Difference between revisions of "ApCoCoA-1:FGLM.FGLM"
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<type>list</type> | <type>list</type> | ||
| − | <type> | + | <type>apcocoaserver</type> |
</types> | </types> | ||
<key>FGLM</key> | <key>FGLM</key> | ||
Revision as of 11:19, 23 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, CoCoA will assume M = Ord(). Please note that the resulting polynomials belong to a different ring than the ones in GBOld.
Ther return value will be the transformed Groebner basis polynomials.
@param GBOld A Groebner basis of a zero-dimensional ideal.
@param M A matrix representing a term ordering.
@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.
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 := FGLM(GBOld, M); Use Q[x, y, z], Ord(M); -- New basis (Lex) BringIn(GBNew);
See also
