Difference between revisions of "CoCoA:FGLM5"
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| − | 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 |
| − | ordering < | + | 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 = | 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. | a different ring than the ones in GBOld. | ||
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>
