Difference between revisions of "ApCoCoA-1:BB.BBasisForMP"
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| − | The input is a list of tuples <tt>[P, T]</tt> where <tt>P</tt> is a polynomial and <tt>T</tt> must be a term of the support of <tt>P</tt> such that <tt>deg(P) = deg(T)</tt>. This function computes the border basis of the zero-dimensional ideal generated by the polynomials <tt>P</tt> with respect to the given term marking. The output is a list of tuples <tt>[P, T]</tt> denoting a border basis of <tt>I</tt> where <tt>P</tt> is a polynomial and <tt>T</tt> is the term of the support of <tt>P</tt> such that <tt>deg(P) = deg(T)</tt> and <tt>T</tt> is a border term. An error will | + | The input is a list of tuples <tt>[P, T]</tt> where <tt>P</tt> is a polynomial and <tt>T</tt> must be a term of the support of <tt>P</tt> such that <tt>deg(P) = deg(T)</tt>. This function computes the border basis of the zero-dimensional ideal <tt>I</tt> generated by the polynomials <tt>P</tt> with respect to the given term marking. The output is a list of tuples <tt>[P, T]</tt> denoting a border basis of <tt>I</tt> where <tt>P</tt> is a polynomial and <tt>T</tt> is the term of the support of <tt>P</tt> such that <tt>deg(P) = deg(T)</tt> and <tt>T</tt> is a border term. An error will be raised if the given term marking does not lead to a successful computation. |
<itemize> | <itemize> | ||
<item>@param <em>F</em> List of tuples <tt>[P, T]</tt> where <tt>P</tt> is a polynomial and <tt>T</tt> must be a term of the support of <tt>P</tt> such that <tt>deg(P) = deg(T)</tt>. The polynomials <tt>P</tt> must generate a zero-dimensional ideal.</item> | <item>@param <em>F</em> List of tuples <tt>[P, T]</tt> where <tt>P</tt> is a polynomial and <tt>T</tt> must be a term of the support of <tt>P</tt> such that <tt>deg(P) = deg(T)</tt>. The polynomials <tt>P</tt> must generate a zero-dimensional ideal.</item> | ||
Revision as of 12:50, 28 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 QQ[x,y]; BB.BBasisForMP([ [,], [,] ]); -------------------------------
