# Difference between revisions of "CoCoA:FGLM5"

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<description> | <description> | ||

− | This function is implemented in ApCoCoALib by Stefan Kaspar(requires an active <ref>CoCoAServer</ref>). | + | This function is implemented in ApCoCoALib by Stefan Kaspar (requires an active <ref>CoCoAServer</ref>). |

<par/> | <par/> | ||

The function <tt>FGLM</tt> calls the CoCoAServer to perform a | The function <tt>FGLM</tt> calls the CoCoAServer to perform a | ||

− | FGLM Groebner Basis conversion. The Groebner Basis contained in list | + | FGLM Groebner Basis conversion. Please note that the ideal generated by |

− | GBOld will be converted into a Groebner Basis with respect to term | + | the given Groebner Basis must be zero-dimensional. The Groebner Basis contained |

+ | in list GBOld will be converted into a Groebner Basis with respect to term | ||

ordering <ttref>Ord</ttref>(M), i.e. M must be a matrix specifying a | ordering <ttref>Ord</ttref>(M), i.e. M must be a matrix specifying a | ||

term ordering. If the parameter M is not specified, CoCoA will assume M = | term ordering. If the parameter M is not specified, CoCoA will assume M = |

## Latest revision as of 16:09, 5 November 2008

## FGLM5

Perform a FGLM Groebner Basis conversion using CoCoAServer

### Description

This function is implemented in ApCoCoALib by Stefan Kaspar (requires an active CoCoAServer).

The function `FGLM` calls the CoCoAServer to perform a

FGLM Groebner Basis conversion. Please note that the ideal generated by

the given Groebner Basis must be zero-dimensional. The Groebner Basis contained in list GBOld will be converted into a Groebner Basis with respect to term ordering <ttref>Ord</ttref>(M), i.e. M must be a matrix specifying a term ordering. If the parameter M is not specified, CoCoA will assume M = <ttref>Ord</ttref>(). Please note that the resulting polynomials belong to a different ring than the ones in GBOld.

#### Example

Use Q[x, y, z], DegRevLex; GBOld := [z^4 -3z^3 - 4yz + 2z^2 - y + 2z - 2, yz^2 + 2yz - 2z^2 + 1, y^2 - 2yz + z^2 - z, x + y - z]; M := LexMat(3); GBNew := FGLM5(GBOld, M); Use Q[x, y, z], Ord(M); -- New basis (Lex) BringIn(GBNew);

### Syntax

FGLM5(GBOld:LIST, M:MAT):LIST FGLM5(GBOld:LIST):LIST

<type>groebner</type> <type>ideal</type> <type>list</type> <type>cocoaserver</type>