# Difference between revisions of "ApCoCoA-1:BB.BBasisForMP"

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− | Computes the border basis of the ideal <tt>I = <F></tt> with respect to the set of marked polynomials <tt>F</tt>. 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>. 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 indicate if the given term marking does not lead to a successful computation. | + | Computes the border basis of the zero-dimensional ideal <tt>I = <F></tt> with respect to the set of marked polynomials <tt>F</tt>. 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>. 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 indicate 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 12:32, 28 September 2009

## BB.BBasisForMP

Computes the border basis of an ideal generated by marked polynomials.

### Syntax

BB.BBasisForMP(F:LIST of LIST):LIST of LIST

### Description

Computes the border basis of the zero-dimensional ideal `I = <F>` with respect to the set of marked polynomials `F`. 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)`. 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 indicate 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([ [,], [,] ]); -------------------------------