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

From ApCoCoAWiki

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<title>BB.BBasis</title> | <title>BB.BBasis</title> | ||

<short_description>Compute the border basis of a zero-dimensional ideal.</short_description> | <short_description>Compute the border basis of a zero-dimensional ideal.</short_description> | ||

− | <syntax>BB.BBasis(I:IDEAL):LIST of POLY</syntax> | + | |

+ | <syntax> | ||

+ | BB.BBasis(I:IDEAL):LIST of POLY | ||

+ | </syntax> | ||

<description> | <description> | ||

<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. |

## Revision as of 14:43, 24 April 2009

## BB.BBasis

Compute the border basis of a zero-dimensional ideal.

### Syntax

BB.BBasis(I:IDEAL):LIST of POLY

### 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.

Let `sigma` be a degree compatible term ordering. The function `BBasis` calls the ApCoCoAServer to compute the O_sigma(I)-border basis of the zero-dimensional input ideal `I` and returns it as a list of polynomials.

The return value will be the computed border basis.

@param

*I*A zero-dimensional ideal of which to compute a border basis.@return A list of border basis polynomials.

#### Example

Use QQ[x, y], DegLex; I := Ideal([x^2, xy + y^2]); BB := BBasis(I); BB; ------------------------------- [xy + y^2, x^2, y^3, xy^2] -------------------------------