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

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FGLM Groebner Basis conversion. The Groebner Basis contained in list
 
FGLM Groebner Basis conversion. The Groebner Basis contained in list
 
GBOld will be converted into a Groebner Basis with respect to term
 
GBOld will be converted into a Groebner Basis with respect to term
ordering <tt>Ord(M)</tt>, i.e. M must be a matrix specifying a
+
ordering <tt>[[CoCoA4.7:Ord|Ord]](M)</tt>, i.e. M must be a matrix specifying a
term ordering. Please note that the resulting polynomials belong to
+
term ordering. If the parameter M is not specified, CoCoA will assume M =
a different ring than the ones in GBOld. If the parameter M is not
+
[[CoCoA4.7:Ord|Ord]](). Please note that the resulting polynomials belong to
specified, CoCoA will assume M = Ord().
+
a different ring than the ones in GBOld.
  
 
<example>
 
<example>

Revision as of 10:13, 16 October 2007

FGLM

Perform a FGLM Groebner Basis conversion

Syntax

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

Description

The function FGLM calls the CoCoAServer to perform a

FGLM Groebner Basis conversion. 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.

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

GBasis5, and more