CoCoA:FGLM5

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

GBasis5, and more

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