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

From ApCoCoAWiki

(Category update.) |
(Added parameter and return value list.) |
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The return value will be the computed border basis. | The return value will be the computed border basis. | ||

+ | <itemize> | ||

+ | <item>@param <em>I</em> A zero-dimensional ideal of which to compute a border basis.</item> | ||

+ | <item>@return A list of border basis polynomials.</item> | ||

+ | </itemize> | ||

<example> | <example> | ||

Use Q[x, y], DegLex; | Use Q[x, y], DegLex; |

## Revision as of 13:33, 22 April 2009

## BBasis

Compute the border basis of a zero-dimensional ideal.

### Syntax

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 <formula>\sigma</formula> be a degree compatible term ordering. The function `BBasis` calls the ApCoCoAServer to compute the <formula>\mathcal{O}_\sigma(I)</formula>-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 Q[x, y], DegLex; I := Ideal([x^2, xy + y^2]); BB := BBasis(I); BB; ------------------------------- [xy + y^2, x^2, y^3, xy^2] -------------------------------