# Difference between revisions of "ApCoCoA-1:FGLM.FGLM"

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<item>@param <em>GBOld</em> A Groebner basis of a zero-dimensional ideal.</item> | <item>@param <em>GBOld</em> A Groebner basis of a zero-dimensional ideal.</item> | ||

+ | <item>@return A Groebner basis of the ideal generated by the polynomials of GBOld. The polynomials of the new Groebner basis will belong to the polynomial ring with term ordering specified by M or Ord() in case M is not given.</item> | ||

+ | </itemize> | ||

+ | The following parameter is optional. | ||

+ | <itemize> | ||

<item>@param <em>M</em> A matrix representing a term ordering.</item> | <item>@param <em>M</em> A matrix representing a term ordering.</item> | ||

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

<example> | <example> |

## Revision as of 13:41, 28 April 2009

## FGLM.FGLM

Perform a FGLM Groebner Basis conversion using ApCoCoAServer.

### Syntax

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

### 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.

The function `FGLM` calls the ApCoCoAServer 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 Ord(M), i.e. M must be a matrix specifying a term ordering. If the parameter M is not specified, ApCoCoA will assume M = Ord(). Please note that the resulting polynomials belong to a different ring than the ones in GBOld.

The return value will be the transformed Groebner basis polynomials.

@param

*GBOld*A Groebner basis of a zero-dimensional ideal.@return A Groebner basis of the ideal generated by the polynomials of GBOld. The polynomials of the new Groebner basis will belong to the polynomial ring with term ordering specified by M or Ord() in case M is not given.

The following parameter is optional.

@param

*M*A matrix representing a term ordering.

#### Example

Use QQ[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 := FGLM(GBOld, M); Use QQ[x, y, z], Ord(M); -- New basis (Lex) BringIn(GBNew); ------------------------------- [z^6 - z^5 - 4z^4 - 2z^3 + 1, y - 4/7z^5 + 5/7z^4 + 13/7z^3 + 10/7z^2 - 6/7z - 2/7, x + 4/7z^5 - 5/7z^4 - 13/7z^3 - 10/7z^2 - 1/7z + 2/7] -------------------------------