ApCoCoA:BB.BBasisForMP

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<command>

 <title>BB.BBasisForMP</title>
 <short_description>Computes the border basis of a zero-dimensional ideal generated by marked polynomials.</short_description>
 

<syntax> BB.BBasisForMP(F:LIST of LIST):LIST of LIST </syntax>

 <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. <par/> 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. <itemize>

 <item>@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.</item>
 <item>@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.</item>

</itemize> <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> <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>

 </description>
 <types>
   <type>borderbasis</type>
   <type>ideal</type>
 </types>
 <see>BB.BBasis</see>
 <see>BB.BBasisForOI</see>
 <key>BBasisForMP</key>
 <key>BB.BBasisForMP</key>
 <key>borderbasis.BBasisForMP</key>
 <wiki-category>Package_borderbasis</wiki-category>

</command>