Difference between revisions of "ApCoCoA-1:BB.BBasisForMP"
(Updated description. (Skaspar)) |
(Updated examples.) |
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</itemize> | </itemize> | ||
<example> | <example> | ||
| − | Use | + | Use Q[x,y], DegLex; |
| − | |||
| + | F := [ | ||
| + | [ x^2 + xy - 1/2y^2 - x - 1/2y, xy ], | ||
| + | [ y^3 - y, y^3 ], | ||
| + | [ xy^2 - xy, xy^2 ] | ||
| + | ]; | ||
| + | |||
| + | BB.BBasisForMP(F); | ||
| + | |||
| + | [[x^2 + xy - 1/2y^2 - x - 1/2y, xy], | ||
| + | [y^3 - y, y^3], | ||
| + | [xy^2 + x^2 - 1/2y^2 - x - 1/2y, xy^2], | ||
| + | [x^3 - x, x^3], | ||
| + | [x^2y - 1/2y^2 - 1/2y, x^2y]] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | <example> | ||
| + | Use Q[x,y,z], DegLex; | ||
| + | |||
| + | F := [ | ||
| + | [ x^2 + xy + y^2 - x - 1, x^2 ], | ||
| + | [ xy + y^2 + z, xy ], | ||
| + | [ -x^2 + yz + z + 1, x^2 ] | ||
| + | ]; | ||
| + | |||
| + | BB.BBasisForMP(F); | ||
| + | |||
| + | [[x^2 - x - z - 1, x^2], | ||
| + | [xy + z^2 + x + z + 1, xy], | ||
| + | [yz - x, yz], | ||
| + | [y^2 - z^2 - x - 1, y^2], | ||
| + | [x^2z - xz - z^2 - z, x^2z], | ||
| + | [xz^2 + xz - z^2 + 2x + y, xz^2], | ||
| + | [xyz - x - z - 1, xyz], | ||
| + | [z^3 + xz + z^2 + x + 2z + 1, z^3], | ||
| + | [yz^2 - xz, yz^2]] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
Revision as of 13:59, 29 September 2009
BB.BBasisForMP
Computes the border basis of a zero-dimensional ideal generated by marked polynomials.
Syntax
BB.BBasisForMP(F:LIST of LIST):LIST of LIST
Description
The input is a list of tuples [P, T] where P is a polynomial and T must be a term of the support of P such that deg(P) = deg(T). This function computes the border basis of the zero-dimensional ideal I generated by the polynomials P with respect to the given term marking. The output is a list of tuples [P, T] denoting a border basis of I where P is a polynomial and T is the term of the support of P such that deg(P) = deg(T) and T is a border term. An error will be raised if the given term marking does not lead to a successful computation.
@param F List of tuples [P, T] where P is a polynomial and T must be a term of the support of P such that deg(P) = deg(T). The polynomials P must generate a zero-dimensional ideal.
@return A list of tuples [P, T] denoting a border basis of I where P is a polynomial and T is the term of the support of P such that deg(P) = deg(T) and T is a border term.
Example
Use Q[x,y], DegLex; F := [ [ x^2 + xy - 1/2y^2 - x - 1/2y, xy ], [ y^3 - y, y^3 ], [ xy^2 - xy, xy^2 ] ]; BB.BBasisForMP(F); [[x^2 + xy - 1/2y^2 - x - 1/2y, xy], [y^3 - y, y^3], [xy^2 + x^2 - 1/2y^2 - x - 1/2y, xy^2], [x^3 - x, x^3], [x^2y - 1/2y^2 - 1/2y, x^2y]] -------------------------------
Example
Use Q[x,y,z], DegLex; F := [ [ x^2 + xy + y^2 - x - 1, x^2 ], [ xy + y^2 + z, xy ], [ -x^2 + yz + z + 1, x^2 ] ]; BB.BBasisForMP(F); [[x^2 - x - z - 1, x^2], [xy + z^2 + x + z + 1, xy], [yz - x, yz], [y^2 - z^2 - x - 1, y^2], [x^2z - xz - z^2 - z, x^2z], [xz^2 + xz - z^2 + 2x + y, xz^2], [xyz - x - z - 1, xyz], [z^3 + xz + z^2 + x + 2z + 1, z^3], [yz^2 - xz, yz^2]] -------------------------------
