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

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<syntax>BB.ASgens(K:INT,OO:LIST):LIST</syntax> | <syntax>BB.ASgens(K:INT,OO:LIST):LIST</syntax> | ||

<description> | <description> | ||

− | Computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by <ref>ASneighbors</ref>(OO). The inputs are an integer K in the range 1..Len(<ref>ASneighbors</ref>(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring BBS=K[c_{ij}]. | + | Computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by <ref>BB.ASneighbors</ref>(OO). The inputs are an integer K in the range 1..Len(<ref>BB.ASneighbors</ref>(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring BBS=K[c_{ij}]. |

<itemize> | <itemize> | ||

− | <item>@param <em>K</em> The generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by <ref>ASneighbors</ref>(OO) will be computed.</item> | + | <item>@param <em>K</em> The generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by <ref>BB.ASneighbors</ref>(OO) will be computed.</item> |

<item>@param <em>OO</em> A list of terms representing an order ideal.</item> | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | ||

− | <item>@return A list of generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by <ref>ASneighbors</ref>(OO). The polynomials will belong to the ring BBS=K[c_{ij}].</item> | + | <item>@return A list of generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by <ref>BB.ASneighbors</ref>(OO). The polynomials will belong to the ring BBS=K[c_{ij}].</item> |

</itemize> | </itemize> | ||

<example> | <example> |

## Revision as of 10:59, 24 April 2009

## BB.ASgens

Compute the generators of the vanishing ideal of a border basis scheme.

### Syntax

BB.ASgens(K:INT,OO:LIST):LIST

### Description

Computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by BB.ASneighbors(OO). The inputs are an integer K in the range 1..Len(BB.ASneighbors(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring BBS=K[c_{ij}].

@param

*K*The generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by BB.ASneighbors(OO) will be computed.@param

*OO*A list of terms representing an order ideal.@return A list of generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by BB.ASneighbors(OO). The polynomials will belong to the ring BBS=K[c_{ij}].

#### Example

Use QQ[x,y,z]; BB.ASgens(1, [1,x,y,z]); [BBS :: c[1,5]c[2,1] - c[1,3]c[2,2] + c[1,4]c[3,1] - c[1,2]c[3,2] + c[1,2]c[4,1] - c[1,1]c[4,2], BBS :: c[2,2]c[2,3] - c[2,1]c[2,5] - c[2,4]c[3,1] + c[2,2]c[3,2] - c[2,2]c[4,1] + c[2,1]c[4,2], BBS :: c[3,2]^2 + c[2,2]c[3,3] - c[3,1]c[3,4] - c[2,1]c[3,5] - c[3,2]c[4,1] + c[3,1]c[4,2] - c[1,1], BBS :: c[3,2]c[4,2] + c[2,2]c[4,3] - c[3,1]c[4,4] - c[2,1]c[4,5] + c[1,2]] -------------------------------