ApCoCoA-1:BB.BBasisForMP
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
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
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]] -------------------------------
