Syntax

Gin(I: IDEAL): IDEAL
Gin(I: IDEAL, Range: INT): IDEAL
    

Summary

generic initial ideal

Description

This function returns the [probabilistic] gin (generic initial ideal) of the ideal I. It is attained by computing the leading term ideal of g(I), where g is a random change of coordinates with integer coefficients in [-Range, Range], the default is [-100, 100]. This process is repeated until 4 consecutive change of coordinates give the same leading term ideal.

example

    
Use R ::= Q[x,y,z];  -- the default term-ordering is DegRevLex
Gin(Ideal(y^2-xz, x^2z-yz^2));
Ideal(x^2, xy^2, y^4)
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Use R ::= Q[x,y,z], Lex;
Gin(Ideal(y^2-xz, x^2z-yz^2), 20);
Ideal(x^2, xy^2, xyz^2, xz^4, y^6)
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