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TriangularSets -- triangular decompositions of polynomial ideals


This package allows to decompose polynomial ideals into triangular sets
i1 : R = QQ[a..h, MonomialOrder=>Lex];
i2 : I = ideal {a*d - b*c, c*f - d*e, e*h - f*g};

o2 : Ideal of R
i3 : triangularize I

o3 = {{a*d - b*c, e, f} / d, {a*d - b*c, c*f - d*e, e*h - f*g} / {d, f, h},
     {c, d, f, h}, {c, d, e*h - f*g} / h, {b, d, e, f}, {c, d, e, f}, {a*d -
     b*c, c*f - d*e, g, h} / {d, f}, {b, d, f, h}, {c, d, g, h}}

o3 : List

The method triangularize is implemented in M2 only for monomial and binomial ideals. For the general case we interface to Maple.

This package also provides methods for manipulating triangular sets:




This documentation describes version 0.1 of TriangularSets.

Source code

The source code from which this documentation is derived is in the file TriangularSets.m2. The auxiliary files accompanying it are in the directory TriangularSets/.


For the programmer

The object TriangularSets is a package.